scholarly journals Behavioral Time Scale Plasticity of Place Fields: Mathematical Analysis

2021 ◽  
Vol 15 ◽  
Author(s):  
Ian Cone ◽  
Harel Z. Shouval
Keyword(s):  
Synaptic Plasticity ◽  
Fixed Points ◽  
Time Scales ◽  
Convergence Time ◽  
Simple Mathematical Model ◽  
System Parameters ◽  
Temporal Correlations ◽  
Postsynaptic Activity ◽  
Naturally Occurring ◽  
Place Fields

Traditional synaptic plasticity experiments and models depend on tight temporal correlations between pre- and postsynaptic activity. These tight temporal correlations, on the order of tens of milliseconds, are incompatible with significantly longer behavioral time scales, and as such might not be able to account for plasticity induced by behavior. Indeed, recent findings in hippocampus suggest that rapid, bidirectional synaptic plasticity which modifies place fields in CA1 operates at behavioral time scales. These experimental results suggest that presynaptic activity generates synaptic eligibility traces both for potentiation and depression, which last on the order of seconds. These traces can be converted to changes in synaptic efficacies by the activation of an instructive signal that depends on naturally occurring or experimentally induced plateau potentials. We have developed a simple mathematical model that is consistent with these observations. This model can be fully analyzed to find the fixed points of induced place fields and how these fixed points depend on system parameters such as the size and shape of presynaptic place fields, the animal's velocity during induction, and the parameters of the plasticity rule. We also make predictions about the convergence time to these fixed points, both for induced and pre-existing place fields.

scholarly journals Behavioral Time Scale Plasticity of Place Fields: Mathematical Analysis

2020 ◽  
Author(s):  
Harel Z. Shouval ◽  
Ian Cone
Keyword(s):  
Mathematical Model ◽  
Synaptic Plasticity ◽  
Fixed Points ◽  
Time Scales ◽  
Simple Mathematical Model ◽  
System Parameters ◽  
Temporal Correlations ◽  
Postsynaptic Activity ◽  
Naturally Occurring ◽  
Place Fields

AbstractTraditional synaptic plasticity experiments and models depend on tight temporal correlations between pre- and postsynaptic activity. These tight temporal correlations, on the order of tens of milliseconds, are incompatible with significantly longer behavioral time scales, and as such might not be able to account for plasticity induced by behavior. Indeed, recent findings in hippocampus suggest that rapid, bidirectional synaptic plasticity which modifies place fields in CA1 operates at behavioral time scales. These experimental results suggest that presynaptic activity generates synaptic eligibility traces both for potentiation and depression, which last on the order of seconds. These traces can be converted to changes in synaptic efficacies by the activation of an instructive signal that depends on naturally occurring or experimentally induced plateau potentials. We have developed a simple mathematical model that is consistent with these observations. This model can be fully analyzed to find the fixed points of induced place fields, the convergence to these fixed points, and how these fixed points depend on system parameters such as the size and shape of presynaptic place fields, the animal’s velocity, and the parameters of the plasticity rule.

scholarly journals Synapse Plasticity in Motor, Sensory, and Limbo-Prefrontal Cortex Areas as Measured by Degrading Axon Terminals in an Environment Model of Gerbils (Meriones unguiculatus)

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Janina Neufeld ◽  
Gertraud Teuchert-Noodt ◽  
Keren Grafen ◽  
York Winter ◽  
A. Veronica Witte
Keyword(s):  
Prefrontal Cortex ◽  
Synaptic Plasticity ◽  
Meriones Unguiculatus ◽  
Secondary Lysosome ◽  
Axon Terminals ◽  
Environment Model ◽  
Naturally Occurring ◽  
Synapse Plasticity ◽  
Map Adaptation ◽  
Cortical Map

