Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism

Abstract

Markov kinetic models were used to synthesize a complete description of synaptic transmission, including opening of voltage-dependent channels in the presynaptic terminal, release of neurotransmitter, gating of postsynaptic receptors, and activation of second-messenger systems. These kinetic schemes provide a more general framework for modeling ion channels than the Hodgkin-Huxley formalism, supporting a continuous spectrum of descriptions ranging from the very simple and computationally efficient to the highly complex and biophysically precise. Examples are given of simple kinetic schemes based on fits to experimental data that capture the essential properties of voltage-gated, synaptic and neuromodulatory currents. The Markov formalism allows the dynamics of ionic currents to be considered naturally in the larger context of biochemical signal transduction. This frame, work can facilitate the integration of a wide range of experimental data and promote consistent theoretical analysis of neural mechanisms from molecular interactions to network computations.

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

“…An incoming spike due to the firing of a pre-synaptic neuron causes the release of neurotransmitters that diffuse across the synaptic gap and bind to receptors in the cell membrane of the post-synaptic neuron. This induces a time-dependent change in the membrane conductance that may be modelled as a second-order Markov scheme leading to the so-called alpha function response (Destexhe et al 1994). Combining this with the effects of discrete delays due to the …”

A Geometric Comparison of Single Chain Multi-State Models of Ion Channel Gating

“…Hodgkin and Huxley used specific forms for how the rate functions depend on the voltage, but we will name any model of the form (14) as an Hodgkin-Huxley type chain, or simply HH chain. The equivalence between these two models as described above was first noted by Fitzhugh (1965) although with some notational differences, and has been described by others, for example, Destexhe et al (1994). Fitzhugh also noted that this equivalence is not dependent on the rates (α and β) being constants.…”

“…Such models can also be used for ligand-dependent channels (Destexhe et al, 1994). Thermodynamic arguments (Eyring et al, 1949;Tsien and Noble, 1969;Hill and Chen, 1972;Hille, 1992) relate the transition between states to either a charge surmounting a free-energy barrier, or rotation of a rigid dipole.…”

Twenty years of ModelDB and beyond: building essential modeling tools for the future of neuroscience

“…Hodgkin and Huxley 1952, which helped launch computational neuroscience, is cited by more ModelDB models (185) than any other model. The next three models most cited by other ModelDB models are from three distinct areas of research: kinetic synaptic models for networks (ModelDB 18500; multiple papers including Destexhe et al 1994; 74 citing models, 372 downloads), the Izhikevich model for spiking neurons (ModelDB 39948; multiple papers beginning with Izhikevich 2003; 73 citing models, 1219 downloads), and a model investigating the role of morphology (ModelDB 2488; Mainen and Sejnowski 1996; 73 citing models, 1438 downloads). Citations counts are as of August 1, 2016; download counts are as of July 20, 2016 and count only unique non-search engine IP addresses.…”