WEBVTT 00:00:00.000 --> 00:00:00.580 align:middle line:90% 00:00:00.580 --> 00:00:02.440 align:middle line:84% The following content is provided 00:00:02.440 --> 00:00:06.340 align:middle line:84% by MIT OpenCourseWare under a Creative Commons license. 00:00:06.340 --> 00:00:08.470 align:middle line:84% Additional information about our license 00:00:08.470 --> 00:00:10.870 align:middle line:84% and MIT OpenCourseWare in general 00:00:10.870 --> 00:00:13.090 align:middle line:90% is available at ocw.mit.edu. 00:00:13.090 --> 00:00:31.991 align:middle line:90% 00:00:31.991 --> 00:00:32.574 align:middle line:90% PROFESSOR: OK. 00:00:32.574 --> 00:00:36.550 align:middle line:90% 00:00:36.550 --> 00:00:37.160 align:middle line:90% Welcome. 00:00:37.160 --> 00:00:43.690 align:middle line:84% Welcome to the second discussion of networks and the second 00:00:43.690 --> 00:00:47.240 align:middle line:84% to last talk of lecture of this course. 00:00:47.240 --> 00:00:51.160 align:middle line:84% There's a very important set of lectures 00:00:51.160 --> 00:00:55.000 align:middle line:84% after that from the students I'm looking forward to. 00:00:55.000 --> 00:01:00.880 align:middle line:84% So last time we talked about the use of computers 00:01:00.880 --> 00:01:05.620 align:middle line:84% to model various complicated systems in mainly 00:01:05.620 --> 00:01:11.200 align:middle line:84% cellular systems, ranging from highly cooperative, even 00:01:11.200 --> 00:01:16.840 align:middle line:84% bistable bifurcation so that where a cell makes a decision, 00:01:16.840 --> 00:01:20.680 align:middle line:84% a discussion of chromosome copy number and its implications 00:01:20.680 --> 00:01:25.750 align:middle line:84% and a large chunk of time on flux balance optimization where 00:01:25.750 --> 00:01:28.540 align:middle line:84% we can look at many of these things 00:01:28.540 --> 00:01:30.880 align:middle line:84% from the standpoint of optimization. 00:01:30.880 --> 00:01:37.870 align:middle line:84% Now, today, to paraphrase a famous local politician, 00:01:37.870 --> 00:01:41.530 align:middle line:84% we will ask not what computers can do for biology, 00:01:41.530 --> 00:01:44.290 align:middle line:84% but what biology can do for computers. 00:01:44.290 --> 00:01:47.530 align:middle line:84% And of course we'll go back and forth 00:01:47.530 --> 00:01:52.750 align:middle line:84% and try to look at what this interesting dynamic 00:01:52.750 --> 00:01:56.540 align:middle line:84% between the experimental and the computational side. 00:01:56.540 --> 00:02:00.130 align:middle line:84% And so how can biology aid algorithm development, 00:02:00.130 --> 00:02:03.310 align:middle line:84% to return the favor and aid biology? 00:02:03.310 --> 00:02:05.440 align:middle line:84% But not only algorithm development 00:02:05.440 --> 00:02:08.020 align:middle line:84% to not only inspiring algorithm development, 00:02:08.020 --> 00:02:13.330 align:middle line:84% but actually implementing hardware and software 00:02:13.330 --> 00:02:16.400 align:middle line:90% in biological systems. 00:02:16.400 --> 00:02:17.890 align:middle line:90% We'll talk about that. 00:02:17.890 --> 00:02:22.870 align:middle line:84% And ranging from molecular computing to cellular computing 00:02:22.870 --> 00:02:27.970 align:middle line:84% and then back to inspiring algorithms again. 00:02:27.970 --> 00:02:32.260 align:middle line:84% So slide 3, what is it that we're really talking about, 00:02:32.260 --> 00:02:35.920 align:middle line:84% that computation needs in terms of aid? 00:02:35.920 --> 00:02:37.450 align:middle line:90% How do we get-- 00:02:37.450 --> 00:02:39.093 align:middle line:90% what are the real issues here? 00:02:39.093 --> 00:02:41.260 align:middle line:84% And we've mentioned a couple of times in the course, 00:02:41.260 --> 00:02:42.927 align:middle line:84% probably initially, when we were talking 00:02:42.927 --> 00:02:44.770 align:middle line:84% about dynamic programming and related 00:02:44.770 --> 00:02:49.570 align:middle line:84% topics, of how a problem in computer science scales. 00:02:49.570 --> 00:02:51.970 align:middle line:84% Typically, you'll have one key input, 00:02:51.970 --> 00:02:58.210 align:middle line:84% size in, and then the running time or sometimes the memory 00:02:58.210 --> 00:03:01.180 align:middle line:84% has an upper bound which we've been referring 00:03:01.180 --> 00:03:04.210 align:middle line:84% to as the order of some function of that end 00:03:04.210 --> 00:03:09.710 align:middle line:84% or end as the length of a string or the size of the problem. 00:03:09.710 --> 00:03:13.390 align:middle line:84% There are other symbols that are slightly more rarely used. 00:03:13.390 --> 00:03:17.230 align:middle line:84% There's in addition to the upper bound, there's lower bound. 00:03:17.230 --> 00:03:21.112 align:middle line:84% Sometimes you can get an exact bound or equal bound. 00:03:21.112 --> 00:03:22.570 align:middle line:84% And how does this play out when you 00:03:22.570 --> 00:03:25.347 align:middle line:90% have specific instances of n? 00:03:25.347 --> 00:03:27.430 align:middle line:84% Now of course, this when you say this something is 00:03:27.430 --> 00:03:31.090 align:middle line:84% on the order of or upper bound of a function of n, 00:03:31.090 --> 00:03:33.820 align:middle line:84% you don't always necessarily describe the constants. 00:03:33.820 --> 00:03:35.470 align:middle line:84% But to give you a ballpark, when you 00:03:35.470 --> 00:03:40.240 align:middle line:84% have n ranging from 1 to 1,000 and the polynomial 00:03:40.240 --> 00:03:46.090 align:middle line:84% ranging from linear to quadratic to 10th power, 00:03:46.090 --> 00:03:51.340 align:middle line:84% and then the exponential or factorial. 00:03:51.340 --> 00:03:54.340 align:middle line:84% And you can see that for very small n, 00:03:54.340 --> 00:03:59.710 align:middle line:84% you can get cases where a polynomial performance 00:03:59.710 --> 00:04:04.020 align:middle line:84% computation time can be longer than an exponential computation 00:04:04.020 --> 00:04:04.520 align:middle line:90% time. 00:04:04.520 --> 00:04:07.070 align:middle line:84% So exponential isn't necessarily bad news, 00:04:07.070 --> 00:04:09.610 align:middle line:84% depending on the size of your problem. 00:04:09.610 --> 00:04:11.560 align:middle line:84% But it gets to be bad news very quickly. 00:04:11.560 --> 00:04:16.750 align:middle line:84% As N increases, you quickly get over large numbers 00:04:16.750 --> 00:04:20.500 align:middle line:84% on the far right hand side that are computationally 00:04:20.500 --> 00:04:24.190 align:middle line:84% intractable with any known computer. 00:04:24.190 --> 00:04:28.232 align:middle line:84% So we mentioned computational complexity 00:04:28.232 --> 00:04:30.190 align:middle line:84% is one of the various definitions of complexity 00:04:30.190 --> 00:04:31.315 align:middle line:90% at the beginning of course. 00:04:31.315 --> 00:04:33.490 align:middle line:84% This is not the one we chose to be 00:04:33.490 --> 00:04:36.280 align:middle line:84% closest to the definition of living complexity. 00:04:36.280 --> 00:04:39.520 align:middle line:84% But it's one that's very frequently used in the computer 00:04:39.520 --> 00:04:40.130 align:middle line:90% science field. 00:04:40.130 --> 00:04:41.922 align:middle line:84% I just want to introduce a few of the terms 00:04:41.922 --> 00:04:45.130 align:middle line:84% here just so you've heard them in this context. 00:04:45.130 --> 00:04:50.020 align:middle line:84% We have-- and it basically refers to the issues brought up 00:04:50.020 --> 00:04:52.930 align:middle line:84% in the previous slide of whether it takes, whether it's scales 00:04:52.930 --> 00:04:55.330 align:middle line:84% by a polynomial, which is generally desirable, 00:04:55.330 --> 00:04:59.030 align:middle line:84% or whether it's scales exponentially or worse. 00:04:59.030 --> 00:05:02.410 align:middle line:84% And so we have P are problems that we 00:05:02.410 --> 00:05:04.860 align:middle line:84% can solve in polynomial deterministic time. 00:05:04.860 --> 00:05:08.240 align:middle line:84% Deterministic is just described the fact 00:05:08.240 --> 00:05:11.180 align:middle line:84% that the algorithms will do the same thing time after time, 00:05:11.180 --> 00:05:16.210 align:middle line:84% which is the typical computer that we feel comfortable using. 00:05:16.210 --> 00:05:21.140 align:middle line:84% And an example of problems in the P class, 00:05:21.140 --> 00:05:24.070 align:middle line:84% the dynamic programming, which we've used numerous times. 00:05:24.070 --> 00:05:26.260 align:middle line:84% It scales polynomial and the polynomial just 00:05:26.260 --> 00:05:29.770 align:middle line:84% depends on the problem slightly from square to the sixth power 00:05:29.770 --> 00:05:31.630 align:middle line:90% we've seen. 00:05:31.630 --> 00:05:36.040 align:middle line:84% NP has a number of subsets, but overall, it 00:05:36.040 --> 00:05:39.100 align:middle line:84% means it's not the deterministic polynomial time 00:05:39.100 --> 00:05:40.460 align:middle line:90% to get the solutions. 00:05:40.460 --> 00:05:43.690 align:middle line:84% The solutions are checkable in polynomial time, 00:05:43.690 --> 00:05:51.430 align:middle line:84% but are generally felt to not be currently 00:05:51.430 --> 00:05:55.450 align:middle line:84% feasible in polynomial time for the determination as opposed 00:05:55.450 --> 00:05:56.380 align:middle line:90% to checking. 00:05:56.380 --> 00:06:00.070 align:middle line:84% An example of this were actually the inventors 00:06:00.070 --> 00:06:05.200 align:middle line:84% of various encryption schemes such as RSA. 00:06:05.200 --> 00:06:08.320 align:middle line:84% The R and the S and the A, referring to the last names 00:06:08.320 --> 00:06:09.940 align:middle line:90% of the authors. 00:06:09.940 --> 00:06:11.560 align:middle line:84% In a certain sense, they're banking 00:06:11.560 --> 00:06:19.420 align:middle line:84% on the difficulty of cracking these codes in polynomial time. 00:06:19.420 --> 00:06:21.970 align:middle line:84% You can use the codes if you know it. 00:06:21.970 --> 00:06:23.950 align:middle line:84% You can check it, that is to say, 00:06:23.950 --> 00:06:27.200 align:middle line:84% but you can't crack it, unless someone comes through 00:06:27.200 --> 00:06:28.935 align:middle line:84% with breakthrough on the NP problems. 00:06:28.935 --> 00:06:30.310 align:middle line:84% Because if you solve one of them, 00:06:30.310 --> 00:06:32.950 align:middle line:90% you can solve all of them. 00:06:32.950 --> 00:06:34.450 align:middle line:84% And then they're subsets of this. 00:06:34.450 --> 00:06:37.090 align:middle line:84% This is a little less critical for today's discussion. 00:06:37.090 --> 00:06:40.480 align:middle line:84% But there's NP complete, an example of which 00:06:40.480 --> 00:06:42.880 align:middle line:90% is the traveling salesman. 00:06:42.880 --> 00:06:45.100 align:middle line:84% Can you get through all the vertices 00:06:45.100 --> 00:06:50.860 align:middle line:84% on the trip with a mileage below some threshold. 00:06:50.860 --> 00:06:53.170 align:middle line:84% And an MP hard version of that same thing 00:06:53.170 --> 00:06:55.600 align:middle line:84% is what's the minimum mileage that you can get, 00:06:55.600 --> 00:07:00.010 align:middle line:84% not just less than x, but how much less than x? 00:07:00.010 --> 00:07:04.060 align:middle line:84% And the worst case scenario is undecidable, where you really, 00:07:04.060 --> 00:07:07.120 align:middle line:84% even given an unlimited amount of time and space, 00:07:07.120 --> 00:07:08.530 align:middle line:90% you can't tell whether it is. 00:07:08.530 --> 00:07:11.093 align:middle line:84% And the classic one is the program halting problem 00:07:11.093 --> 00:07:13.510 align:middle line:84% where you don't know whether your program is going to halt 00:07:13.510 --> 00:07:16.900 align:middle line:84% and probably all of you have run into that problem. 