Still little is known about naturally occurring synaptogenesis in the adult neocortex and related impacts of epigenetic influences. We therefore investigated (pre)synaptic plasticity in various cortices of adult rodents, visualized by secondary lysosome accumulations (LA) in remodeling axon terminals. Twenty-two male gerbils from either enriched (ER) or impoverished rearing (IR) were used for quantification of silver-stained LA. ER-animals showed rather low LA densities in most primary fields, whereas barrel and secondary/associative cortices exhibited higher densities and layer-specific differences. In IR-animals, these differences were evened out or even inverted. Basic plastic capacities might be linked with remodeling of local intrinsic circuits in the context of cortical map adaptation in both IR- and ER-animals. Frequently described disturbances due to IR in multiple corticocortical and extracortical afferent systems, including the mesocortical dopamine projection, might have led to maladaptations in the plastic capacities of prefronto-limbic areas, as indicated by different LA densities in IR- compared with ER-animals.

The Neuromolecular Brain

Neuro ◽  
2013 ◽  
Author(s):  
Nikolas Rose ◽  
Joelle M. Abi-Rached
Keyword(s):  
Gene Expression ◽  
Synaptic Plasticity ◽  
Learning And Memory ◽  
Time Scales ◽  
Molecular Level ◽  
Human Life ◽  
Neuronal Circuits ◽  
Molecular Processes ◽  
Nerve Development ◽  
The Brain

This chapter examines the neuromolecular and plastic brain. Ideas about plasticity and the openness of brains to environment influences, from initial evidence about nerve development, through the recognition that synaptic plasticity was the very basis of learning and memory, to evidence about the influence of environment on gene expression and the persistence throughout life of the capacity to make new neurons—all this made the neuromolecular brain seem exquisitely open to its milieu, with changes at the molecular level occurring throughout the course of a human life and thus shaping the growth, organization, and regeneration of neurons and neuronal circuits at time scales from the millisecond to the decade. This was an opportunity to explore the myriad ways in which the milieu got “under the skin,” implying an openness of these molecular processes of the brain to biography, sociality, and culture, and hence perhaps even to history and politics.

scholarly journals Monotone flows and fixed points for dynamic systems on time scales

1994 ◽  
Vol 28 (1-3) ◽  
pp. 185-189 ◽  
Author(s):  
V. Lakshmikantham ◽  
B. Kaymakçalan
Keyword(s):  
Fixed Points ◽  
Time Scales ◽  
Dynamic Systems

scholarly journals Hippocampal Spine Head Sizes are Highly Precise

2015 ◽  
Author(s):  
Thomas M Bartol ◽  
Cailey Bromer ◽  
Justin P Kinney ◽  
Michael A Chirillo ◽  
Jennifer N Bourne ◽  
...  
Keyword(s):  
Synaptic Plasticity ◽  
Strong Correlation ◽  
Time Window ◽  
Synaptic Activity ◽  
Electron Microscopic ◽  
Synaptic Contacts ◽  
Amount Of Information ◽  
Spine Head ◽  
Postsynaptic Activity

Hippocampal synaptic activity is probabilistic and because synaptic plasticity depends on its history, the amount of information that can be stored at a synapse is limited. The strong correlation between the size and efficacy of a synapse allowed us to estimate the precision of synaptic plasticity. In an electron microscopic reconstruction of hippocampal neuropil we found single axons making two or more synaptic contacts onto the same dendrites which would have shared histories of presynaptic and postsynaptic activity. The postsynaptic spine heads, but not the spine necks, of these pairs were nearly identical in size. The precision is much greater than previous estimates and requires postsynaptic averaging over a time window many seconds to minutes in duration depending on the rate of input spikes and probability of release.

scholarly journals Competition for synaptic building blocks shapes synaptic plasticity

2017 ◽  
Author(s):  
Jochen Triesch ◽  
Anh Duong Vo ◽  
Anne-Sophie Hafner
Keyword(s):  
Mathematical Model ◽  
Synaptic Plasticity ◽  
Learning And Memory ◽  
Time Scales ◽  
Building Blocks ◽  
Neurotransmitter Receptors ◽  
Rapid Exchange ◽  
Heterosynaptic Plasticity ◽  
Spontaneous Fluctuations ◽  
Receptor Pool

