A thermodynamic description for physiological transmembrane transport [version 2; referees: 2 approved]

A general formulation for both passive and active transmembrane transport is derived from basic thermodynamical principles. The derivation takes into account the energy required for the motion of molecules across membranes, and includes the possibility of modeling asymmetric flow. Transmembrane currents can then be described by the general model in the case of electrogenic flow. As it is desirable in new models, it is possible to derive other well known expressions for transmembrane currents as particular cases of the general formulation. For instance, the conductance-based formulation for current turns out to be a linear approximation of the general formula for current. Also, under suitable assumptions, other formulas for current based on electrodiffusion, like the constant field approximation by Goldman, can also be recovered from the general formulation. The applicability of the general formulations is illustrated first with fits to existing data, and after, with models of transmembrane potential dynamics for pacemaking cardiocytes and neurons. The general formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport

Synchronization, Oscillator Death, and Frequency Modulation in a Class of Biologically Inspired Coupled Oscillators

The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of synchronous biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength, coupling type, and noise play in the synchronization of a system of coupled, non-linear oscillators. First, we study a deterministic model based on Van der Pol coupled oscillators, modeling a population of diffusively coupled cells, to find regions in the parameter space for which synchronous oscillations emerge and to provide conditions under which diffusive coupling kills the synchronous oscillation. Second, we study how noise and coupling interact and lead to synchronous oscillations in linearly coupled oscillators, modeling the interaction between various pacemaker populations, each having an endogenous circadian clock. To do so, we use the Fokker-Planck equation associated to the system. We show how coupling can tune the frequency of the emergent synchronous oscillation, which provides a general mechanism to make fast (ultradian) pacemakers slow (circadian) and synchronous via coupling. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used to guide further studies of coupled oscillations in biophysical non-linear models

Membranes with the Same Ion Channel Populations but Different Excitabilities

Electrical signaling allows communication within and between different tissues and is necessary for the survival of multicellular organisms. The ionic transport that underlies transmembrane currents in cells is mediated by transporters and channels. Fast ionic transport through channels is typically modeled with a conductance-based formulation that describes current in terms of electrical drift without diffusion. In contrast, currents written in terms of drift and diffusion are not as widely used in the literature in spite of being more realistic and capable of displaying experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are mathematically related: conductance-based currents are linear approximations of drift-diffusion currents. However, conductance-based models of membrane potential are not first-order approximations of drift-diffusion models. Bifurcation analysis and numerical simulations show that the two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with drift-diffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed in response to excitatory synaptic input, and across different levels of ion channel expression. In general, the electrophysiological profiles of membranes modeled with drift-diffusion and conductance-based models having identical ion channel populations are different, potentially causing the input-output and computational properties of networks constructed with these models to be different as well. The drift-diffusion formulation is thus proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels

Geometry and nonlinear dynamics underlying excitability phenotypes in biophysical models of membrane potential

The main goal of this dissertation was to study the bifurcation structure underlying families of low dimensional dynamical systems that model cellular excitability. One of the main contributions of this work is a mathematical characterization of profiles of electrophysiological activity in excitable cells of the same identified type, and across cell types, as a function of the relative levels of expression of ion channels coded by specific genes. In doing so, a generic formulation for transmembrane transport was derived from first principles in two different ways, expanding previous work by other researchers. The relationship between the expression of specific membrane proteins mediating transmembrane transport and the electrophysiological profile of excitable cells is well reproduced by electrodiffusion models of membrane potential involving as few as 2 state variables and as little as 2 transmembrane currents. Different forms of the generic electrodiffusion model presented here can be used to study the geometry underlying different forms of excitability in cardiocytes, neurons, and other excitable cells, and to simulate different patterns of response to constant, time-dependent, and (stochastic) time- and voltage-dependent stimuli. In all cases, an initial analysis performed on a deterministic, autonoumous version of the system of interest is presented to develop basic intuition that can be used to guide analyses of non-autonomous or stochastic versions of the model. Modifications of the biophysical models presented here can be used to study complex physiological systems involving single cells with specific membrane proteins, possibly linking different levels of biological organization and spatio-temporal scales.Release 09-Jun-201

Relationship Between Nearly-Coincident Spiking and Common Excitatory Synaptic Input in Motor Neurons

The activities of pairs of mammalian motor neurons (MNs) receiving varying degrees of common excitatory synaptic input were simulated to study the relationship between nearly-coincident spiking and common excitatory drive. The somatic membrane potential of each MN was modeled using a single compartment model. Each MN was modeled toreceive synaptic contacts from hundreds of pre-synaptic fibers. The percentage of pre-synaptic fibers that diverged to supply both MNs of a pair with common synaptic input could be varied from 0 (no common inputs) to 100% (all common inputs). Spikes trains on separate re-synaptic fibers were independent of one another and were modeled as realizations of renewal processes with mean firing rates (10 - 50Hz) resembling that associated with supra-spinal input. Maximum synaptic conductances and time constants were varied across synapsesto match experimentally observed somatic EPSPs. The number of active pre-synaptic fibers to each MN was adjusted in order that the firingrates of MNs were between 8 and 15 Hz. For each common input condition, 100 s of concurrent spiking activity of the MNs was usedto construct cross-correlation histograms. The sizes of the central peaks in the histograms were quantified using both the k' (Ellaway and Murthy 1985) and CIS (Nordstrom et al. 1992) indices ofsynchrony. Monotonically increasing linear relationships between the proportion of common synaptic input and the magnitude of synchronywere observed for both indices. For example, the model predicted that 10% common input would yield a CIS value of 0.27 whereas 100% commoninput would yield a CIS value of 1.5. These values are within the range of values observed experimentally. These results, therefore,provide a means to translate measures of nearly-coincident spiking into plausible renditions of synaptic connectivity

Transcription regulation and cellular differentiation in B subtilis: Excitability and bifurcation structures

Non UBCUnreviewedAuthor affiliation: UNAMFacult

Excitability and randomness in the dynamics of gene expression

Many different organisms are capable of regulating their gene expression to adjust their physiology and possibly change their phenotype in response to cues from the environment. There is a growing body of evidence that some differentiation processes exhibit excitability and change their behaviour influenced by random processes. I will show examples and discuss different problems of possible interest involving random extensions of deterministic, nonlinear dynamical systems.Non UBCUnreviewedAuthor affiliation: UNAMFacult

Profiles of DD and CB responses to excitatory synaptic input.

<p>All simulations with  = 2.5 with increasing numbers of excitatory synapses assuming the average number of activated synapses per input axon  = 10.</p