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 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 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.

scholarly journals Competition for synaptic building blocks shapes synaptic plasticity

eLife ◽  
2018 ◽  
Vol 7 ◽  
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

Changes 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.

scholarly journals Multidimensional generalization of phyllotaxis

2019 ◽  
pp. 153-160 ◽  
Author(s):  
Andrei Lodkin
Keyword(s):  
Mathematical Model ◽  
Fixed Points ◽  
Bifurcation Diagram ◽  
Large Family ◽  
Divergence Angle ◽  
Simple Mathematical Model ◽  
Biological Objects ◽  
Golden Number ◽  
Living Objects

The regular spiral arrangement of various parts of biological objects (leaves, florets, etc.), known as phyllotaxis, could not find an explanation during several centuries. Some quantitative parameters of the phyllotaxis (the divergence angle being the principal one) show that the organization in question is, in a sense, the same in a large family of living objects, and the values of the divergence angle that are close to the golden number prevail. This was a mystery, and explanations of this phenomenon long remained “lyrical”. Later, similar patterns were discovered in inorganic objects. After a series of computer models, it was only in the XXI century that the rigorous explanation of the appearance of the golden number in a simple mathematical model has been given. The resulting pattern is related to stable fixed points of some operator and depends on a real parameter. The variation of this parameter leads to an interesting bifurcation diagram where the limiting object is the SL(2;Z)-orbit of the golden number on the segment [0,1]. We present a survey of the problem and introduce a multidimensional analog of phyllotaxis patterns. A conjecture about the object that plays the role of the golden number is given.

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