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Molecular Diffusion

Over the last year my escapades and capers have been primarily directed at the study of synaptic potentiation from a neurodynamics perspective. Currently, I'm examining the membrane diffusion of neurotransmitter receptors and modeling how these particles swarm and potentiate synapses. It has been an interesting transition into these topics - prior to these projects I worked primarily with brain tissue and mice, but now I find myself spending most of my day programming, running simulations, and working with equations. I'm not sure why, but I find diffusion quite interesting. Stochastic diffusion, like that in Brownian motion, is a pure actuation of the basic properties of statistics. Given that synaptic potentiation is directly mediated by stochastic diffusion and synaptic capture of receptors, it seem that neurons have evolved into innate statistical computers. The result of 100 billion of these statistical computers making 100 trillion connections is the human brain.

MY NOTES ON MODELING DIFFUSION

Computational Modeling

Broadly, neuroinformatics is the computational modeling and simulation of the nervous system. It involves translating quantitative data collected from neurobiology experiments into mathematical representations. From there, this symbolic representation can be used to create computer simulations of neural activity, network processing, molecular dynamics, and other physical processes. I am using MatLab, Python, R, and other tools to build models and animations that are directly based off my own and others empirical observations.

Brain Functional Connectome Project

A connectome is a comprehensive map of the neural networks within the brain. It details the efferent and afferent pathways within and between brain regions. Functional Connectivity refers to the function of a particular brain region and its information processing role within a distributed neural network. The goal of this project is to create a platform where users can jump into the connectome at any given brain region and visually navigate to upstream and downstream regions; along the way, users can learn about the functional role of each brain region. All information has been collected from empirical sources and scientific databases, in particular, the Allan Brain Atlas. Error creating thumbnail: File missing

Brain Molecular Pathways Project

This project aims to provide annotated sets of molecular pathways involved in neural plasticity underlying learning and memory systems. In general, biological pathways display the series of interactions among molecules resulting in functional changes within cells and neural networks. Currently there are large scale projects dedicated to amassing pathway evidence via high-throughput methods. The goal is to translate this unwieldy biopathway data from several empirical databases into visually digestible material, by characterizing the features of molecular cascades most sensitive to an event of interest (e.g. fear conditioning or amphetamine addiction).

Welcome to the official wiki of Brad Monk

Hello and welcome to my wiki. This is where I stash random information and have every intention of linking it all together someday. I'm not sure why you're here.. maybe trying to find one of my other wiki projects OneSci Science News or UCSD Psych Grad wiki? If you are so inclined, recent additions to this wiki can be found in the box on the right. For a non-curated glimpse of my activity you can check out the latest wiki updates. Older wiki content can be accessed using the [search box] or perusing all pages. If you would like to contact me, you can find this info on my home page.

Web Resources

Media

Diffusion to steadystate

Example animation rendered from "particle_diffusion_on_mesh.py"

Dendritic surface diffusion (on 3D mesh) from "particle_diffusion_on_mesh.py"

Example rendering dynamic actin network from "bran_actin_geo_xyz.spi"

Example rendering dynamic actin network from "ActinNetwork.m"

Figures

Fig 1. Cluster model diagrams and synopsis

Fig 1. Cluster model diagrams and synopsis. (A) In the Shouval model, particles form clusters through interactions with their nearest neighbors. Particles dissociate stochastically from the cluster at a constant rate, while the insertion probability for an unoccupied lattice space depends on the number of particles flanking that area. This is computed by convolving the cluster with a nearest-neighbor mask, and evaluating insertion probability based on these field weights. (B) The Czöndör model simulated the lateral 2D trajectories of AMPARs based on experimentally determined diffusion rates that were mapped to extrasynaptic (Dout), perisynaptic (Din), and synaptic (Dpsd), representations. (C) We incorporated key features from these two models into a single multilayer model where synaptic clustering of scaffold protein were simulated using the Shouval formulation and AMPAR surface diffusion was simulated using parameters from the Czöndör model. In addition, (a) we allowed scaffold particles to interact with nearby AMPARs effecting their diffusion rate; in turn, these interactions could impart stabilizing effects on the cluster by increasing lattice insertion propensity in the vicinity under a surface AMPAR. Geometric values for this model included: (b) dendritic segment length, (c) synapse spacing, (d) synaptic area, (e) spine area.