00:07:16.900 --> 00:07:19.070 align:middle line:90% I'm just being funny. 00:07:19.070 --> 00:07:22.210 align:middle line:84% So but I mean, it is a real-- the program halting problem 00:07:22.210 --> 00:07:25.840 align:middle line:84% is a serious mathematical construct. 00:07:25.840 --> 00:07:26.340 align:middle line:90% OK. 00:07:26.340 --> 00:07:29.068 align:middle line:90% 00:07:29.068 --> 00:07:30.110 align:middle line:90% How do we deal with this? 00:07:30.110 --> 00:07:33.023 align:middle line:84% How do we start thinking about ways 00:07:33.023 --> 00:07:34.690 align:middle line:84% that we've dealt with it before and ways 00:07:34.690 --> 00:07:39.880 align:middle line:84% that biology could change the landscape a little bit? 00:07:39.880 --> 00:07:45.040 align:middle line:84% Usually, what we do when we're faced with an NP hard problem 00:07:45.040 --> 00:07:47.410 align:middle line:90% is cheat in some way or another. 00:07:47.410 --> 00:07:51.490 align:middle line:84% You redefine the problem, so it's in class P, 00:07:51.490 --> 00:07:53.350 align:middle line:90% sometimes sacrificing something. 00:07:53.350 --> 00:07:55.368 align:middle line:90% So you might have-- 00:07:55.368 --> 00:07:57.160 align:middle line:84% if you're interested in tertiary structure, 00:07:57.160 --> 00:07:59.050 align:middle line:84% you may be defined as a secondary. 00:07:59.050 --> 00:08:03.180 align:middle line:84% And we showed that secondary structure for RNase 00:08:03.180 --> 00:08:04.930 align:middle line:84% can be solved with the dynamic programming 00:08:04.930 --> 00:08:07.500 align:middle line:84% algorithm with N squared or worst, N 00:08:07.500 --> 00:08:10.540 align:middle line:90% to the the sixth algorithm. 00:08:10.540 --> 00:08:15.940 align:middle line:84% Whether that is as precise as the most precise tertiary 00:08:15.940 --> 00:08:21.160 align:middle line:84% structure that one could get given infinite exponential time 00:08:21.160 --> 00:08:23.710 align:middle line:90% is an open question. 00:08:23.710 --> 00:08:24.535 align:middle line:90% Probably not. 00:08:24.535 --> 00:08:30.190 align:middle line:90% 00:08:30.190 --> 00:08:33.580 align:middle line:84% If N is a small enough, we showed that exponential times 00:08:33.580 --> 00:08:35.690 align:middle line:90% can be reasonable. 00:08:35.690 --> 00:08:37.630 align:middle line:84% And so you just do an exhaustive search. 00:08:37.630 --> 00:08:39.640 align:middle line:84% Or if you can't do that, then you 00:08:39.640 --> 00:08:44.260 align:middle line:84% use some clever heuristic way of pruning things. 00:08:44.260 --> 00:08:46.210 align:middle line:84% And that's in a certain sense, that's 00:08:46.210 --> 00:08:50.420 align:middle line:84% what most of the approximations are. 00:08:50.420 --> 00:08:52.360 align:middle line:90% So what can biology do? 00:08:52.360 --> 00:08:55.640 align:middle line:84% We'll talk about three examples in today. 00:08:55.640 --> 00:08:57.070 align:middle line:90% One is DNA computing. 00:08:57.070 --> 00:09:00.790 align:middle line:84% One is genetic algorithms and neural networks. 00:09:00.790 --> 00:09:02.920 align:middle line:90% The first one in a certain-- 00:09:02.920 --> 00:09:07.340 align:middle line:84% none of these really actually solve the problem. 00:09:07.340 --> 00:09:09.640 align:middle line:84% The first one is a way of just obtaining 00:09:09.640 --> 00:09:12.250 align:middle line:90% a lot more raw computing power. 00:09:12.250 --> 00:09:14.200 align:middle line:84% I'll show you a quote where they say 00:09:14.200 --> 00:09:15.820 align:middle line:84% they've solved an NP complete problem, 00:09:15.820 --> 00:09:17.470 align:middle line:84% but it's in the same sense that you 00:09:17.470 --> 00:09:21.190 align:middle line:84% can solve any exponential problem by brute force. 00:09:21.190 --> 00:09:23.080 align:middle line:84% That's not really finessing it out 00:09:23.080 --> 00:09:26.860 align:middle line:84% of NP and into P. Genetic algorithms 00:09:26.860 --> 00:09:29.230 align:middle line:84% and neural networks are definitely heuristics. 00:09:29.230 --> 00:09:34.810 align:middle line:84% They're beautifully inspired by two of the greatest algorithms 00:09:34.810 --> 00:09:39.910 align:middle line:84% in the history of life on Earth and that is evolution 00:09:39.910 --> 00:09:44.200 align:middle line:90% and complex brain networks. 00:09:44.200 --> 00:09:45.820 align:middle line:90% And we'll get-- 00:09:45.820 --> 00:09:48.130 align:middle line:84% And so genetic algorithms is based 00:09:48.130 --> 00:09:51.670 align:middle line:84% on the adaptation that occurs during evolution 00:09:51.670 --> 00:09:53.710 align:middle line:84% and recombination and mutagenesis. 00:09:53.710 --> 00:09:56.710 align:middle line:84% And neural network is also about adaptation, 00:09:56.710 --> 00:10:01.630 align:middle line:84% but this is on the time scale of learning. 00:10:01.630 --> 00:10:03.940 align:middle line:84% So we'll first dedicate ourselves 00:10:03.940 --> 00:10:09.040 align:middle line:84% to molecular computing and associated just kind 00:10:09.040 --> 00:10:12.530 align:middle line:84% of put it in the context of nanocomputing in general. 00:10:12.530 --> 00:10:15.460 align:middle line:84% And you can see all the issues in computing, not just 00:10:15.460 --> 00:10:18.440 align:middle line:90% the math module. 00:10:18.440 --> 00:10:25.630 align:middle line:84% So all the steps are assembly of the requisite hardware. 00:10:25.630 --> 00:10:28.900 align:middle line:84% This is some kind of factory operation, typically. 00:10:28.900 --> 00:10:32.530 align:middle line:84% Then there's some of input module, some hardware 00:10:32.530 --> 00:10:35.260 align:middle line:84% and software that's required for getting the data in. 00:10:35.260 --> 00:10:37.000 align:middle line:84% Then there's some sort of memory. 00:10:37.000 --> 00:10:40.900 align:middle line:84% And then there's a central processor, might have math 00:10:40.900 --> 00:10:42.260 align:middle line:90% components and output. 00:10:42.260 --> 00:10:46.780 align:middle line:84% This is from our first lecture, assembly input, memory process, 00:10:46.780 --> 00:10:48.442 align:middle line:90% and output. 00:10:48.442 --> 00:10:49.900 align:middle line:84% And what we want to do with biology 00:10:49.900 --> 00:10:53.800 align:middle line:84% is we want to harvest things from genomics 00:10:53.800 --> 00:10:56.350 align:middle line:84% and from just biological research in general, 00:10:56.350 --> 00:11:00.250 align:middle line:84% use to design better computers either in silico 00:11:00.250 --> 00:11:03.980 align:middle line:84% or in a biological, biochemical sense. 00:11:03.980 --> 00:11:08.890 align:middle line:84% And then, harness evolution, either to make devices or as 00:11:08.890 --> 00:11:12.520 align:middle line:90% part of algorithm development. 00:11:12.520 --> 00:11:19.990 align:middle line:84% We have-- different people have different opinions 00:11:19.990 --> 00:11:22.300 align:middle line:84% about how much longer Moore's law, 00:11:22.300 --> 00:11:29.200 align:middle line:84% the scaling for large scale integrated circuits or curves 00:11:29.200 --> 00:11:32.770 align:middle line:84% files version that goes back to 1900s, about doubling every two 00:11:32.770 --> 00:11:40.190 align:middle line:84% years, the ability to calculate, calculations per second, 00:11:40.190 --> 00:11:41.743 align:middle line:90% per 1,000 [INAUDIBLE]. 00:11:41.743 --> 00:11:43.160 align:middle line:84% There might be another decade left 00:11:43.160 --> 00:11:47.720 align:middle line:84% in the silicone, a large scale integrated circuit. 00:11:47.720 --> 00:11:52.220 align:middle line:84% That's what some people say, or maybe more, maybe less. 00:11:52.220 --> 00:11:54.350 align:middle line:84% So there are three real options here 00:11:54.350 --> 00:12:04.280 align:middle line:84% for that next step, electronic nanocomputing, 00:12:04.280 --> 00:12:07.112 align:middle line:84% optical nanocomputing, molecular nanocomputing 00:12:07.112 --> 00:12:09.320 align:middle line:84% and you could add to this quantum computing, so maybe 00:12:09.320 --> 00:12:11.957 align:middle line:84% four different options for beating Moore's law 00:12:11.957 --> 00:12:13.415 align:middle line:84% or extending Moore's law, depending 00:12:13.415 --> 00:12:15.060 align:middle line:90% on how you look at it. 00:12:15.060 --> 00:12:17.870 align:middle line:84% So let's just walk through them quickly, one at a time. 00:12:17.870 --> 00:12:22.130 align:middle line:84% Optical computing you can think of as already here 00:12:22.130 --> 00:12:25.250 align:middle line:84% in a sense in that our optical fiber networks have 00:12:25.250 --> 00:12:27.830 align:middle line:84% very fast switches that are required 00:12:27.830 --> 00:12:30.545 align:middle line:84% for a good deal of our fastest internet. 00:12:30.545 --> 00:12:33.290 align:middle line:90% 00:12:33.290 --> 00:12:34.910 align:middle line:84% And there are various demonstrations 00:12:34.910 --> 00:12:38.060 align:middle line:84% where you can do optical computing for many 00:12:38.060 --> 00:12:41.690 align:middle line:84% of the tasks, not just the data transfer. 00:12:41.690 --> 00:12:44.690 align:middle line:84% And just like many other things, there's 00:12:44.690 --> 00:12:47.300 align:middle line:84% a desire to shrink this down for cost 00:12:47.300 --> 00:12:48.870 align:middle line:90% of manufacturing and quality. 00:12:48.870 --> 00:12:50.310 align:middle line:90% And so forth. 00:12:50.310 --> 00:12:57.080 align:middle line:84% The advantages of optical over electronic, typical computers 00:12:57.080 --> 00:13:03.080 align:middle line:84% is that they are, for a given set of operations, 00:13:03.080 --> 00:13:04.820 align:middle line:84% there's the general sentiment that it 00:13:04.820 --> 00:13:08.270 align:middle line:90% might be lower heat generation. 00:13:08.270 --> 00:13:12.230 align:middle line:84% It goes at the speed of light, rather than 00:13:12.230 --> 00:13:13.910 align:middle line:84% the slightly lower than speed of light 00:13:13.910 --> 00:13:17.660 align:middle line:84% that typically comes into actual implementations 00:13:17.660 --> 00:13:19.340 align:middle line:90% in electronic circuits. 00:13:19.340 --> 00:13:24.440 align:middle line:84% And here's two examples taken from the literature of getting 00:13:24.440 --> 00:13:27.200 align:middle line:84% natural sort of self-assembly, just 00:13:27.200 --> 00:13:29.060 align:middle line:84% as we've seen in many biological systems, 00:13:29.060 --> 00:13:31.610 align:middle line:84% we get self-assembly of membranes, self-assembly 00:13:31.610 --> 00:13:34.070 align:middle line:90% of multi-protein complexes. 00:13:34.070 --> 00:13:38.930 align:middle line:84% Here you have, you want to make particular kind of size 00:13:38.930 --> 00:13:46.340 align:middle line:84% of optical particles that have the right rank of index 00:13:46.340 --> 00:13:48.210 align:middle line:84% and spacing and shape and so forth. 00:13:48.210 --> 00:13:52.130 align:middle line:84% And you can use self-assembly here for that thing. 