Tuesday, May 12, 2009

Traveling Pulse Amorphous Computer

After a few meetings with John, Nam, Xi, Edward, and Andy in the last few weeks I think I have a plausible molecular gate model that can make some interesting amorphous computations. Specifically, I've been trying to make the "Mexican Wave" -- an amorphous pulse wave.

A variable "A" is encoded by the log ratio of the concentration of two RNA species: a sense strand called "A+" and its anti-sense strand called "A-".

(Image updated 21 May -- Thanks for Erik for pointing out I left off the promoter completion domain)

Gates are molecular beacons that use promoter disruption to squelch the generation of some output strand. For now, all gates are unary operators. The RNAs can be displaced off the beacons by toe-hold mediated strand displacement. This design is basically Winfree lab's transcriptional circuits but where the gate is a hairpin DNA molecular beacon and where variables are encoded by log ratio of sense and anti-sense instead of as a proportionality to concentration of an ssRNA.

(Note I updated this diagram to change the naming convention on this 17 May 2009. Again on 21 May thanks for Erik for noticing I left off the promoter completion domain.)

Gates are modeled as having hyperbolic production curves and can be built according to one of four choices of sense and anti-sense sequence on the inputs and outputs. As a matter of convention, the sense strand is labeled "+" relative to the ssRNAs, not relative to the DNA because the concentration of the RNAs is the variable of interest in these systems.

To explore the model, I created a circuit that I hoped would make an amorphous pulse propagating wave. Below, I switch into electrical analogy which I do for my own sanity. The charge across capacitors represent the two variables which I call "standing" and "tired" by analogy with the Mexican Wave. The gates are labeled like "i+o+" meaning "when input is + the output will be -". (I've changed around the naming convention several times, this update is as of 17 May) The gates without inputs are under constitutive promotion and are labeld only by what they output. All nodes are pulled down by the same RNAases represented here as resistors to ground from each capacitor. The two variables are assumed to diffuse at equal rates. The only changeable parameter is assumed to be the concentrations of the gates.

(Thanks to Xi and John for help reworking this diagram. I updated it on 19 May.)

This circuit can be thought of like this. "Standing" and "tired" are constantly being pulled low by the gates 1 & 2 against the action of the resistors. If the rest of the gates weren't there, this would ensure the system will be "not standing" and "not tired". Gate 3 puts feedback on "standing" thus a small threshold level of "standing" will generate more until it saturates in steady-state against the resistor. Gate 4 increases "tired" if "standing". Gate 5 is in high concentration relative to the other gates and can thus overpower the "standing" variable when "tired".

Here are the 1D amorphous results. The two plots are "standing" (left) and "tired" (right). The X axis of each is space (cyclical coordinates). The Y axis from bottom to top is increasing time. Blue represents a high ratio of - to + strands. Red represents a high ratio of + to - strands. Black represents an even ratio. At time zero, a pulse of + is added to the "standing" variable representing a manual pipetteing operation at some point in space. As time passes (bottom to top) the pulse propagates in both directions at a constant rate until the two pulses hit each other and then stop.

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