So I've been working and playing and studying as usual this semester. My course in nonlinear dynamics is going swimmingly; partly because I've gone through most of the book we're working out of this semester. :) My research is gaining steam on both fronts - evolution and neural. Minecraft has taken over my nightly activities, and on occasion, it's taken over a day or two. :\
The first part of the evolution model will probably focus on cluster (species) activity on even fitness landscapes (all organisms produce the same number of offspring). This is important in addressing two questions. The first deals with the problem of whether species really form when there is no landscape to determine what is most fit for the organisms. Generally, natural selection is considered to take place when the environment organisms live in, along with their natural ability to survive in said environment, generates a selection criteria for its organisms. The selection criteria in our model is determined by the gradient, or landscape, which determines how many offspring a nearby organism may have - their fitness. If you take away the gradient of fitness, then there is effectively no
natural selection. However, the organisms still mutate each generation as dictated by their mutability and generate a diverse set of species. This orientation of the system should be that of
neutral theory, such that diversity arises randomly. Although the mating algorithm of our model intrinsically produces species, I will probably explore how distinguishable those species are throughout the simulations. I suspect that under the condition that every organism in the starting population receives a unique mutability value among a wide range of possible values, the species will go through many complex interactions - making them very inconsistent over many generations. After what might be considered transience, the available organisms will have dwindled their competitors to just a handful of mutabilities. This should reduce the amount of species interactions, so the species will become much more consistent and distinguishable (few interactions with other species). (Note that I don't really have sources that discuss species interactions, so this idea will most likely change.)
The second question addressed with this portion is whether there is a "best" mutability even in the case of neutral theory. I already briefly touched on this idea near the end of the previous paragraph. My intuition suggests that as the organisms compete, no particular set of mutabilities will survive the full simulation. My reasoning is that because there is no selection criteria, there should be no "best" mutability, as long as the organisms can avoid an imposed overpopulation density condition (kill off those too close to an organism). I think my data is already showing that there is a bimodal distribution of surviving mutabilties, which implies that there are two mutabilities which are optimal for survival. The tricky thing is that in all landscape situations, I keep seeing a bimodal distribution of survived mutabilities approximately the same in all cases. I don't yet have a reason why this could be happening.
For the species interaction, I'll probably look at it under the scope of no competition when all organisms are given the same mutability. I have a simple prediction for this. As mutability increases, species interactions will be very rare at first, but then, with a large enough mutability provided, the species will move to a state where they nearly always interact with other species. Hopefully, there should be a small range of mutabilities which will indicate this change in such a way that it can be modeled as a phase transition (like solid to liquid to gas sort of idea). Perhaps I'll even come up with a sort of kinetic energy analogy for mutability and use the fitness landscape to define a potential energy so that I can use statistical physics and thermodynamics principles to model it.
For the neural project, I'll attempt to model
glutamate activity such that neurons in a network desynchronize as the synaptic activity of glutamate falls all while in conditions prone to epileptic activity (neurons synchronize). The term in the model which determines coupling between neurons is that of the synapse. From this term, the strength of influence connected neurons have on each other gives rise to the possibility of synchronization. Luckily, a previous grad student in the lab showed how to gain synchronization in such a way, that it corresponds well with experiments we've done on rats. The change imposed to synchronize the network is the same which models seizure activity (reduced potassium conductance). In the experiments, I noticed that there seem to be several characteristic orchestrations of the
local field potential. The behaviors can be very different, particularly with the endings. The activity may cease abruptly or gradually decay. Furthermore, the length of seizures may vary from tens of seconds to several minutes. These behaviors led me to wonder about HOW the network synchronizes and desynchronizes. There is some literature to back up more specifically the idea I considered more abstractly, which is that glutamate variation changes the coupling strength between neurons. There are a few things to consider with this. First, when excitatory neurons fire, they tend to release glutamate, which is an excitatory
neurotransmitter. This causes the post-synaptic neurons to increase their potential to fire an
action potential as well, thus influencing when connected neurons may fire (driving mechanism to synchrony). However, each neuron has a limited supply of glutamate in vesicles to release, and require supplementation of new glutamate to release and package for further synaptic activity. These processes take time, and may be over long enough periods that allow the network to become effectively disconnected enough so that synchrony of the neurons is lost. Currently, the Wilson model which I will use fixes synaptic conductance (coupling strength). It will be my job to determine an effective model for how synaptic conductance varies in time. Hopefully, the parameters needed are physically plausible within the conditions imposed to garner seizure activity.
Perhaps another detail I can include in my model is that the potassium conductance reduction need only be applied to a small localized subset of the network, thus modeling the experimental system more closely.
SO, yet another long winded explanation of thoughts, but I think I can turn this into the basis for my dissertation proposal. Assuming I really do that, then I can say this mission is a success!