00:13:52.130 --> 00:13:56.510 align:middle line:84% These are examples of where we're getting in the nanometer 00:13:56.510 --> 00:13:57.020 align:middle line:90% range here. 00:13:57.020 --> 00:13:59.960 align:middle line:84% This is a 5 micron scale object here. 00:13:59.960 --> 00:14:06.070 align:middle line:90% 00:14:06.070 --> 00:14:07.880 align:middle line:84% I've chosen this particular example, 00:14:07.880 --> 00:14:12.670 align:middle line:84% there are a number of examples of electronic nanocomputing 00:14:12.670 --> 00:14:16.960 align:middle line:84% where the electronics is getting down to the size of molecules. 00:14:16.960 --> 00:14:19.990 align:middle line:84% Here the molecule chosen is a polymer 00:14:19.990 --> 00:14:23.380 align:middle line:84% of carbon, not a hydrocarbon, but carbon. 00:14:23.380 --> 00:14:26.320 align:middle line:84% It's like the buckyballs which is carbon-60 00:14:26.320 --> 00:14:29.650 align:middle line:84% or graphite rolled up in the tubes, these nanotubes, 00:14:29.650 --> 00:14:35.560 align:middle line:84% can be used as transistor like elements in very tiny circuits. 00:14:35.560 --> 00:14:37.180 align:middle line:90% This is just a schematic. 00:14:37.180 --> 00:14:39.950 align:middle line:84% This isn't actually a micrograph, right. 00:14:39.950 --> 00:14:41.650 align:middle line:84% And here are four circuits that kind of 00:14:41.650 --> 00:14:44.200 align:middle line:84% reflect what might be your first four 00:14:44.200 --> 00:14:49.120 align:middle line:84% projects in an introductory electronics course, 00:14:49.120 --> 00:14:51.880 align:middle line:84% ignoring the fact that you might not use nanotubes. 00:14:51.880 --> 00:14:55.930 align:middle line:84% But you would have voltage in and voltage out. 00:14:55.930 --> 00:14:58.630 align:middle line:84% In other words, this is a transistor like circuit 00:14:58.630 --> 00:15:01.570 align:middle line:84% or an inverter like circuit in the upper left hand 00:15:01.570 --> 00:15:03.070 align:middle line:90% corner of slide 10. 00:15:03.070 --> 00:15:07.960 align:middle line:84% And the nanotube here is in the middle in series 00:15:07.960 --> 00:15:11.050 align:middle line:84% with a resistor going from high voltage to the ground 00:15:11.050 --> 00:15:15.220 align:middle line:84% at the lower part and the voltage in essentially 00:15:15.220 --> 00:15:18.230 align:middle line:84% modulates the voltage out in the nonlinear curve. 00:15:18.230 --> 00:15:21.268 align:middle line:84% And you can see this highly cooperative curve just 00:15:21.268 --> 00:15:22.810 align:middle line:84% like the ones that we've been talking 00:15:22.810 --> 00:15:25.570 align:middle line:84% about in a number of other biological and physical 00:15:25.570 --> 00:15:27.290 align:middle line:90% systems. 00:15:27.290 --> 00:15:29.380 align:middle line:84% The upper right, you have a NOR gate. 00:15:29.380 --> 00:15:32.680 align:middle line:84% Almost every circuit can be made by combinations simply 00:15:32.680 --> 00:15:39.250 align:middle line:84% by [? not ?] [? OARS. ?] This is an inverter plus an [? OAR. ?] 00:15:39.250 --> 00:15:43.150 align:middle line:84% And so you can see that there now have two inputs on the left 00:15:43.150 --> 00:15:44.710 align:middle line:90% and right in 1 and 2. 00:15:44.710 --> 00:15:47.460 align:middle line:84% And they can have states 1-1, 1-0, 0-1, 00:15:47.460 --> 00:15:50.030 align:middle line:90% 0-0, going from left to right. 00:15:50.030 --> 00:15:51.550 align:middle line:84% And you can see only when they're 00:15:51.550 --> 00:15:56.050 align:middle line:84% both 0, does the whole circuit now, output go down to 0 00:15:56.050 --> 00:15:58.310 align:middle line:90% for low voltage for output. 00:15:58.310 --> 00:16:02.110 align:middle line:84% So input, the three possible input combinations 00:16:02.110 --> 00:16:03.988 align:middle line:84% and the last one gets the [? low. ?] 00:16:03.988 --> 00:16:05.530 align:middle line:84% And this is all done this is all done 00:16:05.530 --> 00:16:10.030 align:middle line:84% with these kind of molecular scale nanotubes. 00:16:10.030 --> 00:16:13.790 align:middle line:84% Here's a RAM, required two nanotubes in order to store, 00:16:13.790 --> 00:16:18.670 align:middle line:84% whether it's either where you flip it from open to flip it 00:16:18.670 --> 00:16:21.040 align:middle line:90% from low to high. 00:16:21.040 --> 00:16:22.940 align:middle line:84% And the last example, in the lower right, 00:16:22.940 --> 00:16:24.160 align:middle line:90% you now need 3 nanotubes. 00:16:24.160 --> 00:16:27.310 align:middle line:84% You see, we worked our way up in complexity from 1 to 2 to 3. 00:16:27.310 --> 00:16:30.100 align:middle line:84% And you need 3 in order to get a ring oscillator use. 00:16:30.100 --> 00:16:32.160 align:middle line:84% I mean, that's the way you would think about. 00:16:32.160 --> 00:16:33.535 align:middle line:84% Most easily think about it, where 00:16:33.535 --> 00:16:38.600 align:middle line:84% we have the first one's output affecting the second one. 00:16:38.600 --> 00:16:40.600 align:middle line:84% The second one affecting the third and third one 00:16:40.600 --> 00:16:41.890 align:middle line:90% looping back to the first. 00:16:41.890 --> 00:16:44.890 align:middle line:84% And the result of this as you get a series 00:16:44.890 --> 00:16:47.380 align:middle line:84% of peaks and troughs here, which you 00:16:47.380 --> 00:16:50.080 align:middle line:84% used for synchronizing circuits or generating 00:16:50.080 --> 00:16:55.450 align:middle line:84% other useful sinusoidal processes. 00:16:55.450 --> 00:17:00.040 align:middle line:90% Now that's one example-- 00:17:00.040 --> 00:17:01.810 align:middle line:90% so the optical electronic. 00:17:01.810 --> 00:17:05.119 align:middle line:84% Molecular includes a number of different possibilities, 00:17:05.119 --> 00:17:08.680 align:middle line:84% including DNA which is what we'll focus on, DNA computing. 00:17:08.680 --> 00:17:11.740 align:middle line:84% And this was started by a person, 00:17:11.740 --> 00:17:15.490 align:middle line:84% a physicist famous for thinking out of the box quite a bit. 00:17:15.490 --> 00:17:18.970 align:middle line:84% Feynman in 1959, when he was still fairly young, 00:17:18.970 --> 00:17:22.869 align:middle line:84% gave a talk entitled There's Plenty of Room at the Bottom. 00:17:22.869 --> 00:17:26.109 align:middle line:84% And by that he meant that we can-- 00:17:26.109 --> 00:17:32.350 align:middle line:84% just as we can machine and manufacture objects 00:17:32.350 --> 00:17:36.430 align:middle line:84% under fairly automated fashion, we 00:17:36.430 --> 00:17:39.580 align:middle line:84% should be able to scale that down to the point 00:17:39.580 --> 00:17:41.350 align:middle line:84% where we're manipulating individual atoms. 00:17:41.350 --> 00:17:45.145 align:middle line:84% And he couldn't think of any physical reason, 00:17:45.145 --> 00:17:47.020 align:middle line:84% such as the uncertainty principle or anything 00:17:47.020 --> 00:17:49.103 align:middle line:84% like that, that would prevent one from doing that, 00:17:49.103 --> 00:17:50.620 align:middle line:90% manipulating individual atoms. 00:17:50.620 --> 00:17:53.290 align:middle line:84% And many years later now, he's been proven right and that 00:17:53.290 --> 00:17:57.700 align:middle line:84% we are doing that, albeit not in any really high production 00:17:57.700 --> 00:17:59.650 align:middle line:90% method. 00:17:59.650 --> 00:18:02.200 align:middle line:84% Drexler and his thesis and subsequently 00:18:02.200 --> 00:18:07.280 align:middle line:84% has championed, is probably the right word, this notion 00:18:07.280 --> 00:18:11.140 align:middle line:84% and given it the name nanotechnology and nanosystems 00:18:11.140 --> 00:18:13.510 align:middle line:84% and really fleshed out some of the things 00:18:13.510 --> 00:18:15.220 align:middle line:84% that one might be able to do if you 00:18:15.220 --> 00:18:20.140 align:middle line:84% had a much higher throughput way of dealing with manufacturing 00:18:20.140 --> 00:18:21.760 align:middle line:90% at atomic scale. 00:18:21.760 --> 00:18:25.780 align:middle line:84% However, even he did not really connect all the dots 00:18:25.780 --> 00:18:28.480 align:middle line:84% between where we are now and where and how we 00:18:28.480 --> 00:18:31.330 align:middle line:84% get to the very first nano-assemblers 00:18:31.330 --> 00:18:33.923 align:middle line:90% and nanotechnology. 00:18:33.923 --> 00:18:36.340 align:middle line:84% Since then, there's been kind of a Renaissance of interest 00:18:36.340 --> 00:18:40.310 align:middle line:84% in this with a recognition that biological systems actually 00:18:40.310 --> 00:18:46.660 align:middle line:84% are naturally doing nanotech scale, atomic manipulations. 00:18:46.660 --> 00:18:50.890 align:middle line:84% And you've seen a few examples of that in this course. 00:18:50.890 --> 00:18:56.650 align:middle line:84% But the particular instance that we'll use as a jumping off 00:18:56.650 --> 00:19:00.490 align:middle line:84% point for discussion of all the steps 00:19:00.490 --> 00:19:06.530 align:middle line:84% that could be where biology and molecular mining 00:19:06.530 --> 00:19:09.650 align:middle line:84% could give us new tools, whether it's 00:19:09.650 --> 00:19:16.430 align:middle line:84% from assembly inputs, memory computation output. 00:19:16.430 --> 00:19:25.670 align:middle line:84% We'll start with Len Adleman's pace changing paper in 1994. 00:19:25.670 --> 00:19:32.310 align:middle line:84% This is the A of the RSA that we talked about a few minutes ago. 00:19:32.310 --> 00:19:40.080 align:middle line:84% He was obviously a hardcore and is algorithmics expert 00:19:40.080 --> 00:19:45.420 align:middle line:84% and decided in 1994 to actually do 00:19:45.420 --> 00:19:47.760 align:middle line:84% a paper that required not only algorithmic, 00:19:47.760 --> 00:19:51.120 align:middle line:84% but a huge change in the way you implemented the algorithms. 00:19:51.120 --> 00:19:52.980 align:middle line:84% And then actually to go into the lab 00:19:52.980 --> 00:19:55.320 align:middle line:84% into a biochemical laboratory which 00:19:55.320 --> 00:19:59.130 align:middle line:90% he was not previously trained. 00:19:59.130 --> 00:20:02.730 align:middle line:84% And to author-- it's a single author paper that 00:20:02.730 --> 00:20:04.650 align:middle line:90% included such things as PCR. 00:20:04.650 --> 00:20:05.760 align:middle line:90% That was in 1994. 00:20:05.760 --> 00:20:09.630 align:middle line:84% There was no literature on the subject of DNA computers 00:20:09.630 --> 00:20:10.740 align:middle line:90% before that. 00:20:10.740 --> 00:20:13.650 align:middle line:84% A mere six years later, there were 520 references 00:20:13.650 --> 00:20:14.320 align:middle line:90% on the subject. 00:20:14.320 --> 00:20:17.160 align:middle line:84% So he obviously hit some kind of nerve. 00:20:17.160 --> 00:20:19.140 align:middle line:84% The first few years of that after that 00:20:19.140 --> 00:20:20.490 align:middle line:90% were mainly theoretical. 00:20:20.490 --> 00:20:22.260 align:middle line:90% But I'll show you some examples. 00:20:22.260 --> 00:20:26.790 align:middle line:84% His paper had an experimental component, and some others 00:20:26.790 --> 00:20:29.010 align:middle line:90% that I'll show you. 00:20:29.010 --> 00:20:31.860 align:middle line:84% Since this course is really about that interface, 00:20:31.860 --> 00:20:35.580 align:middle line:84% constantly checking the theory with reality, 00:20:35.580 --> 00:20:38.170 align:middle line:84% those are the ones that I'll emphasize here. 00:20:38.170 --> 00:20:42.420 align:middle line:84% So the question that he asked in 1994 and is still fresh today 00:20:42.420 --> 00:20:45.540 align:middle line:84% is, is there a Hamiltonian path through all the nodes 00:20:45.540 --> 00:20:46.900 align:middle line:90% in a network? 