Abstract
Theoretical and computational frameworks for synaptic plasticity and learning have a long and cherished history, with few parallels within the well-established literature for plasticity of voltage-gated ion channels. In this study, we derive rules for plasticity in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, and assess the synergy between synaptic and HCN channel plasticity in establishing stability during synaptic learning. To do this, we employ a conductance-based model for the hippocampal pyramidal neuron, and incorporate synaptic plasticity through the well-established Bienenstock-Cooper-Munro (BCM)-like rule for synaptic plasticity, wherein the direction and strength of the plasticity is dependent on the concentration of calcium influx. Under this framework, we derive a rule for HCN channel plasticity to establish homeostasis in synaptically-driven firing rate, and incorporate such plasticity into our model. In demonstrating that this rule for HCN channel plasticity helps maintain firing rate homeostasis after bidirectional synaptic plasticity, we observe a linear relationship between synaptic plasticity and HCN channel plasticity for maintaining firing rate homeostasis. Motivated by this linear relationship, we derive a calcium-dependent rule for HCN-channel plasticity, and demonstrate that firing rate homeostasis is maintained in the face of synaptic plasticity when moderate and high levels of cytosolic calcium influx induced depression and potentiation of the HCN-channel conductance, respectively. Additionally, we show that such synergy between synaptic and HCN-channel plasticity enhances the stability of synaptic learning through metaplasticity in the BCM-like synaptic plasticity profile. Finally, we demonstrate that the synergistic interaction between synaptic and HCN-channel plasticity preserves robustness of information transfer across the neuron under a rate-coding schema. Our results establish specific physiological roles for experimentally observed plasticity in HCN channels accompanying synaptic plasticity in hippocampal neurons, and uncover potential links between HCN-channel plasticity and calcium influx, dynamic gain control and stable synaptic learning.
Highlights
Theoretical and computational frameworks for synaptic plasticity have a long and cherished history, with proven utilities ranging from understanding the underlying biophysical and biochemical mechanisms to solving complex engineering problems [1,2,3,4,5,6,7,8]
What changes in the h conductance are required for it to maintain firing rate homeostasis, when it is perturbed by bidirectional synaptic plasticity? What should be the relationship between HCN channel plasticity and synaptic plasticity for the former to counteract the perturbation in the input-output relationship that was imposed by the latter? To answer these questions, we employed a conductance-based model of a hippocampal pyramidal neuron with ion channel kinetics derived from experimental measurements and inserted a synapse made of colocalized AMPAR-NMDAR in the model [13]
This constitutes a perturbation in the firing frequencies (FF) of the neuron for given synaptic drive, and activity homeostasis requires that FF returned to its target levels for all stimulus frequencies (SF)
Summary
Theoretical and computational frameworks for synaptic plasticity have a long and cherished history, with proven utilities ranging from understanding the underlying biophysical and biochemical mechanisms to solving complex engineering problems [1,2,3,4,5,6,7,8]. A prominent postulate, with a large body of experimental and theoretical evidence in support, is that neural systems accomplish such stability through concurrent regulatory mechanisms that recruit plasticity in synaptic and/or intrinsic neuronal properties [1,9,10,11,12,13,14,15,16,17]. We quantitatively examine the validity of this postulate employing conductance-based models and biophysically rooted plasticity rules for the h conductance. We employed the answer to this question to arrive at a calciumdependent plasticity rule (CDPR) for the h conductance such that firing rate homeostasis was maintained when h-channel plasticity accompanied synaptic plasticity. We show that the co-occurrence of the two forms of plasticity enabled retention of synaptic weights within a useful dynamic range, introduced metaplasticity in the synaptic learning rule so that the positive feedback introduced by repeated synaptic potentiation was nullified, and facilitated reliable rate-based information transfer across the neuron when faced with positive feedback introduced by repeated synaptic potentiation
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