A Molecular Basis for Liquid State Information Processors
Dyer, Norman J.
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Information processing by excitable neuronal membranes at the molecular level is modeled, intended to serve the study of neuron behaviors resulting from arbitrary patterns of channel and pump distributions. The simulation consists of saline volumes separated by lipid membranes, and four types of protein transmembrane processes. It is a physics-based hybrid of diffusion, electrodynamics, large molecule kinetics, and positional organization between the elements. Particles are individually instantiated, accelerate under charge forces, may collide elastically, may bind to receptors, and may be transported across the membrane. The four kinetic elements change state thermally and are modulated by forces and ligand bindings. These elements generate signals via particle releases, which may propagate along shaped, 3-dimensional, whole cell, closed surfaces. Model controllables and observables span reasonable physiologic domains and ranges. The simulated membranal system enacts nanoscale ionic collisions and drift, membrane capacitance of charge differentials, and large protein conformational kinetics of transport as stochastically driven finite state machines. The saline tonicities are represented as individual solute particles and certain traits of water (thermally driven collisions, maintaining the Boltzmann velocity distribution of each species of particle as a function of mass and temperature, and solvation shells around ions). Solutes include any number of species of ions and ligands as freely diffusing, drifting particles, each with mass, charge, radius, position, and velocity. Ligands include neurotransmitters, hormones, second messengers, ATP, GTP. Mass, charge and linear momentum are conserved. Membranes serve as dielectric barriers, maintaining charge separation and supporting voltage gradients as a function of charge concentration ratios (per Coulomb and Nernst). Particle charge forces are solved as whole system 3-d N-body electrostatic problem. Local voltages and concentrations determine particle movement through individual open ion channels per their conductivity profiles. Kinetics and affinities of instantiated types of poly-ion pumps, move particle up gradient, which then proceed down concentration gradients, and along capacitated surfaces. The four types of membranal proteins (collectively referred to as actors) are: metabotropic receptors, ion channels (which may contain ionotropic receptors), vesicular release mechanisms, and active transporters (pumps). Each type exhibits informationally-significant conformational change via instantiation of a characteristic state transition matrix (Q matrix), and has the capacity to bind and unbind stochastically according to known kinetics for that type. The external drivers (voltage sensitivity and allosteric binding sites for ligands) warrant transition probability matrices separate from the Q matrix for each modulator combination. The state sequence for each actor is instantiated at each time step as a Markov stochastic process, given the prior state and current modulation. Actors have compartment-wise polarity and transport particles as a function of concentrations, affinity profiles, and kinetics. The kinetic state directed graphs may be sufficiently robust to support temporal pattern recognition and generation. Membranes are shaped into a concatenation of cones, spheres, cylinders and tori so as to generally capture the topology of a neuron type. Actors are distributed realistically over these curved, closed membranes via probability distribution functions. Libraries of actor plaiding patterns are maintained for reuse. Actor position may determine the conductive distances between nearest neighbors and the available capacitive area surrounding each node. Emergent effects of massively parallel actions include propagated graded and/or action potentials. Diffusion/kinetic/electric disturbances may propagate the length of the axon to initiate increases of intracellular calcium concentration at the axon bouton, which in turn drive the kinetics of neurotransmitter release at the synapse. Particle -uptake and sequestration are supported. Actor function and distribution are of adequate quantities to maintain bio-physiologic concentrations throughout normal channel opening patterns over time. Energy flows generally are not represented, except to drive the pumps. ATP is instantiated as particles and may be converted to ADP+Pi particles in binding with pump ATPases. Pumps then may initiate cascades driving other energy-consuming actions (constrained implicitly as transition probabilities). Information flow is of the essence, and all elements and processes are optimized around verifiable information processing roles according to neuron type and the modalities of each type. The dimensions of information flow are spatial_pattern x temporal_pattern. The whole cell model employs a novel set of proportionate scaling functions of time, space and quantity. Distinctive areas of membrane are “excised” from the whole cell model as canonical patches for intensive one-to-one molecule modeling. Patches may then returned to the whole cell via cloning and tiling with some interpolations according to a multiscale scheme.