00:20:46.900 --> 00:20:50.250 align:middle line:84% So we've been talking about interesting biological 00:20:50.250 --> 00:20:50.760 align:middle line:90% networks. 00:20:50.760 --> 00:20:52.890 align:middle line:84% But here, just in any network where 00:20:52.890 --> 00:20:57.960 align:middle line:84% the black nodes are connected by directed edges 00:20:57.960 --> 00:20:59.700 align:middle line:90% in this directed graph. 00:20:59.700 --> 00:21:03.210 align:middle line:84% You want to go from the start, S, to the terminus T, 00:21:03.210 --> 00:21:07.200 align:middle line:84% from 1 to 6, obeying the arrows and going through every point 00:21:07.200 --> 00:21:09.120 align:middle line:90% once. 00:21:09.120 --> 00:21:10.980 align:middle line:90% How do you do this? 00:21:10.980 --> 00:21:13.140 align:middle line:90% And how do you do it in DNA? 00:21:13.140 --> 00:21:16.850 align:middle line:84% So an example of one here is going from S to 3 to 5 00:21:16.850 --> 00:21:21.240 align:middle line:90% to 2 to 4 to T. 00:21:21.240 --> 00:21:24.705 align:middle line:84% So the way you do it, first in broad strokes, 00:21:24.705 --> 00:21:29.700 align:middle line:84% you encode the graph, both the nodes, black spots, 00:21:29.700 --> 00:21:33.780 align:middle line:84% and the edges into single-stranded DNA sequences. 00:21:33.780 --> 00:21:37.140 align:middle line:84% Then you create all possible paths 00:21:37.140 --> 00:21:39.510 align:middle line:84% as by using overlapping sequences 00:21:39.510 --> 00:21:44.310 align:middle line:84% to indicate which node is connected to which other node 00:21:44.310 --> 00:21:46.660 align:middle line:90% by an edge in which direction. 00:21:46.660 --> 00:21:49.170 align:middle line:84% So you can actually have directionality, just 00:21:49.170 --> 00:21:52.050 align:middle line:90% because DNA has directionality. 00:21:52.050 --> 00:21:55.440 align:middle line:84% And you use DNA hybridization now to do that step. 00:21:55.440 --> 00:21:57.450 align:middle line:90% Now, the first step is linear. 00:21:57.450 --> 00:21:59.400 align:middle line:84% Encoding the graph is linear with the number 00:21:59.400 --> 00:22:02.430 align:middle line:84% of points in the graph, the number of places 00:22:02.430 --> 00:22:05.980 align:middle line:90% in the Hamiltonian path. 00:22:05.980 --> 00:22:07.500 align:middle line:84% The second step is not something-- 00:22:07.500 --> 00:22:11.400 align:middle line:84% and that you would do by having your computer program a DNA 00:22:11.400 --> 00:22:14.010 align:middle line:84% synthesizer which is an automated machine that we've 00:22:14.010 --> 00:22:17.760 align:middle line:90% described a couple of times. 00:22:17.760 --> 00:22:20.560 align:middle line:84% But the second step is out of your hands. 00:22:20.560 --> 00:22:26.370 align:middle line:84% This is something that happens automatically when you put DNA 00:22:26.370 --> 00:22:27.500 align:middle line:90% in the solution. 00:22:27.500 --> 00:22:29.640 align:middle line:84% If you design these sequences carefully 00:22:29.640 --> 00:22:31.530 align:middle line:84% so they don't cross hybridize very much, 00:22:31.530 --> 00:22:33.150 align:middle line:84% then the only way they can assemble 00:22:33.150 --> 00:22:35.760 align:middle line:90% is the way you want it. 00:22:35.760 --> 00:22:38.160 align:middle line:84% Then, you finally determine where the solution exists, 00:22:38.160 --> 00:22:42.490 align:middle line:84% and this is something which is almost constant in complexity. 00:22:42.490 --> 00:22:45.240 align:middle line:84% So the entire thing scales very gracefully 00:22:45.240 --> 00:22:49.415 align:middle line:84% instead of scaling exponentially as the Hamiltonian path problem 00:22:49.415 --> 00:22:50.040 align:middle line:90% normally would. 00:22:50.040 --> 00:22:55.080 align:middle line:84% This gives the appearance of scaling linearly in time, which 00:22:55.080 --> 00:22:58.920 align:middle line:84% is really one of the best case scenarios for polynomial time 00:22:58.920 --> 00:23:01.050 align:middle line:84% and certainly better than exponential. 00:23:01.050 --> 00:23:02.370 align:middle line:90% So how do we actually do that? 00:23:02.370 --> 00:23:03.250 align:middle line:90% That was broad strokes. 00:23:03.250 --> 00:23:04.458 align:middle line:90% This is a more detailed view. 00:23:04.458 --> 00:23:07.500 align:middle line:84% And you can see how this really seems like it's going to work. 00:23:07.500 --> 00:23:14.070 align:middle line:84% You have each of the nodes encoded by sequences, 00:23:14.070 --> 00:23:19.950 align:middle line:84% let's say, red and tan here on the top left of slide 14. 00:23:19.950 --> 00:23:25.680 align:middle line:84% And you have, if you want to connect node 3 with node 4, 00:23:25.680 --> 00:23:29.370 align:middle line:84% so that you take the right hand in, the 3 prime end which 00:23:29.370 --> 00:23:31.050 align:middle line:90% is sorta greenish tan. 00:23:31.050 --> 00:23:35.160 align:middle line:84% And you connect it now to the other end of, 00:23:35.160 --> 00:23:37.800 align:middle line:84% that is to say the 5 prime end of node 4 00:23:37.800 --> 00:23:39.300 align:middle line:90% just below it, which is blue. 00:23:39.300 --> 00:23:42.970 align:middle line:84% So now you have this hybrid which is ordered. 00:23:42.970 --> 00:23:46.590 align:middle line:84% So it's an arrow going from 3 to 4 00:23:46.590 --> 00:23:49.320 align:middle line:84% and that edge has this particular sequence 00:23:49.320 --> 00:23:50.820 align:middle line:90% going from 5 prime to 3 prime. 00:23:50.820 --> 00:23:54.000 align:middle line:84% Now, in practice, you want the edges to be complementary, not 00:23:54.000 --> 00:23:55.505 align:middle line:90% identical to the nodes. 00:23:55.505 --> 00:23:56.880 align:middle line:84% And so all the nodes are actually 00:23:56.880 --> 00:24:00.420 align:middle line:84% represented as reverse sequences in the lower left hand 00:24:00.420 --> 00:24:02.940 align:middle line:90% part of slide 14. 00:24:02.940 --> 00:24:07.230 align:middle line:84% And so represent all the edges that connect nodes 00:24:07.230 --> 00:24:09.150 align:middle line:90% in this directional manner. 00:24:09.150 --> 00:24:13.590 align:middle line:84% And then an example of how you would connect 00:24:13.590 --> 00:24:19.380 align:middle line:84% three nodes, 3 to 4 to 5 by two connecting directional edges, 00:24:19.380 --> 00:24:21.720 align:middle line:90% 3, 4, 4, 5 is shown here. 00:24:21.720 --> 00:24:24.720 align:middle line:84% All the nodes are in reverse compliments 00:24:24.720 --> 00:24:28.170 align:middle line:84% and all the edges are in the forward direction 00:24:28.170 --> 00:24:30.120 align:middle line:90% as arbitrarily defined here. 00:24:30.120 --> 00:24:32.610 align:middle line:84% And you can see how they stitch these together 00:24:32.610 --> 00:24:36.270 align:middle line:84% and you make firm connections that are unambiguous, 00:24:36.270 --> 00:24:40.980 align:middle line:84% non cross-reacting and have a direct directionality. 00:24:40.980 --> 00:24:43.920 align:middle line:84% Now that you are starting to get the idea that now we 00:24:43.920 --> 00:24:45.335 align:middle line:90% can encode this in DNA. 00:24:45.335 --> 00:24:47.460 align:middle line:84% But how are we going to actually do the computation 00:24:47.460 --> 00:24:51.480 align:middle line:84% and how are we going to find out who the winner is? 00:24:51.480 --> 00:24:56.610 align:middle line:84% So what is done, remember, we want to create all the paths 00:24:56.610 --> 00:25:00.100 align:middle line:84% and then to ask whether any of them go through all the points? 00:25:00.100 --> 00:25:02.280 align:middle line:84% And then do any of them go through all the points 00:25:02.280 --> 00:25:03.610 align:middle line:90% exactly once? 00:25:03.610 --> 00:25:06.690 align:middle line:84% So the first thing is to create all the paths from start 00:25:06.690 --> 00:25:08.460 align:middle line:90% to terminus. 00:25:08.460 --> 00:25:10.680 align:middle line:84% And by just throwing in this mixture 00:25:10.680 --> 00:25:13.300 align:middle line:84% of all the edges and all the nodes, 00:25:13.300 --> 00:25:16.020 align:middle line:84% you will create in principle all the paths. 00:25:16.020 --> 00:25:20.610 align:middle line:84% Now you want to write, you will go from the prefix of one 00:25:20.610 --> 00:25:23.610 align:middle line:84% into the suffix of the other in the same way that illustrated 00:25:23.610 --> 00:25:25.570 align:middle line:90% on the previous slide. 00:25:25.570 --> 00:25:27.600 align:middle line:84% And here are some examples of some of the paths, 00:25:27.600 --> 00:25:28.710 align:middle line:90% some are very short. 00:25:28.710 --> 00:25:31.980 align:middle line:84% This only goes through the 1, 2 4, 6, 00:25:31.980 --> 00:25:34.930 align:middle line:84% only goes through 4 the nodes, that's not all 6 of them. 00:25:34.930 --> 00:25:37.500 align:middle line:84% The bottom one goes through too many nodes and some of them 00:25:37.500 --> 00:25:39.810 align:middle line:90% it's going through repetitively. 00:25:39.810 --> 00:25:42.953 align:middle line:84% But you get the idea is that you can define the path in terms 00:25:42.953 --> 00:25:44.370 align:middle line:84% of all these edges and the reverse 00:25:44.370 --> 00:25:47.280 align:middle line:84% complements which represent the nodes. 00:25:47.280 --> 00:25:50.850 align:middle line:84% But here's the actual algorithm as encoded in DNA 00:25:50.850 --> 00:25:54.690 align:middle line:84% and implemented by practical methods 00:25:54.690 --> 00:26:00.450 align:middle line:84% that a computer scientist can do without too much help, 00:26:00.450 --> 00:26:03.390 align:middle line:84% at least not enough help required for co-authorship. 00:26:03.390 --> 00:26:08.800 align:middle line:84% So we've already encoded the graphs in the DNA sequences. 00:26:08.800 --> 00:26:11.760 align:middle line:84% And this is done by automated oligonucleotide synthesis. 00:26:11.760 --> 00:26:15.870 align:middle line:84% You create all the paths from ST by PCR amplifying from the S 00:26:15.870 --> 00:26:18.270 align:middle line:90% end of the oligo to the T end. 00:26:18.270 --> 00:26:20.790 align:middle line:84% So that means, the mere fact that they PCR amplify 00:26:20.790 --> 00:26:25.210 align:middle line:84% means they must contain node 1 and 6, the start of terminus. 00:26:25.210 --> 00:26:26.100 align:middle line:90% So that's good. 00:26:26.100 --> 00:26:28.620 align:middle line:84% Now, you want to get the ones that visit every node, 00:26:28.620 --> 00:26:34.710 align:middle line:84% so by serial hybridization, you can have nodes 2, 3, 4 and 5 00:26:34.710 --> 00:26:35.760 align:middle line:90% immobilized. 00:26:35.760 --> 00:26:39.810 align:middle line:84% And you bind the PCR products to it, and you'll loop from 2 00:26:39.810 --> 00:26:43.080 align:middle line:84% and then in series you bind to 3, loop from 3, bind to 4, 00:26:43.080 --> 00:26:44.130 align:middle line:90% loop for 4, 5. 00:26:44.130 --> 00:26:47.400 align:middle line:84% So now you know it has 1 in 6 because that's the PCR primers. 00:26:47.400 --> 00:26:49.530 align:middle line:84% It has 2, 3, 4 and 5 because it balances them 00:26:49.530 --> 00:26:52.260 align:middle line:90% in series by hybridization. 00:26:52.260 --> 00:26:55.260 align:middle line:84% Then, but that, you could get some 00:26:55.260 --> 00:27:00.150 align:middle line:84% of those long paths that went through multiple nodes 00:27:00.150 --> 00:27:00.900 align:middle line:90% multiple times. 00:27:00.900 --> 00:27:02.683 align:middle line:84% If you want it to have exactly N nodes, 00:27:02.683 --> 00:27:04.850 align:middle line:84% then what you do is sort of of electric [? thread ?] 