Physical Sciences and Mathematics Commons^™

Allostery In Oligomeric Receptor Models, Gregory D. Conradi Smith

Arts & Sciences Articles

We show how equilibrium binding curves of receptor homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric interactions between receptor monomers (i.e. conformational coupling). The method is completely general; it begins with an arbitrary undirected graph representing the topology of a monomer state-transition diagram and ends with an algebraic expression for the equilibrium binding curve of a receptor oligomer composed of two or more …

Transcriptome Of Neonatal Prebotzinger Complex Neurones In Dbx1 Reporter Mice, John A. Hayes, (…), Ronald D. Smith, Gregory D. Smith, Margaret S. Saha, Christopher A. Del Negro

Arts & Sciences Articles

We sequenced the transcriptome of brainstem interneurons in the specialized respiratory rhythmogenic site dubbed preBotzinger Complex (preBotC) from newborn mice. To distinguish molecular characteristics of the core oscillator we compared preBotC neurons derived from Dbx1-expressing progenitors that are respiratory rhythmogenic to neighbouring non-Dbx1-derived neurons, which support other respiratory and non-respiratory functions. Results in three categories are particularly salient. First, Dbx1 preBotC neurons express kappa-opioid receptors in addition to mu-opioid receptors that heretofore have been associated with opiate respiratory depression, which may have clinical applications. Second, Dbx1 preBotC neurons express the hypoxia-inducible transcription factor Hif1a at levels three-times higher than non-Dbx1 …

Cycle Bases Of Reduced Powers Of Graphs, Richard H. Hammack, Gregory Smith

Arts & Sciences Articles

We define what appears to be a new construction. Given a graph G and a positive integer k, the reduced kth power of G, denoted G^(k), is the configuration space in which k indistinguishable tokens are placed on the vertices of G, so that any vertex can hold up to k tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex. We present propositions related to the structural properties of reduced graph powers and, most significantly, provide …

Calcium Homeostasis In A Local/Global Whole Cell Model Of Permeabilized Ventricular Myocytes With A Langevin Description Of Stochastic Calcium Release, Xiao Wang, Seth H. Weinberg, Gregory D. Smith, Yan Hao, Eric A. Sobie

Arts & Sciences Articles

Population density approaches to modeling local control of Ca2+ induced Ca2+ release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca2+ signals. Unfortunately, the computational complexity of such "local/global" whole cell models scales with the number of Ca2+ release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca2+ concentration ([Ca2+]). The computational efficiency of this approach no longer depends on the …

The Influence Of Ca2+ Buffers On Free [Ca2+] Fluctuations And The Effective Volume Of Ca2+ Microdomains, Seth H. Weinberg, Gregory D. Smith

Arts & Sciences Articles

Intracellular calcium (Ca2+) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca2+ binding proteins (Ca2+ buffers) play an important role in regulating Ca2+ concentration ([Ca2+]). Buffers typically slow [Ca2+] temporal dynamics and increase the effective volume of Ca2+ domains. Because fluctuations in [Oa(2+)] decrease in proportion to the square-root of a domain's physical volume, one might conjecture that buffers decrease [Ca2+] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca2+ signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic …

Buffer- And Diffusion-Mediated Calcium Concentration Fluctuations Accelerate The Stochastic Dynamics Of Calcium-Triggered Events, Seth H. Weinberg, Gregory D. Smith

Arts & Sciences Articles

No abstract provided.

Analysis Of Spark Versus Non-Spark Mediated Sr Calcium Leak Using A Langevin Description Of Stochastic Calcium Release, Xiao Wang, Seth H. Weinberg, Gregory D. Smith, Yan Hao, Eric A. Sobie

Arts & Sciences Articles

No abstract provided.

A Population Density Domain Model For Calcium-Inactivation Of L-Type Calcium Channels, Kiah Hardcastle, Seth H. Weinberg, Gregory D. Smith

Arts & Sciences Articles

No abstract provided.

Calcium Concentration Fluctuations And Subspace Volume Influence Calcium-Regulated Calcium Channel Gating And Subspace Dynamics, Seth H. Weinberg, Gregory D. Smith

Arts & Sciences Articles

No abstract provided.

Discrete-State Stochastic Models Of Calcium-Regulated Calcium Influx And Subspace Dynamics Are Not Well-Approximated By Odes That Neglect Concentration Fluctuations, Seth H. Weinberg, Gregory D. Smith

Arts & Sciences Articles

Cardiac myocyte calcium signaling is often modeled using deterministic ordinary differential equations (ODEs) and mass-action kinetics. However, spatially restricted “domains” associated with calcium influx are small enough (e.g., 10−17 liters) that local signaling may involve 1–100 calcium ions. Is it appropriate to model the dynamics of subspace calcium using deterministic ODEs or, alternatively, do we require stochastic descriptions that account for the fundamentally discrete nature of these local calcium signals? To address this question, we constructed a minimal Markov model of a calcium-regulated calcium channel and associated subspace. We compared the expected value of fluctuating subspace calcium concentration (a result …