AbstractChanges in the efficacies of synapses are thought to be the neurobiological basis of learning and memory. The efficacy of a synapse depends on its current number of neurotransmitter receptors. Recent experiments have shown that these receptors are highly dynamic, moving back and forth between synapses on time scales of seconds and minutes. This suggests spontaneous fluctuations in synaptic efficacies and a competition of nearby synapses for available receptors. Here we propose a mathematical model of this competition of synapses for neurotransmitter receptors from a local dendritic pool. Using minimal assumptions, the model produces a fast multiplicative scaling behavior of synapses. Furthermore, the model explains a transient form of heterosynaptic plasticity and predicts that its amount is inversely related to the size of the local receptor pool. Overall, our model reveals logistical tradeoffs during the induction of synaptic plasticity due to the rapid exchange of neurotransmitter receptors between synapses.

Modeling Synaptic Plasticity in Conjunction with the Timing of Pre- and Postsynaptic Action Potentials

2000 ◽  
Vol 12 (2) ◽  
pp. 385-405 ◽  
Author(s):  
Werner M. Kistler ◽  
J. Leo van Hemmen
Keyword(s):  
Synaptic Plasticity ◽  
Action Potentials ◽  
Neuron Model ◽  
Temporal Distribution ◽  
Temporal Coding ◽  
Synaptic Action ◽  
Temporal Correlations ◽  
Spiking Neuron Model ◽  
Experimental Findings

We present a spiking neuron model that allows for an analytic calculation of the correlations between pre- and postsynaptic spikes. The neuron model is a generalization of the integrate-and-fire model and equipped with a probabilistic spike-triggering mechanism. We show that under certain biologically plausible conditions, pre- and postsynaptic spike trains can be described simultaneously as an inhomogeneous Poisson process. Inspired by experimental findings, we develop a model for synaptic long-term plasticity that relies on the relative timing of pre- and post-synaptic action potentials. Being given an input statistics, we compute the stationary synaptic weights that result from the temporal correlations between the pre- and postsynaptic spikes. By means of both analytic calculations and computer simulations, we show that such a mechanism of synaptic plasticity is able to strengthen those input synapses that convey precisely timed spikes at the expense of synapses that deliver spikes with a broad temporal distribution. This may be of vital importance for any kind of information processing based on spiking neurons and temporal coding.

Synchronized Dynamics of Hyperchaotic Flows via an Improved Finite-Time Adaptive Controller Design

2020 ◽  
Vol 48 ◽  
pp. 49-62
Author(s):  
Edwin A. Umoh ◽  
Ogechukwu N. Iloanusi
Keyword(s):  
Uniform Convergence ◽  
Finite Time ◽  
Controller Design ◽  
Adaptive Controller ◽  
Coupled Systems ◽  
Convergence Time ◽  
Adaptive Controllers ◽  
System Parameters ◽  
Unknown System ◽  
Asymptotic Convergence Rate

We proposed a performance-improved finite-time adaptive synchronizing controllers and parameter update laws for coupling the dynamics of identical 4D hyperchaotic flows. The four-dimensional hyperchaotic flows consists of 12 terms and 11 system parameters and possessed very rich dynamics and larger parameter space. The performance of the proposed finite-time adaptive synchronizing controller was enhanced by the introduction of scalar quantities known as global controller strength coefficients and parameter update strength coefficients respectively, into the algebraically-derived control and parameter update structures, in order to constrained overshoots of the trajectories of the coupled systems and accelerate their rate of uniform convergence in finite time. Numerical simulation results obtained confirmed that the uniform asymptotic convergence rate of the coupling trajectories was faster, while the parameter update laws give a stable identification of the unknown system parameters in a global synchronizing time. A comparative analysis of the convergence time of the proposed adaptive controllers with recently published works indicated that the proposed controller has faster rates of uniform convergence of system trajectories.

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