00:27:04.850 --> 00:27:12.450 align:middle line:84% [? excising. ?] And here if you have a calibration curve 00:27:12.450 --> 00:27:14.100 align:middle line:84% as shown on the bottom of slide 16, 00:27:14.100 --> 00:27:20.310 align:middle line:84% we have known DNA size markers and known PCR products going, 00:27:20.310 --> 00:27:27.540 align:middle line:84% showing you have one of these DNA nodes, 2, 3, 00:27:27.540 --> 00:27:28.710 align:middle line:90% all the way up to 6. 00:27:28.710 --> 00:27:32.130 align:middle line:84% And if you find a solution that has all these properties, 00:27:32.130 --> 00:27:35.250 align:middle line:84% PCRs, does serial hybridization to all the nodes 00:27:35.250 --> 00:27:40.290 align:middle line:84% and is the right length, such as the one in column 6, 00:27:40.290 --> 00:27:42.760 align:middle line:84% then you know you've got a solution. 00:27:42.760 --> 00:27:45.310 align:middle line:84% And that was Len Adleman's argument 00:27:45.310 --> 00:27:48.430 align:middle line:84% that he had DNA computing working. 00:27:48.430 --> 00:27:52.370 align:middle line:84% Six years later, we now have, or as of six years later, 00:27:52.370 --> 00:27:57.490 align:middle line:84% there were now over 500 examples of this. 00:27:57.490 --> 00:28:02.440 align:middle line:84% I'll show you this example as both as an introduction 00:28:02.440 --> 00:28:05.560 align:middle line:84% to the satisfiability problem and also 00:28:05.560 --> 00:28:08.320 align:middle line:84% as showing that you can do RNA computing 00:28:08.320 --> 00:28:12.910 align:middle line:84% and that you can encode two-dimensional objects 00:28:12.910 --> 00:28:14.690 align:middle line:84% and it illustrates a number of things. 00:28:14.690 --> 00:28:17.520 align:middle line:84% The problem here is a test problem, very simple test 00:28:17.520 --> 00:28:18.020 align:middle line:90% board. 00:28:18.020 --> 00:28:20.950 align:middle line:90% It's not 8 by 8, but 3 by 3. 00:28:20.950 --> 00:28:25.010 align:middle line:84% And you've got an artificial number of knights here. 00:28:25.010 --> 00:28:26.830 align:middle line:84% And those of you who know chess know 00:28:26.830 --> 00:28:30.730 align:middle line:84% that these knights can attack in a curious combination 00:28:30.730 --> 00:28:32.140 align:middle line:90% of straight and diagonal. 00:28:32.140 --> 00:28:33.350 align:middle line:90% And it doesn't really matter. 00:28:33.350 --> 00:28:37.030 align:middle line:84% The point is there are a variety of arrangements 00:28:37.030 --> 00:28:40.060 align:middle line:84% of any number of knights such that none of them 00:28:40.060 --> 00:28:42.310 align:middle line:84% can attack each other and they're all kind of at peace 00:28:42.310 --> 00:28:43.240 align:middle line:90% here. 00:28:43.240 --> 00:28:45.850 align:middle line:84% And that the object of this algorithm 00:28:45.850 --> 00:28:48.130 align:middle line:90% is to find those combinations. 00:28:48.130 --> 00:28:51.070 align:middle line:84% And here's-- and you do it by cloning. 00:28:51.070 --> 00:28:54.640 align:middle line:84% So that was something that was not in the previous example. 00:28:54.640 --> 00:28:56.830 align:middle line:84% By cloning, you can find each of the solutions. 00:28:56.830 --> 00:28:59.620 align:middle line:84% And you then determine what is present 00:28:59.620 --> 00:29:01.060 align:middle line:90% and sits along that clone. 00:29:01.060 --> 00:29:05.470 align:middle line:84% It's kind of like haplotyping or splice form analysis. 00:29:05.470 --> 00:29:07.690 align:middle line:84% You can really only analyze these things 00:29:07.690 --> 00:29:10.515 align:middle line:84% by looking at the product of a single molecule. 00:29:10.515 --> 00:29:11.890 align:middle line:84% And that's what cloning is about, 00:29:11.890 --> 00:29:14.650 align:middle line:84% looking at, amplifying that single molecule up to the point 00:29:14.650 --> 00:29:16.130 align:middle line:90% where you can analyze it. 00:29:16.130 --> 00:29:17.680 align:middle line:90% So that's one thing that's new. 00:29:17.680 --> 00:29:21.610 align:middle line:84% The other thing is new, is you start with an RNA in order 00:29:21.610 --> 00:29:25.520 align:middle line:84% that you can use this powerful method, this enzyme called 00:29:25.520 --> 00:29:28.270 align:middle line:84% RNase H which will-- it has a property 00:29:28.270 --> 00:29:31.270 align:middle line:84% that when you bind a DNA oligonucleotide 00:29:31.270 --> 00:29:36.280 align:middle line:84% to an RNA and their complementary RNase H 00:29:36.280 --> 00:29:40.640 align:middle line:84% will destroy the RNA at that point, 00:29:40.640 --> 00:29:41.930 align:middle line:90% at the point of hybridization. 00:29:41.930 --> 00:29:45.710 align:middle line:84% So it's a way of eliminating an entire molecule 00:29:45.710 --> 00:29:48.350 align:middle line:84% if it happens to have a particular sequence in it. 00:29:48.350 --> 00:29:52.460 align:middle line:84% And so one of the ways that you can ask logical questions 00:29:52.460 --> 00:29:56.210 align:middle line:84% about each molecule in a large complex mixture of molecules 00:29:56.210 --> 00:29:58.700 align:middle line:90% is using this RNase elimination. 00:29:58.700 --> 00:30:02.960 align:middle line:84% And in a way, it's a way of designing an infinite number 00:30:02.960 --> 00:30:04.190 align:middle line:90% of restriction enzymes. 00:30:04.190 --> 00:30:07.370 align:middle line:84% The RNase plus the DNA oligonucleotide 00:30:07.370 --> 00:30:11.133 align:middle line:84% provides in a certain sense, a custom restriction enzyme. 00:30:11.133 --> 00:30:12.800 align:middle line:84% Any case, the other thing that's unusual 00:30:12.800 --> 00:30:15.680 align:middle line:84% here is the idea of using split and pool oligonucleotide 00:30:15.680 --> 00:30:16.460 align:middle line:90% synthesis. 00:30:16.460 --> 00:30:19.040 align:middle line:84% We introduced this in the lecture 00:30:19.040 --> 00:30:27.230 align:middle line:84% where we were introducing drug protein interaction and ways 00:30:27.230 --> 00:30:31.790 align:middle line:84% of synthesizing drugs and other molecules by Poole synthesis. 00:30:31.790 --> 00:30:36.950 align:middle line:84% And the idea behind split Poole synthesis in this case is that 00:30:36.950 --> 00:30:42.020 align:middle line:84% each of the squares in this 3 by 3 matrix can have two states, 00:30:42.020 --> 00:30:43.790 align:middle line:84% either has a knight or it doesn't. 00:30:43.790 --> 00:30:46.670 align:middle line:84% Each of those two states, you can consider a 0 or 1. 00:30:46.670 --> 00:30:49.900 align:middle line:84% You can represent them as two different sequences. 00:30:49.900 --> 00:30:53.870 align:middle line:84% Sequence A or sequence A prime, representing presence 00:30:53.870 --> 00:30:55.380 align:middle line:90% or absence of something. 00:30:55.380 --> 00:30:58.400 align:middle line:90% And so you basically have 2-- 00:30:58.400 --> 00:31:02.000 align:middle line:84% you have 8 squares and so you have 2 00:31:02.000 --> 00:31:03.810 align:middle line:84% to the 9th different possibilities. 00:31:03.810 --> 00:31:09.470 align:middle line:84% And so down below they synthesized a set of polymers 00:31:09.470 --> 00:31:13.250 align:middle line:84% where you have every possible binary state for this 3 00:31:13.250 --> 00:31:15.560 align:middle line:90% by 3 grid. 00:31:15.560 --> 00:31:17.730 align:middle line:84% And that's done by-- you're synthesizing along 00:31:17.730 --> 00:31:19.730 align:middle line:84% and you come to where you're going to synthesize 00:31:19.730 --> 00:31:20.720 align:middle line:90% either A or A prime. 00:31:20.720 --> 00:31:21.830 align:middle line:90% You split it. 00:31:21.830 --> 00:31:25.430 align:middle line:84% Half of this pool gets a A. Half of it gets sequence A prime. 00:31:25.430 --> 00:31:28.720 align:middle line:84% Pull back the other half gets B, half gets B prime. 00:31:28.720 --> 00:31:30.470 align:middle line:84% Pool them and split them and C and C prime 00:31:30.470 --> 00:31:32.252 align:middle line:90% and so forth, all the way out. 00:31:32.252 --> 00:31:33.710 align:middle line:84% You really only need nine of these. 00:31:33.710 --> 00:31:35.310 align:middle line:84% They did 10 for some reason or other. 00:31:35.310 --> 00:31:38.690 align:middle line:84% But the point is to get 2 to the ninth power, 00:31:38.690 --> 00:31:39.740 align:middle line:90% you need nine of these. 00:31:39.740 --> 00:31:41.873 align:middle line:90% And then as you can-- 00:31:41.873 --> 00:31:43.790 align:middle line:84% then you can read them out electrophoretically 00:31:43.790 --> 00:31:47.750 align:middle line:84% just as the electrophoretic readout gave a sizing 00:31:47.750 --> 00:31:51.470 align:middle line:84% in the first DNA computing, you can use 00:31:51.470 --> 00:31:53.360 align:middle line:90% it to get the sizes of these. 00:31:53.360 --> 00:31:55.260 align:middle line:84% And you can see-- you could read out-- 00:31:55.260 --> 00:31:58.760 align:middle line:84% Here's two solutions, BEFH referring to the squares on a 3 00:31:58.760 --> 00:32:02.370 align:middle line:84% by 3 grid and EFC, these are both solutions. 00:32:02.370 --> 00:32:06.140 align:middle line:84% BEFH, the way of reading this off 00:32:06.140 --> 00:32:08.360 align:middle line:84% this combinatorial synthesis from the bottom 00:32:08.360 --> 00:32:13.370 align:middle line:84% is you've got A through I as the possible bit binary signatures. 00:32:13.370 --> 00:32:17.120 align:middle line:84% And then you have two columns, either the 0 column or the 1, 00:32:17.120 --> 00:32:19.010 align:middle line:90% two states, the two sequences. 00:32:19.010 --> 00:32:24.350 align:middle line:84% And as you PCR from the end tag out to each 00:32:24.350 --> 00:32:27.230 align:middle line:84% of these tags, A or A prime, B or B prime, and so forth. 00:32:27.230 --> 00:32:29.330 align:middle line:90% Then you get-- these are all-- 00:32:29.330 --> 00:32:31.035 align:middle line:84% you'll get this graduated series. 00:32:31.035 --> 00:32:32.660 align:middle line:84% It will tell you, you've got a little-- 00:32:32.660 --> 00:32:35.570 align:middle line:90% you've got, A is in the 0 state. 00:32:35.570 --> 00:32:37.940 align:middle line:90% B is in the 1 state. 00:32:37.940 --> 00:32:40.580 align:middle line:90% C and D are in the 0 state. 00:32:40.580 --> 00:32:42.050 align:middle line:90% E is in the 1 state so forth. 00:32:42.050 --> 00:32:44.660 align:middle line:84% And so I've circled B being in the 1 stage showing 00:32:44.660 --> 00:32:47.750 align:middle line:84% that there's a Knight in position B. 00:32:47.750 --> 00:32:51.290 align:middle line:84% And you can go through the same thing for the other solutions. 00:32:51.290 --> 00:32:53.840 align:middle line:84% Each of these to develop as a clone. 00:32:53.840 --> 00:32:55.005 align:middle line:90% And there's an and-- 00:32:55.005 --> 00:32:56.630 align:middle line:84% the neat thing about all these problems 00:32:56.630 --> 00:32:58.070 align:middle line:84% is they have multiple representations. 00:32:58.070 --> 00:32:59.270 align:middle line:90% You represent them in DNA. 00:32:59.270 --> 00:33:01.490 align:middle line:90% You represent them in data. 00:33:01.490 --> 00:33:04.580 align:middle line:84% You can represent them as a Boolean logical set 00:33:04.580 --> 00:33:06.770 align:middle line:84% of operations where these things represent 00:33:06.770 --> 00:33:12.120 align:middle line:84% ANDs and ORs at the bottom of the slide and so on. 00:33:12.120 --> 00:33:16.190 align:middle line:84% And you will see that in the last examples 00:33:16.190 --> 00:33:20.570 align:middle line:84% where I've just kind of breezed through, 00:33:20.570 --> 00:33:24.830 align:middle line:84% where that set of logical operations 00:33:24.830 --> 00:33:28.400 align:middle line:84% is probably one of the favorite points of attack 00:33:28.400 --> 00:33:31.830 align:middle line:90% for DNA computing still today. 