Biology subjects

Herrera-Valdez, M. A.

Publications and source records attributed to Herrera-Valdez, M. A..

8 recordsLinked to original sources

bioRxiv2026

Action Potential Thresholds and Excitability from the Geometry of Membrane Potential

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or bifurcations, the approach focuses on the geometry of membrane potential trajectories. The changes in concavity during the upstroke of an action potential can be directly obtained from a time series of voltages. The concavity criterion is then extended to models based on autonomous dynamical systems where the changes in concavity can be obtained analytically from a curve of inflection points in phase space. The inflection point manifold defines a region required for excitability: all the orbits that cross it contain action potentials, and all the trajectories that contain action potentials are in it. This analytical principle can then be used to define excitability in a dynamical system, and also a measure of excitability that enables quantification and comparisons of excitability across dynamical system. The measure provides a way to compare the excitabilities of systems that model neurons with different electrophysiological phenotypes and consider different stimulus conditions. The traditionally vague physiological concept of electrical excitability is transformed into a rigorous analytical description by considering the time-dependent curvature of the membrane potential. The criterion is robust across smooth, single compartment models of electrical excitability and can be can be extended to single compartment models in higher dimensions, and multicompartment models as well.

neuroscience↗

bioRxiv2026

An Analytical Description for Action Potential Thresholds Defined by Concavity Changes

A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or specific fixed-point bifurcations, the approach focuses on the geometry of membrane potential trajectories. Specifically, the focus is on the concavity changes during the upstroke of an electrical pulse. These changes in concavity form a curve of inflection points that defines a region in phase space crossed by all the action potentials in the system, and containing no non-action potential trajectories. Such region is called the excitability region and its size can be measured, thus providing a measure for the excitability of a dynamical system, and a way to compare the excitability between systems representing different biological phenotypes and stimulus conditions. The work transforms the traditionally vague physiological concept of excitability into a rigorous analytical description applicable across continuous, single compartment models of electrical excitability.

neuroscience↗

bioRxiv2025

A method for analyzing physiological data with multiple non-independent observations

Physiological studies often involve recording multiple observations (e.g., repeated muscle contractions or cardiac cycles) from the same subject. To compare groups of subjects, observations from one subject are then sometimes pooled with observations from other subjects in the same group, and analyses are performed on these pooled data. This approach presents a number of potential problems, including over-or under-representing certain subjects in the sample and non-independence of measurements. There are statistical methods available to deal with repeated measures, but many make assumptions about the distribution and completeness of data. Instead, we developed a method to deal with multiple observations from physiological data that ensures that each subject is represented only once in the analysis (i.e. it avoids pseudoreplication), and makes no assumptions about the distribution of the data. We demonstrate this method using two different physiological datasets: (1) muscle recordings taken from Drosophila melanogaster larvae during fictive crawling, and (2) electrocardiogram recordings taken from human volunteers before, during, and after exercise. Our results show the broad applicability and validity of this method.

physiology↗

bioRxiv2023

Association between electrophysiological phenotypes and Kv2.1 potassium channel expression explained by geometrical analysis

Excitable cells exhibit different electrophysiological profiles while responding to current stimulation in current-clamp experiments. In theory, the differences could be explained by changes in the expression of proteins mediating transmembrane ion transport. Experimental verification by performing systematic, controlled variations in the expression of proteins of the same type (e.g. voltage-dependent, noninactivating Kv2.1 channels) is difficult to achieve in the absence of other changes. However, biophysical models enable this possibility and allows us to assess and characterise the electrophysiological phenotypes associated to different levels of expression of non-inactivating voltage-dependent K-channels of type Kv2.1. To do so, we use a 2-dimensional biophysical model of neuronal membrane potential and study the phase plane geometry and bifurcation structures associated with different levels of Kv2.1 expression with the input current as bifurcation parameter. We find that increasing the expression of Kv2.1 channels reduces the size of the region of the phase plane from which action potentials can be initiated. The changes in expression can also be related to different transitions between rest and repetitive firing in current clamp experiments. For instance, increasing the number of Kv2.1 channels shifts the rheobase current to higher levels, but also expands the dynamic range in which excitatory external current produces repetitive spiking. Our analysis shows that changes in the responses to increasing input currents can be associated to different sequences of fixed point bifurcations. In general, the fixed points are attracting, then repulsive, and later become attracting again as the input current increases, but the bifurcation sequences also include changes in fixed point type, and change qualitatively with the expression of Kv2.1 channels. In the non-repetitive spiking regime with low current stimulation, low expression of Kv2.1 channels yields bifurcation sequences that include transitions between 3 and 1 fixed points, and repetitive firing starts with delays that decrease with increasing current (aggregation). For higher expression of Kv2.1 channels there is only one fixed point that changes in type and attractivity as the input current increases, convergence to rest tends to be oscillatory (resonance), and repetitive spiking starts without noticeable delays. Our models explain how the same neuron is theoretically be capable of including both aggregating and resonant modes of integration for synaptic input, as shown in current clamp experiments.

