Energy Consumption and Entropy Production in a Stochastic Formulation of BCM Learning.

In a series of previous studies, we provided a stochastic description of a theory of synaptic plasticity. This theory, called BCM from the names of the three authors, has been formulated in two ways: the original formulation, where the plasticity threshold is defined as the square of the time-averaged neuronal activity, and a newer formulation, where the plasticity threshold is defined as the time average of the square of the neuronal activity. The newest formulation of the BCM rule of synaptic activity has interesting statistical properties, derived from a risk (or energy) function, the minimization of which leads to seeking of interesting projections in high-dimensional space. Moreover, these two rules, if implemented by a chemical master equation approach, show another interesting difference: the original rule satisfies the detailed balance, whereas the other not. Based on this different behavior, we found a continuous parameterization between these two rules. This parameterization shows a minimum that corresponds to maximum negative eigenvalues of the Jacobian matrix. In addition, the newest rule, due to the fact that it is in a nonequilibrium steady state (NESS), shows a higher level of plasticity than the original rule. This higher level of plasticity has to be interpreted in the framework of open thermodynamical systems and we show that entropy production and energy consumption in the newest rule are both less than in the original BCM rule.

Effect of correlated lateral geniculate nucleus firing rates on predictions for monocular eye closure versus monocular retinal inactivation.

Monocular deprivation experiments can be used to distinguish between different ideas concerning properties of cortical synaptic plasticity. Monocular deprivation by lid suture causes a rapid disconnection of the deprived eye connected to cortical neurons whereas total inactivation of the deprived eye produces much less of an ocular dominance shift. In order to understand these results one needs to know how lid suture and retinal inactivation affect neurons in the lateral geniculate nucleus (LGN) that provide the cortical input. Recent experimental results by Linden showed that monocular lid suture and monocular inactivation do not change the mean firing rates of LGN neurons but that lid suture reduces correlations between adjacent neurons whereas monocular inactivation leads to correlated firing. These, somewhat surprising, results contradict assumptions that have been made to explain the outcomes of different monocular deprivation protocols. Based on these experimental results we modify our assumptions about inputs to cortex during different deprivation protocols and show their implications when combined with different cortical plasticity rules. Using theoretical analysis, random matrix theory and simulations we show that high levels of correlations reduce the ocular dominance shift in learning rules that depend on homosynaptic depression (i.e., Bienenstock-Cooper-Munro type rules), consistent with experimental results, but have the opposite effect in rules that depend on heterosynaptic depression (i.e., Hebbian/principal component analysis type rules).

Recovery from monocular deprivation using binocular deprivation.

Ocular dominance (OD) plasticity is a robust paradigm for examining the functional consequences of synaptic plasticity. Previous experimental and theoretical results have shown that OD plasticity can be accounted for by known synaptic plasticity mechanisms, using the assumption that deprivation by lid suture eliminates spatial structure in the deprived channel. Here we show that in the mouse, recovery from monocular lid suture can be obtained by subsequent binocular lid suture but not by dark rearing. This poses a significant challenge to previous theoretical results. We therefore performed simulations with a natural input environment appropriate for mouse visual cortex. In contrast to previous work, we assume that lid suture causes degradation but not elimination of spatial structure, whereas dark rearing produces elimination of spatial structure. We present experimental evidence that supports this assumption, measuring responses through sutured lids in the mouse. The change in assumptions about the input environment is sufficient to account for new experimental observations, while still accounting for previous experimental results.

Synaptic homeostasis and input selectivity follow from a calcium-dependent plasticity model.

Modifications in the strengths of synapses are thought to underlie memory, learning, and development of cortical circuits. Many cellular mechanisms of synaptic plasticity have been investigated in which differential elevations of postsynaptic calcium concentrations play a key role in determining the direction and magnitude of synaptic changes. We have previously described a model of plasticity that uses calcium currents mediated by N-methyl-D-aspartate receptors as the associative signal for Hebbian learning. However, this model is not completely stable. Here, we propose a mechanism of stabilization through homeostatic regulation of intracellular calcium levels. With this model, synapses are stable and exhibit properties such as those observed in metaplasticity and synaptic scaling. In addition, the model displays synaptic competition, allowing structures to emerge in the synaptic space that reflect the statistical properties of the inputs. Therefore, the combination of a fast calcium-dependent learning and a slow stabilization mechanism can account for both the formation of selective receptive fields and the maintenance of neural circuits in a state of equilibrium.

Converging evidence for a simplified biophysical model of synaptic plasticity.

Different mechanisms that could form the molecular basis for bi-directional synaptic plasticity have been identified experimentally and corresponding biophysical models can be constructed. However, such models are complex and therefore it is hard to deduce their consequences to compare them to existing abstract models of synaptic plasticity. In this paper we examine two such models: a phenomenological one inspired by the phenomena of AMPA receptor insertion, and a more complex biophysical model based on the phenomena of AMPA receptor phosphorylation. We show that under certain approximations both these models can be mapped on to an equivalent, calcium-dependent, differential equation. Intracellular calcium concentration varies locally in each postsynaptic compartment, thus the plasticity rule we extract is a single-synapse rule. We convert this single synapse plasticity equation to a multi-synapse rule by incorporating a model of the NMDA receptor. Finally we suggest a mathematical embodiment of metaplasticity, which is consistent with observations on NMDA receptor properties and dependence on cellular activity. These results, in combination with some of our previous results, produce converging evidence for the calcium control hypothesis including a dependence of synaptic plasticity on the level of intercellular calcium as well as on the temporal pattern of calcium transients.