Young and Aged Neuronal Tissue Dynamics With a Simplified Neuronal Patch Cellular Automata Model.

Realistic single-cell neuronal dynamics are typically obtained by solving models that involve solving a set of differential equations similar to the Hodgkin-Huxley (HH) system. However, realistic simulations of neuronal tissue dynamics -especially at the organ level, the brain- can become intractable due to an explosion in the number of equations to be solved simultaneously. Consequently, such efforts of modeling tissue- or organ-level systems require a lot of computational time and the need for large computational resources. Here, we propose to utilize a cellular automata (CA) model as an efficient way of modeling a large number of neurons reducing both the computational time and memory requirement. First, a first-order approximation of the response function of each HH neuron is obtained and used as the response-curve automaton rule. We then considered a system where an external input is in a few cells. We utilize a Moore neighborhood (both totalistic and outer-totalistic rules) for the CA system used. The resulting steady-state dynamics of a two-dimensional (2D) neuronal patch of size 1, 024 × 1, 024 cells can be classified into three classes: (1) Class 0-inactive, (2) Class 1-spiking, and (3) Class 2-oscillatory. We also present results for different quasi-3D configurations starting from the 2D lattice and show that this classification is robust. The numerical modeling approach can find applications in the analysis of neuronal dynamics in mesoscopic scales in the brain (patch or regional). The method is applied to compare the dynamical properties of the young and aged population of neurons. The resulting dynamics of the aged population shows higher average steady-state activity 〈a(t → ∞)〉 than the younger population. The average steady-state activity 〈a(t → ∞)〉 is significantly simplified when the aged population is subjected to external input. The result conforms to the empirical data with aged neurons exhibiting higher firing rates as well as the presence of firing activity for aged neurons stimulated with lower external current.

How many trimers? Modeling influenza virus fusion yields a minimum aggregate size of six trimers, three of which are fusogenic.

Conflicting reports in leading journals have indicated the minimum number of influenza hemagglutinin (HA) trimers required for fusion to be between one and eight. Interestingly, the data in these reports are either almost identical, or can be transformed to be directly comparable. Different statistical or phenomenological models, however, were used to analyze these data, resulting in the varied interpretations. In an attempt to resolve this contradiction, we use PABM, a brane calculus we recently introduced, enabling an algorithmic systems biology approach that allows the problem to be modeled in a manner following a biological logic. Since a scalable PABM executor is still under development, we sufficiently simplified the fusion model and analyzed it using the model checker, PRISM. We validated the model against older HA-expressing cell-to-cell fusion data using the same parameters with the exception of three, namely HA and sialic acid (SA) surface densities and the aggregation rate, which were expected to be different as a result of the difference in the experimental setup. Results are consistent with the interpretation that a minimum aggregate size of six HA trimers, of which three undergo a conformational change to become fusogenic, is required for fusion. Of these three, two are free, while one is bound. Finally, we determined the effects of varying the SA surface density and showed that only a limited range of densities permit fusion. Our results demonstrate the potential of modeling in providing more precise interpretations of data.

Gravity-assisted segregation of granular materials of equal mass and size.

High-resolution segregation is demonstrated for elastic granular materials of the same mass and size. Each grain starts at a randomly selected position in the entrance facet of a cylinder, accelerates downwards due to gravity, and then bounces against a massive obstacle with a collision cross section that is proportional to the facet size. Bounce dynamics of the falling grain is a function of its relative elasticity with the obstacle. Subsequent collisions of the grain with the wall are assumed to be perfectly elastic. In the absence of interparticle collisions, grain focusing occurs at points along the cylinder axis. In the absence of rotation, focusing occurs regardless of the initial locations and (downward) velocities of the grains at the entrance facet. The focus location depends only on the coefficient of restitution of the falling particle and the obstacle size. Grains arrive at the focus in temporally localized bursts even if released simultaneously from the facet. Efficient segregation is, therefore, achieved without additional mechanical work (e.g., shaking, spinning) on the system configuration.