Introducing Particle Structure and a Modified Reaction Generation Algorithm.
This work has been inspired partly in discussions with Kepa Ruiz-Mirazo and others at the Autonomy workshop at ALife X, so thanks to those chaps. The following pages describe work in progress that attempts to introduce particle structure to the random chemistries that were developed here. These random chemistries demonstrated to be incapable of continued increase in light absorption and heat production over time.
Methods for simulating lipid water behaviours, flows, semipermeability etc will be necessary. Some interesting techniques have been tried in 'amorphous computing'. See references, especially stuff on Grey-Scott type models of self-replicating spots. I would love to be able to model such systems fast, and with a generative chemistry.
Methods for modeling particle structure are required. One technique used in chemoinformatics is chemical fingerprinting in which chemical groups are represented as binary bits, and the molecule is a string. See NCAF meeting notes and speaker notes.
Research is being conducted into the relationship between entropy, thermodynamics and natural selection, e.g. Eric Smith's work. This may be helpful in determining how to treat the reactor and understanding what to measure about the reactor!
Visualization techniques for visualizing a very diverse chemical network topology will be required. See NCAF contacts for advice on this problem once network data is generated!
References
1. Amorphous computing minimal discrete models.
2. Reaction-Diffusion type equations can be used to model the evolution of metabolism on 2D surfaces, e.g.
- Gray Scott Model. Mass conserving chemical reactions on each grid position, with diffusion between grids. This type of model has been used by Hedgehog etc to do models of hypercycles in space. Also, Andreea has been interested in this stuff for PACE. Kaneko has also worked on this spot replication. This type of model may be a good place to address my ideas about syncytia, and group selection acting on metabolism in such systems.
- See Munteanu and Sole's paper on self-replicating spots here.
- Self-replicating spots have been produced in experimental systems. See the nature paper here. and here.
- In fact there is a huge amount of work on these self-replicating spots. Why hadn't I looked at them earlier! See here.
- The crucial thing missing from the above work is to align it to an interesting model of generative chemistry.
- The role of information in such systems is discussed in the paper by Lindgren and Eriksson here.
- Simulation techniques webpage.
Maximization of the Steady-State Light Absorbing Rate of a Chemical Network by Using a GA to Evolve Catalysts.
Generate a chemical network according to a random process, e.g. initialize a system with a and b molecules. Give the inital pair of molecules a certain energy Ea and Eb. Generate new reactions by choosing a pair of molecules (randomly or according to some function) and making another pair of molecules which may contain a null molecule, i.e. ligation. Also, one reacting molecule might also be null, i.e. cleavage. Each new reaction may be an irriversible light absorbing reaction with probability P. Otherwise it is a heat releasing reversible reaction, with K determined by the difference in free energy between reactants and products. Let the initial rates of these reactions be determined randomly. The generative algorithm may be dynamic or non-dynamic, i.e. the whole reaction network may be generated before any reactions are simulated, or the generation of the reaction network may depend on the concentrations obtained during simulation. There should be a function which generates this network according to some parameters and returns the network object.
This will result in a chemical network which if we allow it to run for a while should settle down into a steady state rate of light absorption. Assume this is the only set of chemical reactions that is possible, and that it does contain plenty of potential re-cycling loops, some of which are even autocatalytic. The whole network can be generated from a and b molecules, but it may not be the case that the whole network can be generated from other subsets of molecules, e.g. aab molecules, for example if there is no reaction capable of seperating ab into a and b.
Then take the network specification and evolve the rates of catalysis of each non-light absorbing step. Assume that catalytic efficiency can range from 0 (i.e. an inhibitor of a reaction), to 1000, i.e. allowing the reaction to reach equilibrium very rapidly. Assume that there is absolutely no constraint on the capacity for catalysis, and that ANY reaction network can be evolved, within the constraints of the initially randomly generated set of reactions. We ask, can a GA increase the steady-state light absorbing rate of the randomly generated chemical network, by evolving a particular pattern of catalytic properties? The GA works as follows. 100 instances of the reaction network are produced, each with a different set of catalytic rates. The ones with the highest steady-state light absorbing capacity are selected for in pair-wise tournament selection. Mutation of catalytic rates by a multiplicative factor is carried, out, i.e. the rate is either doubled or halved, within the range 0 - 1000.
Is it possible for the GA to straighforwardly evolve maximal re-cycling networks from the original network? What is the structure of the maximal re-cycling network, e.g. are the re-cycling loops very short? Presumably this would be the easiest solution, just find the shortest possible re-cycling loop from light absorbing molecule product back to light absorbing molecule, and send all other depleting reaction rates to zero.
