A key question about SimSoup networks (and 'proto-metabolic' networks) is their stability. SimSoup model output so far has shown that a network can have stable and meta-stable states. This conclusion has been based on observation of plots of the numbers of Molecules of particular types, and rates of Interactions of particular types. This is useful, but a more global measure of the overall behaviour of a network is needed.
One approach to this is to establish a measure of the difference between network states at different times. The latest version of SimSoup (to be released shortly) includes such a measure, the Manhattan Distance.
As suggested by its name, Manhattan Distance is the distance between two points on a grid, where the distance must be travelled along the grid, and not diagonally. For example, if we have a two dimensional grid with each point in the grid identified by a pair of co-ordinates (x,y), the Manhattan Distance between the points (2,6) and (5,3) is:-
Manhattan Distance can be measured between two points in any Euclidean space, regardless of the dimensionality of the space. That is, it works just as well for a space with 200 dimensions as it does for a space with two dimensions.
In the context of SimSoup, we can define the state of the network in terms of the numbers of Molecules of each Molecule Type. We then envisage a space with one dimension for each Molecule Type, so that a particular point in this space defines a network state. This is the idea of Compositional Space as used by Doron Lancet's group at the Weizmann Institute (for example, see The Molecular Roots of Compositional Inheritance).
The similarity of two points in Compositional Space is sometimes measured in terms of the scalar product of (normalised) vectors from the origin towards each of the two points. I prefer to use Manhattan Distance, because this is directly related to the number of differences in molecular composition.
The plot above shows the Manhattan Distance between the compositional makeup of a SimSoup network at different times. The network setup and initial conditions are the same as for the earlier news item here on 23 October (see below).
The most straightforward way to read the plot is horizontally from left to right. The point at the far right of each 'row' corresponds to the compositional makeup of the network at a point in time (the 'Base Time'). Points to the left correspond to the compositional makeup at earlier times, with the darkness of each point indicating the Manhattan Distance from the compositional makeup at the Base Time. A light coloured point therefore indicates a time at which the compositional makeup was close to that at the (later) Base Time.
The following observations can be made:-
The plots below show that a SimSoup network has states that are persistent over long periods, but that there can be spontaneous transitions between these states.
The Reactor starts in a state in which the total rate of interactions (not shown) is low. At time 50,000, seven Molecules of random type are added Reactor takes on much more active behaviour. There are no further external perturbations after this (other than the normal inflow and outflow). Everything that happens after time 50,000 is the result of the stochastic application of the reaction rules.
The first plot shows that the number or Molecules of a particular type can be relatively stable over long periods, and that there can then be a transition to another network state in which the number of Molecules of the type is relatively stable, but in a different region. For example, there is a transition at about time 650,000 in which the number of Molecules of Type 169 falls from a stable value of about 4000 to a lower value of about 3000. Other Molecule Types show similar meta-stable behaviour.
The second and third plots show the rates of selected Interaction Types. It can be seen that there are important transitions at times (approx.) 500,000, 650,000 and 820,000.
The enhanced statistics output included in SimSoup yesterday have already produced an interesting result. The plot shown below was produced by a SimSoup run with a chemical network including 200 Molecule Types and 254 Catalytic Transformations, each of which is a pair of Interaction Types (a Compound Interaction) of the following form:-
In this Compound Interaction, X is a catalyst, and I is an Intermediate,
The chemical network is given a constant food supply of three Molecules (of each of three fixed types) at each timestep. There is also a slow leakage from the Reactor.
The Reactor starts in a state in which the total rate of interactions (not shown) is low. At time 50,000, seven Molecules of random type are added. The result is that the network immediately enters a high overall interaction rate state. The plot shows the change in the interaction rate for three selected Interaction Types. It can be seen that at time 50,000 there is a drop in the rate of Interaction Type 105. Interaction Types 114 and 160, which previouly did not happen at all, start occurring at this point.
The new state persists until just after time 600,000. At that point the Reactor enters a new state; the plots show a substantial decrease in the rate of Interaction Type 105, and a corresponding increase in the rates of Interactiion Types 114 and 160.
This new state is not the result of an externally input perturbation. It must have been triggered by a specific condition occurriing in the Reactor. Perhaps this was related to the drop in the rate of Interaction Type 160. The new state persists over a long period (up to and beyond time 1,600,000), although it is interesting to note that there is a substantial variation from 'norm' just before time 1,200,000.
This first run of SimSoup using its enhanced statistics output shows that a SimSoup network can have multiple stable (or meta-stable) high metabolic rate states.
Development work is continuing on SimSoup. The main focus at present is on features required to enable more statistics to be produced by the system to support Artificial Chemistry experiments. Enhancements to the development version of SimSoup since Version 0.2 was released include:-
Current plans for further development include:-
This is to announce the release of version 0.2 of the SimSoup Artificial Chemistry simulator. Screenshots are available here.
The features in SimSoup version 0.2 include:-
I hope you enjoy the program, and will welcome any feedback at the email address mentioned on my Home page (see below).