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Many aspects of the brain’s design can be understood as the result of evolutionary drive toward metabolic efficiency. In addition to the energetic costs of neural computation and transmission, experimental evidence indicates that synaptic plasticity is metabolically demanding as well. As synaptic plasticity is crucial for learning, we examine how these metabolic costs enter in learning. We find that when synaptic plasticity rules are naively implemented, training neural networks requires extremely large amounts of energy when storing many patterns. We propose that this is avoided by precisely balancing labile forms of synaptic plasticity with more stable forms. This algorithm, termed synaptic caching, boosts energy efficiency manifold and can be used with any plasticity rule, including back-propagation. Our results yield a novel interpretation of the multiple forms of neural synaptic plasticity observed experimentally, including synaptic tagging and capture phenomena. Furthermore, our results are relevant for energy efficient neuromorphic designs. The brain expends a lot of energy. While the organ accounts for only about 2% of a person’s bodyweight, it is responsible for about 20% of our energy use at rest. Neurons use some of this energy to communicate with each other and to process information, but much of the energy is likely used to support learning. A study in fruit flies showed that insects that learned to associate two stimuli and then had their food supply cut off, died 20% earlier than untrained flies. This is thought to be because learning used up the insects’ energy reserves. If learning a single association requires so much energy, how does the brain manage to store vast amounts of data? Li and van Rossum offer an explanation based on a computer model of neural networks. The advantage of using such a model is that it is possible to control and measure conditions more precisely than in the living brain. Analysing the model confirmed that learning many new associations requires large amounts of energy. This is particularly true if the memories must be stored with a high degree of accuracy, and if the neural network contains many stored memories already. The reason that learning consumes so much energy is that forming long-term memories requires neurons to produce new proteins. Using the computer model, Li and van Rossum show that neural networks can overcome this limitation by storing memories initially in a transient form that does not require protein synthesis. Doing so reduces energy requirements by as much as 10-fold. Studies in living brains have shown that transient memories of this type do in fact exist. The current results hence offer a hypothesis as to how the brain can learn in a more energy efficient way. Energy consumption is thought to have placed constraints on brain evolution. It is also often a bottleneck in computers. By revealing how the brain encodes memories energy efficiently, the current findings could thus also inspire new engineering solutions.

Long-term memories are believed to be stored in the synapses of cortical neuronal networks. However, recent experiments report continuous creation and removal of cortical synapses, which raises the question how memories can survive on such a variable substrate. Here, we study the formation and retention of associative memory in a computational model based on Hebbian cell assemblies in the presence of both synaptic and structural plasticity. During rest periods, such as may occur during sleep, the assemblies reactivate spontaneously, reinforcing memories against ongoing synapse removal and replacement. Brief daily reactivations during rest-periods suffice to not only maintain the assemblies, but even strengthen them, and improve pattern completion, consistent with offline memory gains observed experimentally. While the connectivity inside memory representations is strengthened during rest phases, connections in the rest of the network decay and vanish thus reconciling apparently conflicting hypotheses of the influence of sleep on cortical connectivity.

Hippocampal place cells encode an animal's past, current, and future location through sequences of action potentials generated within each cycle of the network theta rhythm. These sequential representations have been suggested to result from temporally coordinated synaptic interactions within and between cell assemblies. Instead, we find through simulations and analysis of experimental data that rate and phase coding in independent neurons is sufficient to explain the organization of CA1 population activity during theta states. We show that CA1 population activity can be described as an evolving traveling wave that exhibits phase coding, rate coding, spike sequences and that generates an emergent population theta rhythm. We identify measures of global remapping and intracellular theta dynamics as critical for distinguishing mechanisms for pacemaking and coordination of sequential population activity. Our analysis suggests that, unlike synaptically coupled assemblies, independent neurons flexibly generate sequential population activity within the duration of a single theta cycle. When we explore a new place, we naturally create a mental map of the location as we go. This mental map is stored in a region of the brain called the hippocampus, which contains cells called place cells. These cells can carry information about our past, present, and future location in the form of electrical signals. They connect to each other to form networks and it has been proposed that these connections can store the information needed for the mental maps. Real-time maps are represented in the information carried by the electrical signals themselves. A physical location is specified by the individual place cell that is activated, and by the timing of the electrical signal it produces relative to a ‘brain wave’ called the theta rhythm. Brain waves are patterns of electrical signals activated in sets of brain cells and the theta rhythm is produced in the hippocampus of an animal as it explores its surroundings. Previous experiments suggested that when a rat explores an area, several sets of brain cells in the hippocampus are activated in sequence within each cycle of the theta rhythm. As the rat moves forward, the sequence shifts to different sets of cells to reflect the upcoming locations ahead of the rat. It has been thought that these sequences are triggered by the individual connections between the place cells. Here, Chadwick et al. developed mathematical models of the electrical activity in the brains of rats as they explored. They used these models to analyze data from previous experiments and found that the sequences of electrical activity arise from the timing of each cell's activity relative to the theta rhythm, rather than from the connections between the cells. Chadwick et al.'s findings suggest that the mental map may be highly flexible, allowing vast numbers of distinct memories to be stored within the same network of place cells without interference. Future studies will involve investigating the role of brain waves in the forming new mental maps and creating new memories.