neuroscience↗

bioRxiv2022

A biophysical, minimal model to investigate age-related changes in CA1 pyramidal cell electrical activity

Aging is a physiological process that is still poorly understood, especially with respect to effects on the brain. There are open questions about aging that are difficult to answer with an experimental approach. Underlying challenges include the difficulty of recording in vivo single cell and network activity simultaneously with submillisecond resolution, and brain compensatory mechanisms triggered by genetic, pharmacologic, or behavioral manipulations. Mathematical modeling can help address some of these questions by allowing us to fix parameters that cannot be controlled experimentally and investigate neural activity under different conditions. We present a biophysical minimal model of CA1 pyramidal cells (PCs) based on general expressions for transmembrane ion transport derived from basic thermodynamical principles. The model allows directly varying the contribution of ion channels by changing their number. By analyzing the dynamics of the model, we find parameter ranges that reproduce the variability in electrical activity seen in PCs. In addition, increasing the L-type Ca2+ channel expression in the model reproduces age-related changes in excitability that are qualitatively and quantitatively similar to those observed in PCs from aged animals.

biophysics↗

bioRxiv2020

A simple description of biological transmembrane potential from simple biophysical considerations: no equivalent circuits

Biological membranes mediate different physiological processes necessary for life. Ion movement around, into and out of cells, is arguably one of the most important of such processes, as it underlies electrical signalling and communication within and between cells. The difference between the electrical potentials inside and outside a biological membrane, called transmembrane potential, or membrane potential for short, is one of the main biophysical variables affecting ionic movement. Most of the equations that describe the change in membrane potential are based on analogies with resistive-capacitative electrical circuits, with conductance and capacitance proposed in classical studies as measures of the permeable and the impermeable properties of the membrane, respectively. However, the parts in ohmic circuits are not like the biological elements present in the spaces around and within biological membranes. This article presents a simple derivation for an equation describing local changes in transmembrane potential that is not based on electrical circuit analogies. In doing so, concepts like the so-called "membrane capacitance" are explained and generalized. Importantly, the classical model for the membrane potential based on an equivalent RC-circuit is recovered as particular case from the general derivation presented here. Modeling examples are presented to illustrate the use of the derivation and the effects of changing the way charges aggregate around the membrane as a function of the membrane potential.

biophysics↗

bioRxiv2020

Dynamic modulation of glucose utilisation by glucocorticoid rhythms in health and disease

A systems level coordination of physiological rhythms is essential to sustain healthy states, especially in the face of stimuli that may disrupt such rhythms. The timing of meals, medication and chronic stress can profoundly influence metabolism, which depends on the dynamic interactions between glucose, insulin and cortisol. Although the metabolic and stress endocrine axes are simultaneously disrupted in many diseases, a theoretical framework to understand how chronodisruption leads to disease is lacking. By developing a mathematical model of glucose utilisation that accounts for the antagonism between insulin and cortisol, we investigate the dynamic effects of glucose boluses under normal and disrupted cortisol rhythms, including the effects of cortisol agonists and antagonists. We also predict how cortisol rhythms modulate circadian responses to oral glucose diagnostic tests, and analyse the disruptions caused by hypercortisolism. Finally, we predict the mechanisms leading to type 2 diabetes in patients with normal and excess cortisol.

systems biology↗

bioRxiv2018

A model for physiological transmembrane transport derived from thermodynamical principles

A generic 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 generic 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 generic formulation. For instance, the conductance-based formulation for current turns out to be a linear approximation of the generic 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 generic formulation. The applicability of the generic formulations is illustrated first with fits to existing data, and after, with models of transmembrane potential dynamics for pacemaking cardiocytes and neurons. The generic formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.

physiology↗