00:33:31.830 --> 00:33:34.250 align:middle line:84% So what are the problems and the advantages? 00:33:34.250 --> 00:33:38.730 align:middle line:84% The problems are that yes, it is polynomial time. 00:33:38.730 --> 00:33:41.400 align:middle line:84% In fact, it's close to linear time with a number of inputs 00:33:41.400 --> 00:33:41.900 align:middle line:90% in. 00:33:41.900 --> 00:33:44.780 align:middle line:84% In terms of synthesis needs, you know, 00:33:44.780 --> 00:33:47.180 align:middle line:84% your computer tells a synthesizer what to make. 00:33:47.180 --> 00:33:51.050 align:middle line:84% And then enzymes will or hybridisation 00:33:51.050 --> 00:33:57.470 align:middle line:84% will do this highly parallel reaction independent of N. 00:33:57.470 --> 00:33:59.910 align:middle line:90% So basically constant time. 00:33:59.910 --> 00:34:01.970 align:middle line:84% So it's linear time for synthesis, 00:34:01.970 --> 00:34:05.720 align:middle line:84% constant time for the computing, and constant time for the 00:34:05.720 --> 00:34:07.730 align:middle line:90% getting the answer right out. 00:34:07.730 --> 00:34:10.460 align:middle line:84% But you have exponential volumes. 00:34:10.460 --> 00:34:12.500 align:middle line:84% For example, a hundred-node graph, 00:34:12.500 --> 00:34:15.350 align:middle line:84% we've been talking about the various graphs solutions might 00:34:15.350 --> 00:34:17.900 align:middle line:90% be 10 to the 30th molecules. 00:34:17.900 --> 00:34:20.659 align:middle line:84% And if any of you have ever tried 00:34:20.659 --> 00:34:24.679 align:middle line:84% to synthesize a mole or 10 to the 24th molecules, 00:34:24.679 --> 00:34:28.380 align:middle line:84% you realize it would bankrupt our planet to make 10 00:34:28.380 --> 00:34:30.330 align:middle line:90% to the 30th molecules. 00:34:30.330 --> 00:34:34.820 align:middle line:84% So in addition, the elementary steps are slow. 00:34:34.820 --> 00:34:36.850 align:middle line:90% It's highly parallel. 00:34:36.850 --> 00:34:42.190 align:middle line:84% You can imagine having trillions of molecules 00:34:42.190 --> 00:34:45.070 align:middle line:84% computing in parallel, but the elementary steps 00:34:45.070 --> 00:34:48.370 align:middle line:84% of hybridization and DNA polymerase or RNase H 00:34:48.370 --> 00:34:51.610 align:middle line:84% and so forth, typically are in the millihertz range. 00:34:51.610 --> 00:34:55.000 align:middle line:84% That is to say, it might take 1,000 seconds, rather than 00:34:55.000 --> 00:34:57.550 align:middle line:84% gigahertz, which would be a billionth of a second. 00:34:57.550 --> 00:35:02.260 align:middle line:84% So there might be a 10 to the 12th gap in rate 00:35:02.260 --> 00:35:05.890 align:middle line:84% of executing the commands, but there's more, 00:35:05.890 --> 00:35:07.710 align:middle line:84% the hope is that there's more than a 10 00:35:07.710 --> 00:35:10.240 align:middle line:84% to the 12th advantage in parallelism. 00:35:10.240 --> 00:35:15.700 align:middle line:84% In addition, experimental errors mustn't be swept under the rug. 00:35:15.700 --> 00:35:17.440 align:middle line:90% You've got issues with mismatch. 00:35:17.440 --> 00:35:19.390 align:middle line:84% There's a limit that just how cleverly you 00:35:19.390 --> 00:35:21.010 align:middle line:90% can design all these sequences. 00:35:21.010 --> 00:35:23.710 align:middle line:84% As the graph gets bigger, you need 00:35:23.710 --> 00:35:26.495 align:middle line:84% to have more and more sequences involved. 00:35:26.495 --> 00:35:28.120 align:middle line:84% And that means that you're going to get 00:35:28.120 --> 00:35:29.860 align:middle line:84% more and more cross hybridization, 00:35:29.860 --> 00:35:32.120 align:middle line:84% incomplete cleavage, and so forth. 00:35:32.120 --> 00:35:36.640 align:middle line:84% There are-- when this slide 18 says non-reusable, 00:35:36.640 --> 00:35:38.110 align:middle line:90% there are reusable forms. 00:35:38.110 --> 00:35:39.860 align:middle line:84% And we'll get to those in just a minute. 00:35:39.860 --> 00:35:41.152 align:middle line:90% So those are the disadvantages. 00:35:41.152 --> 00:35:43.840 align:middle line:84% What are the promises or the possible advantages? 00:35:43.840 --> 00:35:46.900 align:middle line:84% High parallelism, could be much more than the 10 00:35:46.900 --> 00:35:49.330 align:middle line:90% to the 12th fold loss in speed. 00:35:49.330 --> 00:35:52.612 align:middle line:90% 00:35:52.612 --> 00:35:58.300 align:middle line:84% When computer hardware and people 00:35:58.300 --> 00:36:02.710 align:middle line:84% dream of the next generation of computers, 00:36:02.710 --> 00:36:06.130 align:middle line:84% they hope to get away from the current record, which 00:36:06.130 --> 00:36:10.690 align:middle line:84% is around 10 to the 9th operations per joule 00:36:10.690 --> 00:36:12.760 align:middle line:90% for conventional computers. 00:36:12.760 --> 00:36:16.540 align:middle line:84% Maybe that's not a record but it's conventional computers. 00:36:16.540 --> 00:36:19.558 align:middle line:84% Closer to the 34 times 10 to the 19th operations per joule 00:36:19.558 --> 00:36:21.100 align:middle line:84% that you should be able to squeak out 00:36:21.100 --> 00:36:22.750 align:middle line:90% near the thermodynamic limit. 00:36:22.750 --> 00:36:26.380 align:middle line:84% And as it turns out, many DNA enzymes such as DNA polymerase 00:36:26.380 --> 00:36:28.120 align:middle line:84% are already within a factor of 10 00:36:28.120 --> 00:36:31.390 align:middle line:84% of that goal, while conventional computers are off 00:36:31.390 --> 00:36:36.360 align:middle line:90% by 10 factors of 10 or more. 00:36:36.360 --> 00:36:42.060 align:middle line:84% If one can quote, solve, or one NP-complete solve problem, 00:36:42.060 --> 00:36:42.855 align:middle line:90% you can get many. 00:36:42.855 --> 00:36:48.162 align:middle line:90% 00:36:48.162 --> 00:36:50.370 align:middle line:84% The improvements that we'll just kind of briefly talk 00:36:50.370 --> 00:36:54.960 align:middle line:84% about that keep people excited about this 00:36:54.960 --> 00:36:57.720 align:middle line:84% are that this is a natural way of talking 00:36:57.720 --> 00:36:58.770 align:middle line:90% to biological problems. 00:36:58.770 --> 00:37:01.275 align:middle line:84% If there are biological problems, you can-- 00:37:01.275 --> 00:37:04.240 align:middle line:90% 00:37:04.240 --> 00:37:07.150 align:middle line:84% It may be a smaller step to get to DNA computing, 00:37:07.150 --> 00:37:08.760 align:middle line:84% and there are faster readout methods 00:37:08.760 --> 00:37:13.140 align:middle line:84% just as there are faster and faster computational methods. 00:37:13.140 --> 00:37:15.330 align:middle line:84% And natural selection, evolution, 00:37:15.330 --> 00:37:18.390 align:middle line:84% is something that you can use on DNA computers, which so far has 00:37:18.390 --> 00:37:24.990 align:middle line:84% not been extremely powerful in conventional computers, 00:37:24.990 --> 00:37:28.210 align:middle line:84% although we'll talk about genetic algorithms shortly. 00:37:28.210 --> 00:37:31.200 align:middle line:84% So one way of getting reuse is to have 00:37:31.200 --> 00:37:33.420 align:middle line:84% a so-called sticker-based model or something 00:37:33.420 --> 00:37:36.690 align:middle line:84% where you're basically just using the hybridization 00:37:36.690 --> 00:37:40.390 align:middle line:84% properties without being destructive. 00:37:40.390 --> 00:37:42.580 align:middle line:90% And here's an example. 00:37:42.580 --> 00:37:45.270 align:middle line:84% I'm not going to walk through it too much. 00:37:45.270 --> 00:37:50.490 align:middle line:84% I should point out the all in here includes Adleman again. 00:37:50.490 --> 00:37:55.570 align:middle line:84% And I'll have one more example of his work in just a moment 00:37:55.570 --> 00:37:56.070 align:middle line:90% here. 00:37:56.070 --> 00:38:01.380 align:middle line:84% But there are examples now of work 00:38:01.380 --> 00:38:05.520 align:middle line:84% trying to consider seriously the amount, the volumes of DNA that 00:38:05.520 --> 00:38:10.710 align:middle line:84% are needed and ways of dealing with fault tolerance or error 00:38:10.710 --> 00:38:12.990 align:middle line:84% reduction algorithms where you actually 00:38:12.990 --> 00:38:17.820 align:middle line:84% go through and consciously say, OK, if we had an error here, 00:38:17.820 --> 00:38:19.900 align:middle line:90% how would we compensate for it? 00:38:19.900 --> 00:38:22.230 align:middle line:84% How would we dedicate a little more, a few more 00:38:22.230 --> 00:38:27.130 align:middle line:90% bits to take the next step? 00:38:27.130 --> 00:38:31.260 align:middle line:84% So just like in the night test problem 00:38:31.260 --> 00:38:34.320 align:middle line:84% we had a little bit before, the idea 00:38:34.320 --> 00:38:39.420 align:middle line:84% of using ANDs and ORs of Boolean variables 00:38:39.420 --> 00:38:43.650 align:middle line:84% these X's in slide 21 which can have two states 0 or 1 00:38:43.650 --> 00:38:46.380 align:middle line:84% similar to the Boolean variables that we run across from time 00:38:46.380 --> 00:38:48.630 align:middle line:90% to time in generative models. 00:38:48.630 --> 00:38:52.620 align:middle line:84% And you can have clauses, which are basically 00:38:52.620 --> 00:38:56.580 align:middle line:84% logical operations on the set of Boolean variables. 00:38:56.580 --> 00:39:01.320 align:middle line:90% We have, NOTs and ORs and ANDs. 00:39:01.320 --> 00:39:03.840 align:middle line:84% And this kind of problem is a very general problem, 00:39:03.840 --> 00:39:05.130 align:middle line:90% very interesting one. 00:39:05.130 --> 00:39:08.820 align:middle line:84% And it has been tackled just in very analogous ways 00:39:08.820 --> 00:39:12.150 align:middle line:84% to the ways we've been talking about the previous ones 00:39:12.150 --> 00:39:16.320 align:middle line:84% where you encode the graph in DNA sequences, 00:39:16.320 --> 00:39:19.080 align:middle line:84% thereby creating all the paths by hybridization or something 00:39:19.080 --> 00:39:20.110 align:middle line:90% like that. 00:39:20.110 --> 00:39:34.248 align:middle line:84% And then you read it out with PCR and solid phase. 00:39:34.248 --> 00:39:36.540 align:middle line:84% And you can say, you see here's a quote where they say, 00:39:36.540 --> 00:39:38.940 align:middle line:84% here we solve a NP-complete problem. 00:39:38.940 --> 00:39:44.520 align:middle line:84% They have indeed solved one, but they haven't really turned it 00:39:44.520 --> 00:39:47.220 align:middle line:90% into a polynomial time problem. 00:39:47.220 --> 00:39:49.500 align:middle line:90% It's simply brute force it out. 00:39:49.500 --> 00:39:51.630 align:middle line:84% And this is the most recent one, just 00:39:51.630 --> 00:39:56.190 align:middle line:84% it came out in Science again, Len Adleman on it, and now up 00:39:56.190 --> 00:39:58.440 align:middle line:84% to 20 variables in a three-set problem. 00:39:58.440 --> 00:40:01.300 align:middle line:90% 00:40:01.300 --> 00:40:03.030 align:middle line:90% So that's all about computing. 00:40:03.030 --> 00:40:06.900 align:middle line:84% It may not-- since DNA is relatively slow 00:40:06.900 --> 00:40:10.200 align:middle line:84% at computing per step, highly parallel, 00:40:10.200 --> 00:40:12.870 align:middle line:84% it may not be the best of the various steps in computing 00:40:12.870 --> 00:40:17.653 align:middle line:84% assembly, input, memory, computation, and output. 