Generating A Close-To-Reality Synthetic Population Of Ghana, Tyler Frazier, Andreas Alfons

Arts & Sciences Articles

The purpose of this research is to generate a close-to-reality synthetic human population for use in a geosimulation of urban dynamics. Two commonly accepted approaches to generating synthetic human populations are Iterative Proportional Fitting (IPF) and Resampling with Replacement. While these methods are effective at reproducing one instance of the probability model describing the survey, it is an instance with extremely small variability amongst subgroups and is very unlikely to be the real population. IPF and Resampling with Replacement also rely on pure replication of units from the underlying sample which can increase unrealistic model behavior. In this work we …

Emergence Of Switch-Like Behavior In A Large Family Of Simple Biochemical Networks, Dan Siegal-Gaskins, Maria K. Mejia-Guerra, Gregory D. Smith, Erich Grotewold

Arts & Sciences Articles

Bistability plays a central role in the gene regulatory networks (GRNs) controlling many essential biological functions, including cellular differentiation and cell cycle control. However, establishing the network topologies that can exhibit bistability remains a challenge, in part due to the exceedingly large variety of GRNs that exist for even a small number of components. We begin to address this problem by employing chemical reaction network theory in a comprehensive in silico survey to determine the capacity for bistability of more than 40,000 simple networks that can be formed by two transcription factor-coding genes and their associated proteins (assuming only the …

Effect Of Node-Degree Correlation On Synchronization Of Identical Pulse-Coupled Oscillators, M. Drew Lamar, Gregory D. Smith

Arts & Sciences Articles

We explore the effect of correlations between the in and out degrees of random directed networks on the synchronization of identical pulse-coupled oscillators. Numerical experiments demonstrate that the proportion of initial conditions resulting in a globally synchronous state (prior to a large but finite time) is an increasing function of node-degree correlation. For those networks observed to globally synchronize, both the mean and standard deviation of time to synchronization are decreasing functions of node-degree correlation. Pulse-coupled oscillator networks with negatively correlated node degree often exhibit multiple coherent attracting states, with trajectories performing fast transitions between them. These effects of node-degree …

Automated Reduction Of Calcium Release Site Models Via State Aggregation, Yan Hao, Peter Kemper, Gregory D. Smith

Arts & Sciences Articles

No abstract provided.

Calcium Sparks And Homeostasis In A Minimal Model Of Local And Global Calcium Responses In Quiescent Ventricular Myocytes, Jana M. Hartman, Gregory D. Smith, Eric A. Sobie

Arts & Sciences Articles

"We present a minimal whole cell model that accounts for both local and global aspects of Ca signaling in quiescent ventricular myocytes..."

Modeling The Effects Of Genetic Manipulations Of Calsequestrin On Local Calcium Release And Depletion In Cardiac Myocytes, Ryan P. Carpenter, Gregory D. Smith, Sandor Gyorke

Arts & Sciences Articles

"Cardiac calsequestrin (CASQ2), a Ca buffer localized to the junctional SR (jSR) of cardiac myocytes, is known to bind to the RyR-triadin-junctin complex, participate in the luminal regulation of RyRs, and modulate Ca spark activity..."

A Technique To Accelerate Stochastic Markov Chain Monte Carlo Simulations Of Calcium-Induced Calcium Release In Cardiac Myocytes, George Williams, Mohsin Saleet Jafri, Aristide Chikando, Gregory Smith

Arts & Sciences Articles

No abstract provided.

The Capacity For Multistability In Small Gene Regulatory Networks, Dan Siegal-Gaskins, Erich Grotewold, Gregory D. Smith

Arts & Sciences Articles

Background

Recent years have seen a dramatic increase in the use of mathematical modeling to gain insight into gene regulatory network behavior across many different organisms. In particular, there has been considerable interest in using mathematical tools to understand how multistable regulatory networks may contribute to developmental processes such as cell fate determination. Indeed, such a network may subserve the formation of unicellular leaf hairs (trichomes) in the model plant Arabidopsis thaliana.

Results

In order to investigate the capacity of small gene regulatory networks to generate multiple equilibria, we present a chemical reaction network (CRN)-based modeling formalism and describe …

Enhanced Capacitative Calcium Entry And Sarcoplasmic-Reticulum Calcium Storage Capacity With Advanced Age In Murine Mesenteric Arterial Smooth Muscle Cells, John N. Buchholz, Sean M. Wilson, Ravi Goyal, Gregory D. Smith

Arts & Sciences Articles

Intracellular Ca(2+) signaling is important to perfusion pressure related arterial reactivity and to vascular disorders including hypertension, angina and ischemic stroke. We have recently shown that advancing-age leads to calcium signaling adaptations in mesenteric arterial myocytes from C57 BL/6 mice [Corsso, C.D., Ostrovskaya. O., McAllister, C.E., Murray, K., Hatton, W.J., Gurney, A.M., Spencer, N.J., Wilson, S.M., 2006. Effects of aging on Ca(2+) signaling in murine mesenteric arterial smooth muscle cells. Mech. Ageing Dev. 127, 315-323)] which may contribute to decrements in perfusion pressure related arterial contractility others have shown occur. Even still, the mechanisms underlying the changes in Ca(2+) signaling …

