Related papers: Nerve Impulses Have Three Interdependent Functions…
Mathematical models describing the signals propagating in nerve fibres are described. The emphasis is on the mathematical structures of governing equations while the extremely rich physiological aspects are here not analysed. Based on…
The Hodgkin-Huxley model of nerve pulse propagation relies on ion currents through specific resistors called ion channels. We discuss a number of classical thermodynamic findings on nerves that are not contained in this classical theory.…
Neuronal cells present periodic trains of localized voltage spikes involving a large amount of different ionic channels. A relevant question is whether this is a cooperative effect or it could also be an intrinsic property of individual…
A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or an object part. We use the length of the activity vector to represent the probability that the…
The propagation of an action potential (AP) in a nerve fibre is accompanied by mechanical and thermal effects. In this paper an attempt is made to build up a mathematical model which couples the AP with a possible pressure wave (PW) in the…
We investigate the effects of a quantum entanglement regime within an ion conducting molecule (ion channel) of the neuronal plasma membrane on the onset dynamics of propagating nerve pulses (action potentials). In particular, we model the…
Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine…
How is reliable physiological function maintained in cells despite considerable variability in the values of key parameters of multiple interacting processes that govern that function? Here we use the classic Hodgkin-Huxley formulation of…
In this paper the authors extend [1] and provide more details of how the brain may act like a quantum computer. In particular, positing the difference between voltages on two axons as the environment for ions undergoing spatial…
Both action potentials and mechanosensitive signalling are an important communication mechanisms in plants. Considering an information theoretic framework, this paper explores the effective range of multiple action potentials for a long…
The initial version of the planned paper has gone through a major revision in 2025. First, the paper ended up growing a bit too long, and as a result of that, we decided to split it into two parts. The first part focuses on the model for…
We investigate states of enhanced activity in a biological neuronal network composed of pulse-coupled oscillators. The synaptic couplings between the neurons are dynamic, modeling spike time dependent plasticity. The network exhibits…
The action potential constitutes the digital component of the signaling dynamics of neurons. But the biophysical nature of the full-time course of the action potential associated with changes in membrane potential is mathematically distinct…
Gap junctions are channels in cell membranes allowing ions to pass directly between cells. They connect cells throughout the body, including heart myocytes, neurons, and astrocytes. Propagation mediated by gap junctions can be passive or…
Mathematical models for the generation of the action potential can improve the understanding of physiological mechanisms that are consequence of the electrical activity in neurons. In such models, some equations involving empirically…
In this pedagogical paper a coherent explanation of the resting potential of nerve cells is given in terms of its determining factors. These are the currents of active transport of the ions to which the membrane is permeable, their membrane…
Fundamentally, action potentials in the squid axon are consequence of the entrance of sodium ions during the depolarization of the rising phase of the spike mediated by the outflow of potassium ions during the hyperpolarization of the…
The in silico simulations are widely used in contemporary systems biology including the analysis of nerve pulse propagation. As known from numerous experiments, the propagation of an action potential is accompanied by mechanical and thermal…
The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and…
Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant…