A model for physiological transmembrane transport derived from thermodynamical principles

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 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.

A thermodynamic description for physiological transmembrane transport

F1000Research ◽

10.12688/f1000research.16169.2 ◽

2018 ◽

Vol 7 ◽

pp. 1468 ◽

Cited By ~ 2

Author(s):

Marco Arieli Herrera-Valdez

Keyword(s):

Common Ground ◽

Transmembrane Potential ◽

Thermodynamic Description ◽

Field Approximation ◽

Transmembrane Transport ◽

Constant Field ◽

Asymmetric Flow ◽

Biophysical Study ◽

Transmembrane Currents ◽

Existing Data

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.

A thermodynamic description for physiological transmembrane transport

F1000Research ◽

10.12688/f1000research.16169.1 ◽

2018 ◽

Vol 7 ◽

pp. 1468

Author(s):

Marco Arieli Herrera-Valdez

Keyword(s):

Common Ground ◽

Transmembrane Potential ◽

Thermodynamic Description ◽

Field Approximation ◽

Transmembrane Transport ◽

Generic Model ◽

Constant Field ◽

Asymmetric Flow ◽

Biophysical Study ◽

Transmembrane Currents

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.

A thermodynamic description for physiological transmembrane transport

10.7287/peerj.preprints.1312 ◽

2018 ◽

Author(s):

Marco A Herrera-Valdez

Keyword(s):

Linear Approximation ◽

Common Ground ◽

Transmembrane Potential ◽

Thermodynamic Description ◽

Reversal Potential ◽

Transmembrane Transport ◽

Physiological Mechanisms ◽

Biophysical Study

Physiological mechanisms for passive and active transmembrane transport have been theoretically described using many different approaches. A generic formulation for both passive and active transmembrane transport, is derived from basic thermodynamical principles taking into account macroscopic forward and backward molecular fluxes, relative to a source compartment, respectively. Electrogenic fluxes also depend on the transmembrane potential and can be readily converted into currents. Interestingly, the conductance-based formulation for current is the linear approximation of the generic formulation for current, around the reversal potential. Also, other known formulas for current based on electrodiffusion turn out to be particular examples of the generic formulation. The applicability of the generic formulations is illustrated with models of transmembrane potential dynamics for cardiocytes and neurons. The generic formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.

A thermodynamic description for physiological transmembrane transport

10.7287/peerj.preprints.1312v8 ◽

2018 ◽

Author(s):

Marco A Herrera-Valdez

Keyword(s):

Linear Approximation ◽

Common Ground ◽

Transmembrane Potential ◽

Thermodynamic Description ◽

Reversal Potential ◽

Transmembrane Transport ◽

Physiological Mechanisms ◽

Biophysical Study

Physiological mechanisms for passive and active transmembrane transport have been theoretically described using many different approaches. A generic formulation for both passive and active transmembrane transport, is derived from basic thermodynamical principles taking into account macroscopic forward and backward molecular fluxes, relative to a source compartment, respectively. Electrogenic fluxes also depend on the transmembrane potential and can be readily converted into currents. Interestingly, the conductance-based formulation for current is the linear approximation of the generic formulation for current, around the reversal potential. Also, other known formulas for current based on electrodiffusion turn out to be particular examples of the generic formulation. The applicability of the generic formulations is illustrated with models of transmembrane potential dynamics for cardiocytes and neurons. The generic formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.

A unifying theory to describe transmembrane transport derived from thermodynamic principles

10.7287/peerj.preprints.1312v2 ◽

2015 ◽

Author(s):

Marco A Herrera-Valdez

Keyword(s):

Transmembrane Potential ◽

Functional Form ◽

Molecular Transport ◽

Planck Equation ◽

Transmembrane Transport ◽

Membrane Excitability ◽

Nonlinear Functions ◽

Functional Forms ◽

Membrane Spanning ◽

Transmembrane Currents

Herrera-Valdez. A unifying theory of physiological transmembrane transport Cellular homeostasis involves transmembrane molecular transport that is, in turn, mediated by proteins that enable molecular transport along, or against the (electro) chemical gradient of the molecules being transported. Transmembrane transport has been modelled in many studies using many functional forms that were not always derived from the same assumptions. A generic formulation that describes transmembrane fluxes regardless of whether they are mediated by carrier proteins or by open channels is presented here. The functional form of the flux was obtained from basic thermodynamic principles. Further, taking a slightly different approach, the same generic formulation mentioned above can also be obtained from the Nernst-Planck equation for the case of channel- mediated electrodiffusion. The generic formulation can be regarded as the product of an amplitude term and a driving force term, both nonlinear functions of the transmembrane concentrations of the molecules and possibly the transmembrane potential. The former captures the characteristics of the membrane-spanning protein mediating the transport and the latter is a non-linear function of the transmembrane concentrations of the ions. The generic formulation explicitly shows that the basal rate at which ions cross the membrane is the main difference between currents mediated by pumps and channels. Electrogenic transmembrane fluxes can be converted to currents to construct models of membrane excitability in which all the transmembrane currents have the same functional form. The applicability of the generic derivations presented here is illustrated with models of excitability for neurones and pacemaker cardiocytes.

