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.

皮质回路中的兴奋性突触信号被认为在代谢上是昂贵的。两种基本的大脑功能，学习和记忆，与长期突触可塑性有关，但我们对这些缓慢的生物物理过程的能量学知之甚少。本研究调查了在具有衰减项、随机噪声和神经元放电率对突触电流（适应）的非线性依赖性的 BCM 可塑性扩展版本中存储在塑料突触中的信息的能量需求。结果表明，该模型中的突触权重表现出双稳态。为了分析性地分析系统，将其简化为群体平均塑性突触电流的简单动态平均场。接下来，使用非平衡热力学的概念，我们推导出塑料突触的能量率（熵产生率）和相应的用于编码突触前输入的 Fisher 信息。这种来自化学的能量主要用于对抗突触权重和突触前放电率的波动，它随着突触权重急剧增加，但随着突触前放电的非线性而更均匀。在突触双稳态开始时，Fisher 信息和记忆寿命都急剧增加，增加了几个数量级，但可塑性能量率变化很小。这意味着存储信息精度的巨大提高不必消耗大量的代谢能量，这表明突触信息不受能量消耗的直接限制。有趣的是，对于非常微弱的突触噪声，这种对突触编码精度的限制是由可塑性能量率相对于平均突触前放电的导数强加的，并且这种关系具有与可塑性类型无关的一般特征。对灵长类新皮质的估计表明，BCM 类型突触可塑性的相对代谢成本，作为与快速突触传递和尖峰相关的神经元成本的一小部分，可以从可忽略不计到大量变化，这取决于突触噪声水平和突触前放电。