Neural computations underlying cognitive functions require calibration of the strength of excitatory and inhibitory synaptic connections and are associated with modulation of gamma frequency oscillations in network activity. However, principles relating gamma oscillations, synaptic strength and circuit computations are unclear. We address this in attractor network models that account for grid firing and theta-nested gamma oscillations in the medial entorhinal cortex. We show that moderate intrinsic noise massively increases the range of synaptic strengths supporting gamma oscillations and grid computation. With moderate noise, variation in excitatory or inhibitory synaptic strength tunes the amplitude and frequency of gamma activity without disrupting grid firing. This beneficial role for noise results from disruption of epileptic-like network states. Thus, moderate noise promotes independent control of multiplexed firing rate- and gamma-based computational mechanisms. Our results have implications for tuning of normal circuit function and for disorders associated with changes in gamma oscillations and synaptic strength. When electrodes are placed on the scalp, or lowered into the brain itself, rhythmic waves of electrical activity are seen that reflect the coordinated firing of large numbers of neurons. The pattern of the waves varies between different brain regions, and according to what the animal or person is doing. During sleep and quiet wakefulness, slower brain waves predominate, whereas faster waves called gamma oscillations emerge during cognition—the act of processing knowledge. Gamma waves can be readily detected in a region of the brain called the medial entorhinal cortex (MEC). This brain region is also known for its role in forming the spatial memories that allow an individual to remember how to navigate around an area they have previously visited. Individual MEC cells increase their firing rates whenever an individual is at specific locations. When these locations are plotted in two dimensions, they form a hexagonal grid: this ‘grid cell map’ enables the animal to keep track of its position as it navigates through its environment. To determine how MEC neurons can simultaneously encode spatial locations and generate the gamma waves implicated in cognition, Solanka et al. have used supercomputing to simulate the activity of more than 1.5 million connections between MEC cells. Changing the strength of these connections had different effects on the ability of the MEC to produce gamma waves or spatial maps. However, adjusting the model to include random fluctuations in neuronal firing, or ‘noise’, was beneficial for both types of output. This is partly because noise prevented neuronal firing from becoming excessively synchronized, which would otherwise have caused seizures. Although noise is generally regarded as disruptive, the results of Solanka et al. suggest that it helps the MEC to perform its two distinct roles. Specifically, the presence of noise enables relatively small changes in the strength of the connections between neurons to alter gamma waves—and thus affect cognition—without disrupting the neurons' ability to encode spatial locations. Given that noise reduces the likelihood of seizures, the results also raise the possibility that introducing noise into the brain in a controlled way could have therapeutic benefits for individuals with epilepsy.

Although it is well known that long-term synaptic plasticity can be expressed both pre- and postsynaptically, the functional consequences of this arrangement have remained elusive. We show that spike-timing-dependent plasticity with both pre- and postsynaptic expression develops receptive fields with reduced variability and improved discriminability compared to postsynaptic plasticity alone. These long-term modifications in receptive field statistics match recent sensory perception experiments. Moreover, learning with this form of plasticity leaves a hidden postsynaptic memory trace that enables fast relearning of previously stored information, providing a cellular substrate for memory savings. Our results reveal essential roles for presynaptic plasticity that are missed when only postsynaptic expression of long-term plasticity is considered, and suggest an experience-dependent distribution of pre- and postsynaptic strength changes. Throughout life, animals must learn how to respond accurately to new sensations and environments, while retaining knowledge of previous experiences. Learning is widely believed to modify the connections (called synapses) between neurons of the cerebral cortex and other brain areas. This process is known as synaptic plasticity. Experimentally, presynaptic and postsynaptic changes have been identified, but it is not known what advantages there are to changing both components when, in principle, changing either might suffice. To investigate this, Costa et al. developed a mathematical model of synaptic plasticity that captured both pre- and postsynaptic changes, based on a number of experiments over the last decade from recordings in the rat sensory cortices. There were two major findings from this model. First, if both presynaptic and postsynaptic changes occur, the modeling results indicated that sensory perception could become more precise, as has been recently found in the rat auditory system. Second, because the details of presynaptic and postsynaptic changes are different, previously triggered changes leave behind a type of memory trace that allows apparently forgotten information to be rapidly relearned. Interestingly, similar asymmetries have been reported in other brain regions. One future challenge is to understand whether these findings constitute a general principle of plasticity in the brain.

