Introduction to Theoretical Neurobiology

Tuckwell, Henry C.

doi:10.1017/cbo9780511623202

Cited by 470 publications

(208 citation statements)

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“…At the level of the individual neuron, relatively little is known about the computing operations which take place in the dendritic arborization in vivo. Most of our current hypothesis on in vivo mammalian neurons derives from a large body of work made on neuronal modellings or from simulations of more realistic neurons based on morphometric techniques associated with compartmental modelling (see references in Jack et al, 1975;MacGregor, 1987;Tuckwell, 1988;Koch and Segev, 1989;McKenna et al, 1992). In a previous work (Bras etal., 1987a,b), we used a 3D reconstruction computerized microscope station to obtain a high spatial resolution description of the dendritic arborization of brain stem motoneurons.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Geometry and Electrotonic Architecture of Dendritic Arborization of Brain Stem Motoneuron

Bras

Коrogod

Driencourt

et al. 1993

Eur J of Neuroscience

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We describe how the stochastic geometry of dendritic arborization of a single identified motoneuron of the rat affects the local details of its electrotonic structure. After describing the 3D dendritic geometry at high spatial resolution, we simulate the distribution of voltage gradients along dendritic branches under steady-state and transient conditions. We show that local variations in diameters along branches and asymmetric branchings determine the non-monotonous features of the heterogeneous electrotonic structure. This is defined by the voltage decay expressed as a function of the somatofugal paths in physical distances (voltage gradient). The fan-shaped electrotonic structure demonstrates differences between branches which are preserved when simulations are computed from different values of specific membrane resistivity although the absolute value of their voltages is changed. At given distances from soma and over long paths, some branches display similar voltages resulting in their grouping which is also preserved when specific membrane resistivity is changed. However, the mutual relation between branches inside the group is respecified when different values of specific membrane resistivity are used in the simulations. We find that there are some invariant features of the electrotonic structure which are related to the geometry and not to the electrical parameters, while other features are changed by altering the electrical parameters. Under transient conditions, the somatofugal invasion of the dendritic tree by a somatic action potential shifts membrane potentials (above 10 mV) of dendritic paths for unequal distances from the soma during several milliseconds. Electrotonic reconfigurations and membrane shifts might be a mechanism for postsynaptic plasticity.

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Section: Introductionmentioning

confidence: 99%

Stochastic Geometry and Electrotonic Architecture of Dendritic Arborization of Brain Stem Motoneuron

Bras

Коrogod

Driencourt

et al. 1993

Eur J of Neuroscience

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“…Since the input is the same for all DP neurons, their firing rate will also be the same. One obtains (Tuckwell, 1988)

r_{D} = {[τ_{r} + τ_{m} \log (\frac{V_{r} - μ}{V_{t h} - μ})]}^{- 1} Θ (μ - V_{t h}) ​ .

…”

Section: Resultsmentioning

confidence: 99%

Subtractive, divisive and non-monotonic gain control in feedforward nets linearized by noise and delays

Mejías¹,

Payeur²,

Selin³

et al. 2014

Front. Comput. Neurosci.

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The control of input-to-output mappings, or gain control, is one of the main strategies used by neural networks for the processing and gating of information. Using a spiking neural network model, we studied the gain control induced by a form of inhibitory feedforward circuitry—also known as “open-loop feedback”—, which has been experimentally observed in a cerebellum-like structure in weakly electric fish. We found, both analytically and numerically, that this network displays three different regimes of gain control: subtractive, divisive, and non-monotonic. Subtractive gain control was obtained when noise is very low in the network. Also, it was possible to change from divisive to non-monotonic gain control by simply modulating the strength of the feedforward inhibition, which may be achieved via long-term synaptic plasticity. The particular case of divisive gain control has been previously observed in vivo in weakly electric fish. These gain control regimes were robust to the presence of temporal delays in the inhibitory feedforward pathway, which were found to linearize the input-to-output mappings (or f-I curves) via a novel variability-increasing mechanism. Our findings highlight the feedforward-induced gain control analyzed here as a highly versatile mechanism of information gating in the brain.

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“…The equation became one of the most important classes of nonlinear differential equations because of their applicability in chemical kinetics, 36 logistic population growth models, 79 neurophysiology, 80 nuclear reactor theory, 81 the spread of early farming in Europe, 82 and so on.…”

Section: The Fisher's Equationmentioning

confidence: 99%

Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

Loyinmi

Akinfe

2020

Engineering Reports

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In this research work, we propose an unprecedented hybrid algorithm which involves the coupling of a new integral transform, namely, the Elzaki transform and the well‐known homotopy perturbation method called the Elzaki homotopy transformation perturbation method (EHTPM) to solve for the exact solution of three distinct types of Fisher's equation, namely, the Fisher's equation of two cases, the sixth‐order Fisher's equation and the nonlinear diffusion equation of the Fisher type. These equations are prominent in mathematical biology and highly applicable in genetic propagation, population dynamics, stochastic processes, combustion theory, as well as a prototype model for a spreading flame, and so on. The efficacy and authenticity of this method was established via convergence and error analysis, and shows that the solutions obtained from EHTPM are unique and convergent. The results of EHTPM when compared with the exact results, homotopy results, and results from the other existing literature via table of comparison, 3D plots, and the convergence plots validates that EHTPM is an efficient and reliable tool of providing exact solutions to a wider class of nonlinear partial differential equations in a simple and straightforward manner, with no discretization, linearization, computation of Adomian polynomials, and devoid of errors.

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Introduction to Theoretical Neurobiology

Cited by 470 publications

References 0 publications

Stochastic Geometry and Electrotonic Architecture of Dendritic Arborization of Brain Stem Motoneuron

Stochastic Geometry and Electrotonic Architecture of Dendritic Arborization of Brain Stem Motoneuron

Subtractive, divisive and non-monotonic gain control in feedforward nets linearized by noise and delays

Exact solutions to the family of Fisher's reaction‐diffusion equation using Elzaki homotopy transformation perturbation method

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