Next we ask whether it is possible to maximize the recycling capacity of the network in a more self-organised manner that does not depend on natural selection! For example, assume that there is a patchwork of abitoic catalysts in the environment that are capable of the same sort of rate control as obtained by the GA! In fact we could take the catalytic configuration that we had evolved with the GA and implant this in some patches so that we guarantee there IS the right configuration of catalysts to maximize re-cycling rates (at least to the extent that the GA did so). We ask, what sorts of self-organizing process might allow a greater number of patches to use these catalysts than initially in existence? Presumably, the chemical system should be able to 'cover' and 'uncover' catalysts in the system, i.e. assume that the entire abiotic range of catalysts COULD be 'uncovered' in any one square, and that catalysts can be transported between squares associated with certain chemicals. Under what conditions would the system be able to increase the total flux of the surface to the same extent as the GA has maximized the flux? WHY would there be a tendency for re-cycling systems to bootstrap themselves to become better at re-cycling?
Also, we may wish to test to what extent the chemical network by EXCLUDING species could maximize flux. The GA, instead of being given the capacity to evolve catalysts, is given the capacity to alter the effective concentration between particles, e.g. a particles may be reduced in effective concentration compared to b particles. A matrix of particle types vs. particle types describes the alterations to effective concentrations that are possible. This simulates the effect of being able to obtain phase seperation between particle subsets.
We wish to understand whether phase seperation can self-organize in such a chemical network without having to use a GA. The GA has shown that if phase seperation were possible then re-cycling capacity would increase. What self-organizing processes are able to mediate this phase seperation? For example, if we randomly assign repulsions and attractions to species in proportion to the matrix calculated by the GA, then does phase seperation result that has the same effect on light absorption rate as in the non-spatial case!?
Some recycling systems have the capacity to recursively generate functional constraints. These are the systems that will increase their capacity for re-cycling. What allows a system to recursively generate functional constraints? Some sort of heredity is necessary. In the GA systems we have been able to alter the properties of a metabolic network by artificial means, e.g. changing catalytic rates of changing pairwise activities. In practice, this is typically thought to require sequence encoded catalytic information and the capacity for specifying the mutual repulsiveness of particles! We cannot rightly assume that these are self-organizing properties of a randomly generated chemical network present on a surface.
Results
The following evolutionary run shows a chemical network's catalytic rates being evolved in order to maximize the 'steady state' light absorption rate after 10000 Eular integration steps.
The following network of 100 reactions was produced randomly using the software downloadable here.
The metabolic network above is drawn with WilmaScope downloadable freely here. The size of the balls represent the concentration of species at steady state before any evolution of catalytic parameters. Thir color represents their free energy. Thick blue arrows with green tips represent light absorbing reactions. Fine edges represent heat-producing reactions. Note the many terminal species that are present at negligable or zero concentration.
The graph below shows the "steady-state" "FLUX|" after 10000 iterations of the simulation, and near the begining of the evolutionary run.
You notice that there is no light absorbing edge visible. Large flux passes through one reaction. Most reactions have little flux through them. The "flux" of a reaction defined here refers to the sum of the rates of forward and backward propensities through a reaction, not the difference of these propeneties. The later is investigated later, and is a means of detecting real cyclic flux.
The picture above is the network after evolution. Again there are NO light absorbing reactions with high flux. This is odd since we were selecting the networks on this basis. What is noticable is that two of the three starting chemicals ("cccccccc" and "aaaaaaaa") have very high concentrations at steady state suggesting they have been excluded from reactions. A more careful examination of the light absorbing fluxes will be needed in order to understand how the network has become adapted to maximize resting light absorption rate. It would be useful to make all the light absorbing flux arrows proportionally thicker and also to display them seperately. Also, it would be useful to visualize ONLY the difference between forward and backward flux in a reaction, to identify flux cycles.
Two other similar evolutionary runs are shown below. One in which 10% of reactions are light absorbing, and another (like the one above) in which 20% of reactions are light absorbing.
10% Light absorbing reactions.
Above: Fitness over generations.
Above: Initial chemical network.
Above: Final Evolved Fluxes. Not the motif below, of a light absorbing reaction without any re-cycling of its products. The flux through the light absorbing reaction appears to have been delayed until the fitness assessment at the end of the run. So there appears to have been some cheating, since it does not seem at first glance that this ihgh flux can really be maintained!
20% Light Absorbing Reactions.
Compared to the above two chemical networks, this network massively increased its steady state light absorption rate to apx 15000.
The initial network is shown above, and the fluxes and chemical concentrations after evolution are shown below.
It is possible (likely even) that the light absorbing flux is HIDDEN under the large heat producing flux. Perhaps even the SAME reaction is involved in heat production and light absorption. It is necessary to be able to manipulate the edges in this diagram to be able to ensure that fluxes do not get hidden within other flux edges! If this is not occuring, then how the light absorbing flux is being increased is a mystery! Further analysis of this network is required NOW.
Results 1: Statistics of 'A only' Networks.
The main finding so far is that if a network is initialized with many types of atom, using the above generative mechanism it is generally the case that thermodynamicaly feasible cycles are rare, i.e. the network although connected, does not contain sufficient underlying phenotypic variation for the GA to exploit catalytically. Introducing rearrangement reactions transforms the chemical network into a chemical network that effectively consists of only one type of atom, e.g. an 'a only' network, since all species containing the same composition of atom can effectively be considered as the same entity. In this case, many randomly generated networks will contain cycles. The statistics of cycles in 'a only' or 'single atom' or 'maximal rearrangement' chemical networks can be empirically determined. A random 'A only' network is generated with random catalytic rates and run to equalibrium. An algorithm detects the maximally light absorbing reaction at steady state and then determines all the cycles that are responsible for maintaining the flux through this reaction at steady state. We examine the statistics of the cycle lengths and fluxes through these cycles as a function of their length for a set of randomly generated 'a only' networks.
[Enter results here.]
Results 2: Amorphous Grid Computing as a Means to Simulate Surface Chemistry.
The simulation of a large surface consisting of patches where each patch runs an ODE for one time step requiring the iteration through a loop of Eular steps is prohibitively slow for large chemical networks. Computational constraints also arise due to the need to simulate complex processes of interaction between patches, e.g. diffusion models that depend on the composition of patches in complex ways that might simulate phase seperation, membrane formation etc... Therefore it is desirable to develop the following software platform. A program is required that can be downloaded by many users (possibly a Java program). This program allows me to upload reaction-diffusion rules to that persons computer which I can then run and which can interact with other copies of the program. Each copy of the program on a persons computer simulates a patch on a surface. I need to be able to modify the details of what each persons computer is running, without them having to download a new piece of software. It is hoped that 1000's of computers will run this program, so allowing a large heterogenous surface to be simulated.
Modeling Diffusion and Other Surface Chemical Dynamics
The following code is used to test the self-organizing properties of various algorithms that simulate chemical motion on surfaces. Diffusion, selective permeability, amphipathicity etc... are all desirable features that we wish to be able to model.
The following code for Cocoa and XCode in C++ can be downloaded here. This allows you to visualize the chemical network generated above on a surface, subject to some very simple "finite element" diffusion rules. The files containing the full and simplified versions of the chemical network can also be downloaded. You need to set the directory to point to these files in your hard disk. The directory name goes in the world.cpp file in the world constructor. You can then change the chemical network description file and so simulate any network subject to chemical diffusion that you like. This is a similar program to that used for surface ecosystem 'evolution'.
What interaction rules in a spatial system are capable of establishing a wide variety of patterns, especially membranes with semi-permeability.
Interaction Rules
1. Diffusion with distinct between-species diffusion rates.
1. A matrix Dij defines the extent of repulsion between a species i and species j on a grid square. The higher the value, the more rapidly those two species leave the square that they occupy. The total rate at which a species i leaves its square is the sum of Dij over all j. Consider the following examples. Imagine there exist two species A and B that are completely unreactive. They have the following Dij matrix...
| A | B | |
| A | 0 | 1 |
| B | 1 | 0 |
i.e. A and B are cross-repelling, but are not self-repelling.
2. Calculation of Chemical Potential of a Species Using a Moore Naighbourhood. Movement is determined by the potential gradient.
The same potential matrix is used as above, except here the potential for diffusion of a species on a central patch is determined by applying the above sum across the Moore neighbourhood of the cell.
i. - Diffusion of species i from patch a to b is in proportion to the potential of species i on patch a, multiplied by the concentration of species i on patch a.
ii. - Diffusion of species i from patch a to b is proportional to dP/(e^dP - 1), where dP is the potential difference between i on a and b. Some examples of this system for two unreactive particles a and b are shown below. This is a deterministic version of the Lattice Gas method used by Naoki Ono et al.
Results from model 2 ii are shown in the next page.