Encoding of behavioral episodes as spike sequences during hippocampal theta oscillations provides a neural substrate for computations on events extended across time and space. However, the mechanisms underlying the numerous and diverse experimentally observed properties of theta sequences remain poorly understood. Here we account for theta sequences using a novel model constrained by the septo-hippocampal circuitry. We show that when spontaneously active interneurons integrate spatial signals and theta frequency pacemaker inputs, they generate phase precessing action potentials that can coordinate theta sequences in place cell populations. We reveal novel constraints on sequence generation, predict cellular properties and neural dynamics that characterize sequence compression, identify circuit organization principles for high capacity sequential representation, and show that theta sequences can be used as substrates for association of conditioned stimuli with recent and upcoming events. Our results suggest mechanisms for flexible sequence compression that are suited to associative learning across an animal’s lifespan. Nerve cells in the brain exchange information via electrical impulses. In a given brain area, the electrical impulses at any particular moment can be thought of as forming a code that represents an aspect of the outside world. For example, groups of nerve cells in the hippocampus generate a type of code called a theta sequence, which represents a series of recent and upcoming events. The specific timing of electrical impulses within a theta sequence is crucial in creating certain types of memory. There are two major classes of nerve cell in the brain: excitatory cells activate impulses in neighbouring cells, while inhibitory cells act to temporarily block impulses from other nerve cells. Many groups, or “circuits”, of nerve cells contain combinations of both cell types to control how and when they communicate. Previous studies show that both types of cell are active within theta sequences, but it is not known precisely how they contribute to creating the sequences. Chadwick et al. developed a new mathematical model that simulates how theta sequences can emerge from circuits of both excitatory and inhibitory nerve cells. The connections between these simulated cells are based on experimental data from real nerve cells in the hippocampus. The model predicts that inhibitory cells play an important role in generating theta sequences by interacting with groups of excitatory cells to coordinate the timing of electrical impulses. Furthermore, the model shows how memory capacity depends on these connections. The next step following on from this work is to carry out experiments to test the model’s predictions. This will include monitoring the same group of nerve cells in multiple different situations to find out how their theta sequences change, and recording electrical events in individual nerve cells during theta sequences. If the theory’s predictions are confirmed this would lead to a deeper understanding of how our brains remember sequences of events.

Throughout the brain information is coded in the activity of multiple neurons at once, so called population codes. Population codes are a robust and accurate way of coding information. One can evaluate the quality of population coding by trying to read out the code with a decoder, and estimate the encoded stimulus. In particular when neurons are noisy, coding accuracy has extensively been evaluated in terms of the trial-to-trial variation in the estimate. While most decoders yield unbiased estimators if many neurons are actived, when only a few neurons are active, biases readily emerge. That is, even after averaging, a systematic difference between the true stimulus and its estimate remains. We characterize the shape of this bias for different encoding models (rectified cosine tuning and von Mises functions) and show that it can be both attractive or repulsive for different stimulus values. Biases appear for maximum likelihood and Bayesian decoders. The biases have a non-trivial dependence on noise. We also introduce a technique to estimate the bias and variance of Bayesian least square decoders. The work is of interest to those studying neural populations with a few active neurons.

Growing experimental evidence shows that both homeostatic and Hebbian synaptic plasticity can be expressed presynaptically as well as postsynaptically. In this review, we start by discussing this evidence and methods used to determine expression loci. Next, we discuss the functional consequences of this diversity in pre- and postsynaptic expression of both homeostatic and Hebbian synaptic plasticity. In particular, we explore the functional consequences of a biologically tuned model of pre- and postsynaptically expressed spike-timing-dependent plasticity complemented with postsynaptic homeostatic control. The pre- and postsynaptic expression in this model predicts (i) more reliable receptive fields and sensory perception, (ii) rapid recovery of forgotten information (memory savings), and (iii) reduced response latencies, compared with a model with postsynaptic expression only. Finally, we discuss open questions that will require a considerable research effort to better elucidate how the specific locus of expression of homeostatic and Hebbian plasticity alters synaptic and network computations. This article is part of the themed issue ‘Integrating Hebbian and homeostatic plasticity’.