00:40:17.653 --> 00:40:19.320 align:middle line:84% So we'll explore some of the other ones, 00:40:19.320 --> 00:40:20.520 align:middle line:90% in particular assembly. 00:40:20.520 --> 00:40:23.340 align:middle line:84% To a certain extent, assembling computers is slow 00:40:23.340 --> 00:40:28.410 align:middle line:84% and so it's something where molecular assembly might 00:40:28.410 --> 00:40:29.850 align:middle line:90% have some advantages. 00:40:29.850 --> 00:40:34.500 align:middle line:84% Now this particular example, I'm going to emphasize the assembly 00:40:34.500 --> 00:40:38.520 align:middle line:84% aspect of it, but you can think of this as a way of mapping, 00:40:38.520 --> 00:40:42.240 align:middle line:84% these authors have mapped assembly 00:40:42.240 --> 00:40:45.150 align:middle line:84% of an actual two-dimensional piling 00:40:45.150 --> 00:40:52.350 align:middle line:84% onto an abstract but important and powerful computer science 00:40:52.350 --> 00:40:54.540 align:middle line:84% concept which is the general Turing machine, 00:40:54.540 --> 00:40:58.470 align:middle line:84% a machine, kind of a tape-like structure that can compute, 00:40:58.470 --> 00:41:01.020 align:middle line:84% do any kind of general computing, 00:41:01.020 --> 00:41:02.850 align:middle line:90% deterministic computing. 00:41:02.850 --> 00:41:06.990 align:middle line:84% And so they mapped a kind of a physical tiling 00:41:06.990 --> 00:41:12.480 align:middle line:84% as you might have a periodic or a periodic mosaic of tiles 00:41:12.480 --> 00:41:17.190 align:middle line:84% onto this computing machine and onto this kind 00:41:17.190 --> 00:41:21.450 align:middle line:84% of logical operation, XOR on a string of binary bits, 00:41:21.450 --> 00:41:24.780 align:middle line:84% just as we had in the previous couple of slides on the three 00:41:24.780 --> 00:41:26.490 align:middle line:90% stat problem. 00:41:26.490 --> 00:41:30.000 align:middle line:84% I want to emphasize the geometric, physical, version 00:41:30.000 --> 00:41:32.280 align:middle line:84% of it because we're trying to make a transition now 00:41:32.280 --> 00:41:36.400 align:middle line:84% in this paper which combines the DNA computing with DNA 00:41:36.400 --> 00:41:37.750 align:middle line:90% assembly. 00:41:37.750 --> 00:41:41.290 align:middle line:84% Now up it, we have three more or less equivalent 00:41:41.290 --> 00:41:43.660 align:middle line:84% ways of representing the same sequences. 00:41:43.660 --> 00:41:45.610 align:middle line:84% So these are called triple crossovers, 00:41:45.610 --> 00:41:51.460 align:middle line:84% because you can see, let's take a look at say Y2 here, 00:41:51.460 --> 00:41:53.390 align:middle line:84% right in the middle of the slide. 00:41:53.390 --> 00:41:57.820 align:middle line:84% You can see that there are these multiple crossovers where 00:41:57.820 --> 00:42:01.840 align:middle line:84% you have a kind of a recombination event 00:42:01.840 --> 00:42:04.840 align:middle line:84% where you've got two double-stranded DNA molecules 00:42:04.840 --> 00:42:06.370 align:middle line:90% that are exchanging a strand. 00:42:06.370 --> 00:42:08.770 align:middle line:84% And this is not a natural homologous recombination 00:42:08.770 --> 00:42:10.720 align:middle line:84% of N in the sense they're non homologous, 00:42:10.720 --> 00:42:13.450 align:middle line:84% and this thing is kind of trapped in this crossover. 00:42:13.450 --> 00:42:17.110 align:middle line:84% And the crossover, when you have multiple crossovers, 00:42:17.110 --> 00:42:19.630 align:middle line:84% you can make a piece of DNA that now 00:42:19.630 --> 00:42:21.250 align:middle line:90% has more than just two ends. 00:42:21.250 --> 00:42:22.720 align:middle line:84% You can have multiple sticky ends. 00:42:22.720 --> 00:42:25.510 align:middle line:84% You can have, say in this case, in the upper part, 00:42:25.510 --> 00:42:33.780 align:middle line:84% you can see four different ends with 1, 2, 3, 00:42:33.780 --> 00:42:35.730 align:middle line:90% 4 crossover strands here. 00:42:35.730 --> 00:42:40.830 align:middle line:84% And each of these, you can see on the far right, 00:42:40.830 --> 00:42:45.720 align:middle line:84% a 5 base 3 prime overhang, and a 7 base 5 prime overhang 00:42:45.720 --> 00:42:48.120 align:middle line:84% and some flush ends on the far left. 00:42:48.120 --> 00:42:51.360 align:middle line:84% And so each of these things has ability 00:42:51.360 --> 00:42:54.720 align:middle line:84% to stick to other tiling elements. 00:42:54.720 --> 00:42:58.860 align:middle line:84% And you can see that you can put together a fairly-- 00:42:58.860 --> 00:43:03.300 align:middle line:84% a two-dimensional structure, which 00:43:03.300 --> 00:43:06.120 align:middle line:90% can be as intricate as a mosaic. 00:43:06.120 --> 00:43:07.900 align:middle line:84% It does not have to repeat itself, 00:43:07.900 --> 00:43:09.900 align:middle line:84% or it can repeat itself if you want 00:43:09.900 --> 00:43:15.120 align:middle line:84% to use visual tools such as Fourier 00:43:15.120 --> 00:43:17.920 align:middle line:84% transforms to look at a repeating structure. 00:43:17.920 --> 00:43:21.180 align:middle line:84% And you can see, you can engineer in restriction sites 00:43:21.180 --> 00:43:26.400 align:middle line:84% to help you analyze the structure on a gel-based assay 00:43:26.400 --> 00:43:27.910 align:middle line:90% on the far left. 00:43:27.910 --> 00:43:30.060 align:middle line:84% We've seen enough gel-based assays tonight already, 00:43:30.060 --> 00:43:32.393 align:middle line:84% I won't belabor, we're not going to walk you through it. 00:43:32.393 --> 00:43:35.100 align:middle line:84% But you can see that there's-- even though this is not 00:43:35.100 --> 00:43:40.170 align:middle line:84% straight DNA as the previous two or three examples were, 00:43:40.170 --> 00:43:43.620 align:middle line:84% this is a much more complicated branched structure. 00:43:43.620 --> 00:43:48.150 align:middle line:84% Nevertheless, you can turn it into a linear readout 00:43:48.150 --> 00:43:50.670 align:middle line:90% with electrophoretic sizes. 00:43:50.670 --> 00:43:55.020 align:middle line:84% But you can also look at it as a truly two or three-dimensional 00:43:55.020 --> 00:43:55.950 align:middle line:90% object here. 00:43:55.950 --> 00:43:57.450 align:middle line:90% Here we use atomic-- 00:43:57.450 --> 00:44:01.830 align:middle line:84% they use atomic force microscopy where 00:44:01.830 --> 00:44:05.880 align:middle line:84% a probe with a single atom at its tip 00:44:05.880 --> 00:44:09.240 align:middle line:90% is responding to the force. 00:44:09.240 --> 00:44:14.190 align:middle line:84% That allows that as you touch an object, 00:44:14.190 --> 00:44:18.450 align:middle line:84% the feedback in the system with a scanning tunneling 00:44:18.450 --> 00:44:21.840 align:middle line:84% microscope, usually as part of the feedback, 00:44:21.840 --> 00:44:24.053 align:middle line:84% tells you that you just touched the surface 00:44:24.053 --> 00:44:25.720 align:middle line:84% and you've got to back off a little bit. 00:44:25.720 --> 00:44:29.710 align:middle line:84% And then just scan along and just profiling the surface. 00:44:29.710 --> 00:44:31.680 align:middle line:84% And so here, with two different tiling methods, 00:44:31.680 --> 00:44:36.150 align:middle line:84% this is more a repetitive rather than aperiodic tiling. 00:44:36.150 --> 00:44:38.970 align:middle line:84% You can see that these little pink protrusions, 00:44:38.970 --> 00:44:41.880 align:middle line:84% you can engineer into the tile, not just 00:44:41.880 --> 00:44:45.930 align:middle line:84% the two-dimensional stickiness, sticky tags, 00:44:45.930 --> 00:44:48.780 align:middle line:84% but a third dimension, which is a bump, which 00:44:48.780 --> 00:44:52.500 align:middle line:84% might be a stem loop as we've seen 00:44:52.500 --> 00:44:53.970 align:middle line:90% in other secondary structures. 00:44:53.970 --> 00:44:55.630 align:middle line:84% There's engineering into this DNA. 00:44:55.630 --> 00:44:57.720 align:middle line:84% So now that these bumps will stick up 00:44:57.720 --> 00:45:00.580 align:middle line:84% and be easy targets for the atomic force microscope. 00:45:00.580 --> 00:45:05.340 align:middle line:84% And here you have a bump every second tile, 00:45:05.340 --> 00:45:07.200 align:middle line:90% and that's on the left. 00:45:07.200 --> 00:45:09.240 align:middle line:84% And on the right of slide 27, you 00:45:09.240 --> 00:45:11.010 align:middle line:84% have a more complicated tiling where 00:45:11.010 --> 00:45:13.500 align:middle line:84% you have four different types of tiles 00:45:13.500 --> 00:45:16.560 align:middle line:90% and a bump every fourth one. 00:45:16.560 --> 00:45:22.320 align:middle line:84% And so you expect, you can calculate from the Watson-Crick 00:45:22.320 --> 00:45:25.080 align:middle line:84% model for DNA, or more advanced models of DNA, 00:45:25.080 --> 00:45:30.870 align:middle line:84% even though this is a lattice of brain structures, 00:45:30.870 --> 00:45:33.450 align:middle line:84% you can calculate, it should be about 33 nanometers 00:45:33.450 --> 00:45:34.530 align:middle line:90% between the bumps. 00:45:34.530 --> 00:45:35.700 align:middle line:90% And that's what's observed. 00:45:35.700 --> 00:45:38.370 align:middle line:84% And 65 nanometers is calculated and observed. 00:45:38.370 --> 00:45:40.620 align:middle line:84% You can see the bigger lattice spacing 00:45:40.620 --> 00:45:45.390 align:middle line:84% in these admittedly somewhat fuzzy atomic force micrographs. 00:45:45.390 --> 00:45:47.460 align:middle line:84% But you can see, you get something, 00:45:47.460 --> 00:45:51.300 align:middle line:84% an experimental confirmation of the two-dimensional structures 00:45:51.300 --> 00:45:52.420 align:middle line:90% here. 00:45:52.420 --> 00:45:58.250 align:middle line:84% Now this is self-assembly nanofabrication. 00:45:58.250 --> 00:46:01.590 align:middle line:84% And to some extent, it is inspired by 00:46:01.590 --> 00:46:05.910 align:middle line:84% and can be combined with microfabrication. 00:46:05.910 --> 00:46:08.490 align:middle line:84% This is something where you basically use optics, 00:46:08.490 --> 00:46:12.870 align:middle line:84% you go to the limit of current optical manufacturing 00:46:12.870 --> 00:46:17.130 align:middle line:84% as a microfabrication where it's typically hard to get below 00:46:17.130 --> 00:46:21.120 align:middle line:84% say 100 nanometers or so in feature size. 00:46:21.120 --> 00:46:23.400 align:middle line:90% Here you can see this is-- 00:46:23.400 --> 00:46:26.460 align:middle line:84% and this is the microfabrication used 00:46:26.460 --> 00:46:29.370 align:middle line:90% to make your computer chips. 00:46:29.370 --> 00:46:32.370 align:middle line:84% But it's, in this case, it's used 00:46:32.370 --> 00:46:34.500 align:middle line:84% to actually make moving parts, parts that move 00:46:34.500 --> 00:46:35.560 align:middle line:90% relative to one another. 00:46:35.560 --> 00:46:44.170 align:middle line:84% And that motion actually has useful applications. 00:46:44.170 --> 00:46:47.280 align:middle line:84% The first such useful application that I'm aware 00:46:47.280 --> 00:46:50.370 align:middle line:84% is putting these things into air bag sensors. 00:46:50.370 --> 00:46:54.150 align:middle line:84% And the idea is that when you're driving your large automobile 00:46:54.150 --> 00:46:57.660 align:middle line:84% and run into a even larger object, 00:46:57.660 --> 00:47:02.230 align:middle line:84% you suddenly decelerate, either by brakes or some other method. 