Abstract
Excitatory synaptic signaling in cortical circuits is thought to be metabolically expensive. Two fundamental brain functions, learning and memory, are associated with long-term synaptic plasticity, but we know very little about energetics of these slow biophysical processes. This study investigates the energy requirement of information storing in plastic synapses for an extended version of BCM plasticity with a decay term, stochastic noise, and nonlinear dependence of neuron’s firing rate on synaptic current (adaptation). It is shown that synaptic weights in this model exhibit bistability. In order to analyze the system analytically, it is reduced to a simple dynamic mean-field for a population averaged plastic synaptic current. Next, using the concepts of nonequilibrium thermodynamics, we derive the energy rate (entropy production rate) for plastic synapses and a corresponding Fisher information for coding presynaptic input. That energy, which is of chemical origin, is primarily used for battling fluctuations in the synaptic weights and presynaptic firing rates, and it increases steeply with synaptic weights, and more uniformly though nonlinearly with presynaptic firing. At the onset of synaptic bistability, Fisher information and memory lifetime both increase sharply, by a few orders of magnitude, but the plasticity energy rate changes only mildly. This implies that a huge gain in the precision of stored information does not have to cost large amounts of metabolic energy, which suggests that synaptic information is not directly limited by energy consumption. Interestingly, for very weak synaptic noise, such a limit on synaptic coding accuracy is imposed instead by a derivative of the plasticity energy rate with respect to the mean presynaptic firing, and this relationship has a general character that is independent of the plasticity type. An estimate for primate neocortex reveals that a relative metabolic cost of BCM type synaptic plasticity, as a fraction of neuronal cost related to fast synaptic transmission and spiking, can vary from negligible to substantial, depending on the synaptic noise level and presynaptic firing.
Highlights
Information and energy are intimately related for all physical systems because information has to be written on some physical substrate which always comes at some energy cost (Landauer 1961; Bennett 1982; Leff and Rex 1990; Action Editor: Stefano Fusi This file contains the details of some calculations. (PDF)Berut et al 2012; Parrondo et al 2015)
(b) Energy rate of plastic synapses increases nonlinearly both with the presynaptic firing rate (Figs. 11 and 14) and with average synaptic current or weights (Figs. 13 and 14)
The accuracy of stored information about presynaptic input can increase by several orders of magnitude with only a mild increase in the plasticity energy rate at the onset of bistability (Figs. 17 and 18)
Summary
Information and energy are intimately related for all physical systems because information has to be written on some physical substrate which always comes at some energy cost (Landauer 1961; Bennett 1982; Leff and Rex 1990; Action Editor: Stefano Fusi This file contains the details of some calculations. (PDF)Berut et al 2012; Parrondo et al 2015). Experimental studies (Shulman et al 2004; Logothetis 2008; Alle et al 2009), as well as theoretical calculations based on data (Harris et al 2012; Karbowski 2012), indicate that fast synaptic signaling, i.e. synaptic transmission, together with neuron’s action potentials are the major consumers of metabolic energy. This type of energy use is of electric origin, and is caused by flows of electric charge due to voltage and concentration gradients. This very pumping of electric charge requires large amounts of energy
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