Fig 2. Cluster math

Fig 2. Simulation of particle clustering was conducted using the 2-step equation above [1]. (A) The first step of the on-rate equation (shown in the bottom right of the graph) yields conditional probabilities based on the number of neighbors surrounding a given lattice position (the off-rate equation works similarly). In this formulation each lattice position can have from zero to four neighbors, as displayed on the x-axis. The scalars L and β are used to weight the cumulative effects of multiple neighbors on particle-insertion probability. When the number of neighboring particles exceed L, the conditional probability for insertion is greater than 0.5; β adjusts the slope of this function such that higher values of β result in steeper curves (changes in conditional probability) around L. (B) In the second part of the equation (full equation shown in top left), rate parameters are applied to the conditional probabilities. This figure is showing the various effects of R at the two values of β indicated above (here L=2 and ∆t=0.1 across conditions).

1. 1. 1. Fig 3. AMPARs can stabilize scaffold protein clusters

Fig 3. AMPARs can stabilize scaffold protein clusters. (A) Scaffold protein clusters may dissociate over time unless stabilized by AMPA receptors. In this configuration, a starting cluster of 64 scaffold proteins will steadily degrade over the span of 1 hour [blue]; here however, cluster size is fully maintained through interactions with surface receptors [red]. (B) Scaffold cluster breakdown has a reciprocal effect on AMPAR synaptic numbers. As scaffold proteins become less available for tethering, synaptic expression of surface receptors declines. When cluster size nears the zero-point, surface receptor expression will parallel the perisynaptic steady-state. [values averaged over 10 simulations].

Fig 4. Scaffold protein cluster growth can support synaptic potentiation

Fig 4. Scaffold protein cluster growth can support synaptic potentiation. (A) During a brief (5 min) time-window the tethering coefficient for one subtype of multivalent surface receptors was transiently increased at ‘synapse-1’, allowing it to assist in scaffold protein recruitment. This event induced scaffold protein accretion along the edges of the cluster, which were stabilized by neighboring scaffold particles. Interestingly, this resulted in a long-term increase in scaffold protein cluster size that persisted well after the transient event subsided. (B) The addition of new submembrane protein scaffolding was closely followed by increases in AMPAR synaptic expression. The synaptic quantity of surface particles tends to parallel scaffold protein cluster size, as such, the stable increase of cluster size resulted in a long-term increase of synaptic AMPAR levels.

Fig 5. Scaffold cluster model diagrams and synopsis

Fig 5. Scaffold cluster model diagrams and synopsis. (A) In the scaffold cluster model, SAP particles (red circles) cluster around nodes of actin scaffolding (yellow stars) at the PSD. SAP particles can associated or dissociate stochastically from actin nodes or each other with neighbor-dependent probability rates (similar to the cluster model described above; see SI methods). Actin nodes in this 2D visualization represent the tips of (B) actin scaffolding located in close proximity to the postsynaptic submembrane. This lattice (blue box) is of special consideration because it’s near enough to the submembrane to interact with laterally-diffusing surface receptors. (C) In the full model, AMPAR particles diffused laterally on the surface of a 3D dendritic mesh; in parallel, scaffold-cluster dynamics were simulated in the dendritic spine compartments. SAP particles at the near-membrane lattice could interact with AMPARs diffusing in close proximity, effecting their diffusion rate. In some simulations, AMPAR-SAP interactions could briefly alter actin dynamics in the surrounding vicinity, increasing the probability of de novo actin node formation nearby.

Fig 6. Actin network constrained to spine

Fig 6. Actin network constrained to spine surface mesh. This actin filament network was grown stochastically from the dendritic shaft into the spine. Network structure is dependent on the relative availabilities of G-actin monomers (necessary for polymerization), cofilin (promotes depolymerization and remodeling), and Arp2/3 (induces branching at 70 degree angles). It appears that a postsynaptic density forms naturally under these conditions, with scaffold note packing tightly at the center of the spine head submembrane. Actin branches near the surface will act as scaffolding for scaffold-associated proteins (SAPs) which can cluster around these nodes and tether diffusing surface receptors.