Karbowski, J. | bioRxiv Science

bioRxiv2021

Information encoded in volumes and areas of dendritic spines is nearly maximal across mammalian brains

Many experiments suggest that long-term information associated with neuronal memory resides collectively in dendritic spines. However, spines can have a limited size due to metabolic and neuroanatomical constraints, which should effectively limit the amount of encoded information in excitatory synapses. This study investigates how much information can be stored in the population of sizes of dendritic spines, and whether it is optimal in any sense. It is shown here, using empirical data for several mammalian brains across different regions and physiological conditions, that dendritic spines nearly maximize entropy contained in their volumes and surface areas for a given mean size in cortical and hippocampal regions. Although both short- and heavy-tailed fitting distributions approach 90 - 100% of maximal entropy in the majority of cases, the best maximization is obtained primarily for short-tailed gamma distribution. We find that most empirical ratios of standard deviation to mean for spine volumes and areas are in the range 1.0 {+/-} 0.3, which is close to the theoretical optimal ratios coming from entropy maximization for gamma and lognormal distributions. On average, the highest entropy is contained in spine length (4-5 bits per spine), and the lowest in spine volume and area (2 - 3 bits), although the latter two are closer to optimality. In contrast, we find that entropy density (entropy per spine size) is always suboptimal. Our results suggest that spine sizes are almost as random as possible given the constraint on their size, and moreover the general principle of entropy maximization is applicable and potentially useful to information and memory storing in the population of cortical and hippocampal excitatory synapses, and to predicting their morphological properties. Significance statementIt is believed that information related to long-term memory is stored collectively in the parts of excitatory synapses called dendritic spines. But how efficient is the information capacity given synaptic size variability? Generally, the larger this variability the higher entropy (information capacity) of spine population. However, this process comes at some cost, as larger synapses use more metabolic energy and brain tissue, suggesting a benefit-cost trade-off for storing long-term information. We show that volumes and areas of actual spines in many different parts of the brain across different mammals and conditions adjust simultaneously their variable mean and standard deviation values to nearly maximize entropy of their distributions. This suggests that storing capacity of dendritic spines is nearly maximal, despite large variability in their sizes.

neuroscience↗

bioRxiv2020

Energetics of BCM type synaptic plasticity and storing of accurate information

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 neurons 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 relativemetabolic 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.

neuroscience↗