00:47:02.230 --> 00:47:08.550 align:middle line:84% And when you do, this little bitty device, 00:47:08.550 --> 00:47:11.850 align:middle line:84% a sensor inside your-- somewhere in your car, 00:47:11.850 --> 00:47:16.410 align:middle line:84% will shift one of its parts by at least 0.2 angstroms, 00:47:16.410 --> 00:47:19.710 align:middle line:84% meaning a tenth of an atomic diameter. 00:47:19.710 --> 00:47:21.270 align:middle line:84% That doesn't seem like very much. 00:47:21.270 --> 00:47:21.870 align:middle line:90% And it isn't. 00:47:21.870 --> 00:47:27.720 align:middle line:84% It only causes 100 femtofarads, that means 10 to the -13 00:47:27.720 --> 00:47:29.430 align:middle line:90% farad capacitance change. 00:47:29.430 --> 00:47:34.290 align:middle line:84% But that's quite enough to signal 00:47:34.290 --> 00:47:36.960 align:middle line:84% that a collision has occurred or will occur 00:47:36.960 --> 00:47:41.320 align:middle line:84% and with a very low false positive rate, 00:47:41.320 --> 00:47:43.390 align:middle line:84% those of you who have driven large automobiles 00:47:43.390 --> 00:47:47.500 align:middle line:84% know how infrequently the airbag opens up accidentally. 00:47:47.500 --> 00:47:50.110 align:middle line:84% But when it does deflect by 0.2 angstroms 00:47:50.110 --> 00:47:52.030 align:middle line:90% then it does open up the airbag. 00:47:52.030 --> 00:47:55.270 align:middle line:84% OK, so this is a payoff of microfabrication. 00:47:55.270 --> 00:47:58.270 align:middle line:84% But now we want to combine the nanosystems 00:47:58.270 --> 00:48:01.480 align:middle line:84% that we saw in the DNA computers and in the tiling 00:48:01.480 --> 00:48:03.160 align:middle line:90% with microfabrication. 00:48:03.160 --> 00:48:06.580 align:middle line:84% And I picked this as just one of the very few examples 00:48:06.580 --> 00:48:09.430 align:middle line:84% where microfab meets nanofabrication. 00:48:09.430 --> 00:48:12.700 align:middle line:84% And we'll call it a nano-electromechanical system. 00:48:12.700 --> 00:48:17.020 align:middle line:84% And here, so you've got the microfabrication 00:48:17.020 --> 00:48:20.380 align:middle line:84% of both the posts upon which these things stand, 00:48:20.380 --> 00:48:25.090 align:middle line:84% which is these nickel columns of 80 nanometers, 00:48:25.090 --> 00:48:33.380 align:middle line:84% and the little bars, metal bars, which can be as a micron range. 00:48:33.380 --> 00:48:36.400 align:middle line:84% And you can see them visualized on the left hand photograph 00:48:36.400 --> 00:48:39.640 align:middle line:84% where you have these bars at regular spacings, 00:48:39.640 --> 00:48:44.860 align:middle line:84% and if you look at this publication or the webs that 00:48:44.860 --> 00:48:47.740 align:middle line:84% go along with it, these little bars will spin around. 00:48:47.740 --> 00:48:52.000 align:middle line:84% And what they're spinning on is not a microfabricated motor, 00:48:52.000 --> 00:48:55.990 align:middle line:84% but it is a nano biotech motor, which and actually 00:48:55.990 --> 00:48:59.890 align:middle line:84% it's a protein that most people didn't think of as a motor when 00:48:59.890 --> 00:49:01.270 align:middle line:90% it was first discovered. 00:49:01.270 --> 00:49:06.370 align:middle line:84% It is the protein present in almost all organisms 00:49:06.370 --> 00:49:08.830 align:middle line:84% that is responsible for ATP generation. 00:49:08.830 --> 00:49:12.520 align:middle line:84% Usually, you think of this as making ATP for motors to use, 00:49:12.520 --> 00:49:16.600 align:middle line:84% but this actually, since it is capable of rotary motion, 00:49:16.600 --> 00:49:22.150 align:middle line:84% does move this 1 micron bar around at the rate 00:49:22.150 --> 00:49:28.540 align:middle line:84% that you would expect for the nano-machine 00:49:28.540 --> 00:49:29.695 align:middle line:90% to be generating torque. 00:49:29.695 --> 00:49:32.620 align:middle line:90% 00:49:32.620 --> 00:49:34.870 align:middle line:84% So we're now, we've talked about assembly. 00:49:34.870 --> 00:49:37.470 align:middle line:84% That's an example of an output device, what 00:49:37.470 --> 00:49:39.460 align:middle line:84% sort of input devices we have that 00:49:39.460 --> 00:49:43.180 align:middle line:84% will work at the single molecule level. 00:49:43.180 --> 00:49:46.060 align:middle line:84% Here is, there are many examples. 00:49:46.060 --> 00:49:51.310 align:middle line:84% We've mentioned a few of them in the sequencing, 00:49:51.310 --> 00:49:53.470 align:middle line:84% genotyping lecture where we were talking 00:49:53.470 --> 00:49:56.200 align:middle line:90% about single fluorophores. 00:49:56.200 --> 00:50:02.560 align:middle line:84% Here, you can use another aspect of biology, 00:50:02.560 --> 00:50:06.250 align:middle line:84% which is the self-assembly of membranes to make a very, very 00:50:06.250 --> 00:50:10.960 align:middle line:84% tight, low conductance seal which is only on the order of 2 00:50:10.960 --> 00:50:15.460 align:middle line:84% nanometers thick, but it's enough to make a gigaohm seal, 00:50:15.460 --> 00:50:17.020 align:middle line:90% multi gigaohm seal. 00:50:17.020 --> 00:50:18.970 align:middle line:84% And then you poke a little hole in it 00:50:18.970 --> 00:50:22.210 align:middle line:84% with a single molecule of a protein. 00:50:22.210 --> 00:50:26.650 align:middle line:84% And there are growing ways to do this on inorganic substrates 00:50:26.650 --> 00:50:27.890 align:middle line:90% as well. 00:50:27.890 --> 00:50:32.350 align:middle line:84% So when you have a single protein pore which itself might 00:50:32.350 --> 00:50:35.410 align:middle line:84% be a 1 nanometer opening, it will 00:50:35.410 --> 00:50:37.360 align:middle line:84% allow in the presence of electric field, 00:50:37.360 --> 00:50:39.910 align:middle line:84% indicated by these negative and positive charges 00:50:39.910 --> 00:50:43.900 align:middle line:84% here, yellow negative and positive ions to go through 00:50:43.900 --> 00:50:45.980 align:middle line:90% like sodium chloride. 00:50:45.980 --> 00:50:53.350 align:middle line:84% And they will go through it about up to a million ions 00:50:53.350 --> 00:50:55.790 align:middle line:90% per second, easily. 00:50:55.790 --> 00:50:58.900 align:middle line:84% And when you have a larger molecule, 00:50:58.900 --> 00:51:02.770 align:middle line:84% that's say, a polyanion in the electric field, 00:51:02.770 --> 00:51:04.960 align:middle line:84% it will slowly migrate through this pore. 00:51:04.960 --> 00:51:08.110 align:middle line:84% And while it does so, it blocks the rapid movement 00:51:08.110 --> 00:51:11.830 align:middle line:90% of the smaller ions like sodium. 00:51:11.830 --> 00:51:15.220 align:middle line:90% And you can record, the-- 00:51:15.220 --> 00:51:18.100 align:middle line:84% it doesn't necessarily completely block the channel. 00:51:18.100 --> 00:51:21.370 align:middle line:84% You can record the rate at which sodium will go through 00:51:21.370 --> 00:51:23.620 align:middle line:84% and how it's influenced by the composition 00:51:23.620 --> 00:51:26.750 align:middle line:90% of the polymer going through. 00:51:26.750 --> 00:51:31.630 align:middle line:84% And so here's an example of a bacterial protein. 00:51:31.630 --> 00:51:36.040 align:middle line:84% This is [? Miller ?] et. all, referenced down below. 00:51:36.040 --> 00:51:42.130 align:middle line:84% A bacterial toxin, actually from staph, staphylococcus, 00:51:42.130 --> 00:51:46.900 align:middle line:84% whose goal in life is to kill other organisms, 00:51:46.900 --> 00:51:50.980 align:middle line:84% it's not to provide a handy conduit for RNA 00:51:50.980 --> 00:51:52.780 align:middle line:90% to go through a cell. 00:51:52.780 --> 00:51:55.780 align:middle line:84% But nevertheless in this experiment, when it does, 00:51:55.780 --> 00:51:58.000 align:middle line:84% when a nucleic acid does go through, 00:51:58.000 --> 00:52:01.240 align:middle line:84% it blocks the little red water molecules 00:52:01.240 --> 00:52:04.180 align:middle line:84% and similar sized ions are blocked. 00:52:04.180 --> 00:52:06.790 align:middle line:84% And they're blocked in a way, which 00:52:06.790 --> 00:52:09.760 align:middle line:84% is sensitive to not only the molecule, 00:52:09.760 --> 00:52:11.300 align:middle line:90% but parts of the molecule. 00:52:11.300 --> 00:52:13.600 align:middle line:84% So you can see here, you've got a molecule 00:52:13.600 --> 00:52:18.550 align:middle line:84% with a oligo(A) part and an oligo(C) part. 00:52:18.550 --> 00:52:21.190 align:middle line:84% And you can actually discriminate between these, 00:52:21.190 --> 00:52:25.360 align:middle line:84% both in terms of the rate at which they go through, 00:52:25.360 --> 00:52:27.880 align:middle line:84% each of the parts goes through, and the conductance. 00:52:27.880 --> 00:52:31.030 align:middle line:84% So if you look down in the lower right hand part, 00:52:31.030 --> 00:52:34.690 align:middle line:84% you'll see a 5 picoampere here to the -12 ampere, 00:52:34.690 --> 00:52:37.958 align:middle line:84% 20 picoampere and 120 picoampere levels 00:52:37.958 --> 00:52:39.250 align:middle line:90% for these individual molecules. 00:52:39.250 --> 00:52:45.400 align:middle line:84% And each of these spikes is first the 830 half, 00:52:45.400 --> 00:52:47.830 align:middle line:84% and then the C-70 half going through. 00:52:47.830 --> 00:52:55.150 align:middle line:84% And you can see that the two different conductance levels 00:52:55.150 --> 00:52:56.770 align:middle line:84% that you get, reproducibly go, it's 00:52:56.770 --> 00:53:00.400 align:middle line:84% going through a typically in one direction, first the A, then 00:53:00.400 --> 00:53:04.370 align:middle line:84% the C, and different conductance levels, different rates. 00:53:04.370 --> 00:53:08.230 align:middle line:84% And then 125 amperes is in between molecules where you're 00:53:08.230 --> 00:53:11.590 align:middle line:84% getting the full conductance capability, lots of sodium 00:53:11.590 --> 00:53:13.480 align:middle line:90% is going through. 00:53:13.480 --> 00:53:20.780 align:middle line:84% And just like with other methods that we've seen before, 00:53:20.780 --> 00:53:24.260 align:middle line:84% the use of two dimensions helps get you 00:53:24.260 --> 00:53:26.330 align:middle line:90% better statistical resolution. 00:53:26.330 --> 00:53:31.670 align:middle line:84% Here the two dimensions are the conductance and the time, time, 00:53:31.670 --> 00:53:33.470 align:middle line:84% and the vertical axis and conductance 00:53:33.470 --> 00:53:35.040 align:middle line:90% on the horizontal axis. 00:53:35.040 --> 00:53:39.050 align:middle line:84% And you can see how you can discriminate different types 00:53:39.050 --> 00:53:40.850 align:middle line:90% of polymers by this method. 00:53:40.850 --> 00:53:42.770 align:middle line:84% One molecule of time, each of these dots 00:53:42.770 --> 00:53:45.800 align:middle line:84% represents a single molecular event. 00:53:45.800 --> 00:53:51.540 align:middle line:90% And so we'll take a short break. 00:53:51.540 --> 00:53:52.950 align:middle line:84% And then when we come back, we'll 00:53:52.950 --> 00:53:56.490 align:middle line:84% talk about not molecular computing, 00:53:56.490 --> 00:54:01.800 align:middle line:84% but designing cellular computers and revisit 00:54:01.800 --> 00:54:03.900 align:middle line:90% some of these same themes. 00:54:03.900 --> 00:54:05.450 align:middle line:90% Thanks. 00:54:05.450 --> 00:54:06.000 align:middle line:90%