Reduction Of Calcium Release Site Models Via Fast/Slow Analysis And Iterative Aggregation/Disaggregation, Yan Hao, Peter Kemper, Gregory D. Smith

Arts & Sciences Articles

Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of calcium puffs and sparks. Such models often take the form of stochastic automata networks in which the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. In order to overcome the state-space explosion that occurs in such compositionally defined calcium release site models, we have implemented several automated procedures for model reduction using fast/slow analysis. After categorizing rate constants in the single channel model as …

Oscillation Regularity In Noise-Driven Excitable Systems With Multi-Time-Scale Adaptation, William H. Nesse, Christopher A. Del Negro, Paul C. Bressloff

Arts & Sciences Articles

We investigate oscillation regularity of a noise-driven system modeled with a slow after-hyperpolarizing adaptation current (AHP) composed of multiple-exponential relaxation time scales. Sufficiently separated slow and fast AHP time scales (biphasic decay) cause a peak in oscillation irregularity for intermediate input currents I, with relatively regular oscillations for small and large currents. An analytic formulation of the system as a stochastic escape problem establishes that the phenomena is distinct from standard forms of coherence resonance. Our results explain data on the oscillation regularity of the pre-Bötzinger complex, a neural oscillator responsible for inspiratory breathing rhythm generation in mammals.

Thermal Desorption Of Hydrogen From Carbon Nanosheets, X. Zhao, R. A. Outlaw, J. J. Wang, M. Y. Zhu, Gregory D. Smith, B. C. Holloway

Arts & Sciences Articles

Carbon nanosheets are a unique nanostructure that, at their thinnest configuration, approach a single freestanding graphene sheet. Temperature desorption spectroscopy (TDS) has shown that the hydrogen adsorption and incorporation during growth of the nanosheets by radio frequency plasma-enhanced chemical vapor deposition are significant. A numerical peak fitting to the desorption spectra (300–1273K) via the Polanyi-Wigner equation showed that desorption followed a second order process, presumably by the Langmuir-Hinshelwood mechanism. Six peaks provide the best fit to the TDS spectra. Surface desorption activation energies were determined to be 0.59, 0.63, and 0.65eV for the external graphite surface layers and 0.85, 1.15, …

Detectability Of Excitatory Versus Inhibitory Drive In An Integrate-And-Fire-Or-Burst Thalamocortical Relay Neuron Model, Gregory D. Smith, S. M. Sherman

Arts & Sciences Articles

Although inhibitory inputs are often viewed as equal but opposite to excitatory inputs, excitatory inputs may alter the firing of postsynaptic cells more effectively than inhibitory inputs. This is because spike cancellation produced by an inhibitory input requires coincidence in time, whereas an excitatory input can add spikes with less temporal constraint. To test for such potential differences, especially in the context of the function of thalamocortical (TC) relay nuclei, we used a stochastic “integrate-and-fire-or-burst” TC neuron model to quantify the detectability of excitatory and inhibitory drive in the presence and absence of the low-threshold Ca 2+ current, IT, and …

Mode Locking In A Periodically Forced Integrate-And-Fire-Or-Burst Neuron Model, S. Coombes, R. Owen, Gregory D. Smith

Arts & Sciences Articles

The minimal “integrate-and-fire-or-burst” (IFB) neuron model reproduces the salient features of experimentally observed thalamocortical relay neuron response properties, including the temporal tuning of both tonic spiking (i.e., conventional action potentials) and post-inhibitory rebound bursting mediated by the low-threshold Ca2+ current, IT. In previous work focusing on experimental and IFB model responses to sinusoidal current injection, large regions of stimulus parameter space were observed for which the response was entrained to periodic applied current, resulting in repetitive burst, tonic, or mixed (i.e., burst followed by tonic) responses. Here we present an exact analysis of such mode-locking in the integrate-and-fire-or-burst model under …

Asymptotic Analysis Of Buffered Calcium Diffusion Near A Point Source, Arthur Sherman, Gregory D. Smith, Longxiang Dai, Robert M. Miura

Arts & Sciences Articles

The "domain" calcium (Ca2+) concentration near an open Ca2+ channel can be mod- eled as buffered diffusion from a point source. The concentration profiles can be well approximated by hemispherically symmetric steady-state solutions to a system of reaction-diffusion equations. After nondimensionalizing these equations and scaling space so that both reaction terms and the source amplitude are 0(1), we identify two dimensionless parameters, Cc and Eb, that correspond to the diffusion coefficients of dimensionless Ca2+ and buffer, respectively. Using perturbation methods, we derive approximations for the Ca2+ and buffer profiles in three asymptotic limits: (1) an "excess buffer approximation" (EBA), where …