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A generalized mathematical framework for the calcium control hypothesis describes weight-dependent synaptic

Toviah Moldwin1, Li Shay Azran2,3, Idan Segev2,4

  • 1Edmond and Lily Safra Center for Brain Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel. toviah.moldwin@mail.huji.ac.il.

Journal of Computational Neuroscience
|March 18, 2025
PubMed
Summary

A new mathematical framework, the fixed point - learning rate (FPLR) model, explains how calcium concentrations in the brain control synaptic plasticity for learning and memory storage.

Keywords:
BTSPCalciumCalcium-based plasticityNeural plasticityPlace cellsPlace fieldsProtein synthesisSTDPSynaptic plasticitySynaptic weights

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Area of Science:

  • Neuroscience
  • Computational Neuroscience
  • Mathematical Biology

Background:

  • Synaptic plasticity, including long-term potentiation (LTP) and long-term depression (LTD), is crucial for learning and memory.
  • Calcium ion ([Ca2+]) concentrations in dendritic spines are known regulators of synaptic plasticity.
  • Existing models like SBC and GB describe calcium-based plasticity, but a generalized framework is needed.

Purpose of the Study:

  • To introduce a generalized mathematical model for calcium-based synaptic plasticity, termed the fixed point - learning rate (FPLR) framework.
  • To provide a unified and flexible model that can incorporate diverse experimental findings in synaptic plasticity.
  • To investigate the implications of the FPLR framework for understanding weight-dependence in various plasticity induction protocols.

Main Methods:

  • Developed a generalized mathematical model (FPLR framework) unifying aspects of SBC and GB models.
  • The FPLR model links synaptic weight changes to calcium concentration, defining a fixed point and a calcium-dependent learning rate.
  • Incorporated protein synthesis into the model to capture late-phase plasticity stabilization.

Main Results:

  • The FPLR framework offers a direct interpretation: calcium concentration dictates the target synaptic weight and the rate of change.
  • The model accommodates various experimental observations, including plasticity in cerebellar Purkinje cells and calcium levels with no plasticity.
  • Demonstrated that the asymptotic nature of FPLR leads to weight-dependent plasticity for protocols like spike-timing-dependent plasticity (STDP) and explains behavioral time scale plasticity (BTSP).

Conclusions:

  • The FPLR framework provides a powerful and flexible tool for modeling calcium-based synaptic plasticity.
  • This model offers new insights into the mechanisms underlying learning and memory at the synaptic level.
  • The FPLR framework successfully explains previously observed weight-dependencies in synaptic plasticity, unifying diverse experimental data.