A unifying theory to describe transmembrane transport derived from thermodynamic principles

10.7287/peerj.preprints.1312v4 ◽

2015 ◽

Author(s):

Marco A Herrera-Valdez

Keyword(s):

Transmembrane Potential ◽

Functional Form ◽

Molecular Transport ◽

Planck Equation ◽

Transmembrane Transport ◽

Membrane Excitability ◽

Nonlinear Functions ◽

Functional Forms ◽

Membrane Spanning ◽

Transmembrane Currents

A unifying theory of physiological transmembrane transport. Cellular homeostasis involves transmembrane molecular transport along, or against the (electro) chemical gradient of the molecules being transported. Such transport is typically mediated by membrane-spanning proteins that either carry the molecules across the membrane, or facilitate their (electro)diffusion. Transmembrane transport has been modelled in many studies using many functional forms that were not always derived from the same assump- tions. A generic formulation that describes transmembrane fluxes, mediated either by carrier proteins or by open channels, is presented here. The functional form of the flux was obtained from basic thermodynamic principles. The same generic formulation mentioned above can also be obtained from the Nernst-Planck equation for the case of channel-mediated electrodiffusion. The generic formulation can be regarded as the product of an amplitude term and a driving force term, both nonlinear functions of the transmembrane concentrations of the molecules being transported, and possibly the transmembrane potential. The former captures the characteristics of the membrane- spanning protein mediating the transport and the latter is a non-linear function of the transmembrane concentrations of the ions. The generic formulation explicitly shows that the basal rate at which ions cross the membrane is the main difference between currents mediated by pumps and channels. Electrogenic transmembrane fluxes can be converted to currents to construct models of membrane excitability in which all the transmembrane currents have the same functional form. The applicability of the generic derivations presented here is illustrated with models of excitability for neurones and pacemaker cardiocytes.

A model for passive and active transmembrane transport derived from thermodynamical principles

10.7287/peerj.preprints.1312v7 ◽

2018 ◽

Author(s):

Marco A Herrera-Valdez

Keyword(s):

Common Ground ◽

Transmembrane Potential ◽

Functional Form ◽

Reversal Potential ◽

Kinetic Scheme ◽

Transmembrane Transport ◽

Exponential Functions ◽

Basal Rate ◽

Ionic Fluxes ◽

Transmembrane Flux

All transmembrane ionic fluxes, whether electrodiffusive or driven by active transport, can be thought of in terms of the energy required to move ions across the membrane. A generic formulation for the transmembrane flux of ions is derived from thermodynamical principles combining a kinetic scheme with the Butler-Volmer equation. The formulation describes active (i.e. mediated by pumps) and passive transmembrane transport (e.g. channel-mediated) mechanisms with the same functional form. The flux described by the formulation is a product of a basal rate and a difference of exponential functions that depends on the transmembrane concentrations of the ions undergoing transport, a term that controls the symmetry of the transport, and the direction in which each of the molecules is transported. Electrogenic fluxes described by the generic formulation also depend on the transmembrane potential, and can be readily converted into currents. The linear approximation around the reversal potential for the generic current turns out to be the widely used conductance-based formulation. The derivations presented here show that models of transmembrane potential can be formulated in terms of currents with a common functional form and provide theoretical explanations for the quantitative differences and the qualitative similarities between pump- and channel mediated ionic fluxes. The applicability of the generic formulations is illustrated with models of transmembrane potential that reproduce the dynamics of pacemaking in cardiocytes. The generic formulations presented here provide a common ground for the study of physiological phenomena that depend on transmembrane transport.

A unifying theory to describe transmembrane transport derived from thermodynamic principles

10.7287/peerj.preprints.1312v3 ◽

2015 ◽

Author(s):

Marco A Herrera-Valdez

Keyword(s):

Transmembrane Potential ◽

Functional Form ◽

Molecular Transport ◽

Planck Equation ◽

Transmembrane Transport ◽

Membrane Excitability ◽

Nonlinear Functions ◽

Functional Forms ◽

Membrane Spanning ◽

Transmembrane Currents

Herrera-Valdez. A unifying theory of physiological transmembrane transport Cellular homeostasis involves transmembrane molecular transport mediated by proteins that enable molecular transport along, or against the (electro) chemical gradient of the molecules being transported. Transmembrane transport has been modelled in many studies using many functional forms that were not always derived from the same assumptions. A generic formulation that describes transmembrane fluxes regardless of whether they are mediated by carrier proteins or by open channels is presented here. The functional form of the flux was obtained from basic thermodynamic principles. Further, taking a slightly different approach, the same generic formulation mentioned above can also be obtained from the Nernst-Planck equation for the case of channel- mediated electrodiffusion. The generic formulation can be regarded as the product of an amplitude term and a driving force term, both nonlinear functions of the transmembrane concentrations of the molecules and possibly the transmembrane potential. The former captures the characteristics of the membrane-spanning protein mediating the transport and the latter is a non-linear function of the transmembrane concentrations of the ions. The generic formulation explicitly shows that the basal rate at which ions cross the membrane is the main difference between currents mediated by pumps and channels. Electrogenic transmembrane fluxes can be converted to currents to construct models of membrane excitability in which all the transmembrane currents have the same functional form. The applicability of the generic derivations presented here is illustrated with models of excitability for neurones and pacemaker cardiocytes.

Improved local-constant-field approximation for strong-field QED codes

Physical Review A ◽

10.1103/physreva.99.022125 ◽

2019 ◽

Vol 99 (2) ◽

Cited By ~ 33

Author(s):

A. Di Piazza ◽

M. Tamburini ◽

S. Meuren ◽

C. H. Keitel

Keyword(s):

Strong Field ◽

Field Approximation ◽

Constant Field