According to the synaptic tagging-and-capture hypothesis, long-lasting (late-phase) plasticity requires the synthesis of plasticity-related proteins and the setting of a synaptic tag at the stimulated synapse. It has been hypothesized that this tag is implemented by the complex interplay between dendritic spine geometry and the scaffolding protein actin. To test this, we propose a biophysically-grounded model of late-phase synaptic plasticity considering dynamic and stable actin pools and the size of the PSD in the synapse. In our model, the tag corresponds to the imbalance between the spine volume determined by actin and the volume that would be expected for the current PSD size. We demonstrate the viability of the proposed model by showing that it can account for the experimentally observed synaptic plasticity induced by stimulation of a single synapse, as well as tag-resetting protocols, and heterosynaptic plasticity protocols involving two synapses. Moreover, for the interaction of two consecutive stimuli at the same synapse within around up to an hour, plastic changes stack non-linearly, reminiscent of the spacing effect found in learning and memory studies. In summary, our model both matches experiments and extrapolates well to a wide range of stimulation protocols. Thus, it will be ideally suited to serve as a basis to predict the plasticity effects emerging from the complex activity patterns in recurrent networks. ### Competing Interest Statement The authors have declared no competing interest.

The synaptic vesicle cluster (SVC) is an essential component of chemical synapses, which provides neurotransmitter-loaded vesicles during synaptic activity, at the same time as also controlling the local concentrations of numerous exo- and endocytosis cofactors. In addition, the SVC hosts molecules that participate in other aspects of synaptic function, from cytoskeletal components to adhesion proteins, and affects the location and function of organelles such as mitochondria and the endoplasmic reticulum. We argue here that these features extend the functional involvement of the SVC in synapse formation, signalling and plasticity, as well as synapse stabilization and metabolism. We also propose that changes in the size of the SVC coalesce with changes in the postsynaptic compartment, supporting the interplay between pre- and postsynaptic dynamics. Thereby, the SVC could be seen as an 'all-in-one' regulator of synaptic structure and function, which should be investigated in more detail, to reveal molecular mechanisms that control synaptic function and heterogeneity.

Brain machine interfaces (BMIs) can substantially improve the quality of life of elderly or disabled people. However, performing complex action sequences with a BMI system is onerous because it requires issuing commands sequentially. Fundamentally different from this, we have designed a BMI system that reads out mental planning activity and issues commands in a proactive manner. To demonstrate this, we recorded brain activity from freely-moving monkeys performing an instructed task and decoded it with an energy-efficient, small and mobile field-programmable gate array hardware decoder triggering real-time action execution on smart devices. Core of this is an adaptive decoding algorithm that can compensate for the day-by-day neuronal signal fluctuations with minimal re-calibration effort. We show that open-loop planning-ahead control is possible using signals from primary and pre-motor areas leading to significant time-gain in the execution of action sequences. This novel approach provides, thus, a stepping stone towards improved and more humane control of different smart environments with mobile brain machine interfaces.

Our brains process information using a layered hierarchical network architecture, with abundant connections within each layer and sparse long-range connections between layers. As these long-range connections are mostly unchanged after development, each layer has to locally self-organize in response to new inputs to enable information routing between the sparse in- and output connections. Here we demonstrate that this can be achieved by a well-established model of cortical self-organization based on a well-orchestrated interplay between several plasticity processes. After this self-organization, stimuli conveyed by sparse inputs can be rapidly read out from a layer using only very few long-range connections. To achieve this information routing, the neurons that are stimulated form feed-forward projections into the unstimulated parts of the same layer and get more neurons to represent the stimulus. Hereby, the plasticity processes ensure that each neuron only receives projections from and responds to only one stimulus such that the network is partitioned into parts with different preferred stimuli. Along this line, we show that the relation between the network activity and connectivity self-organizes into a biologically plausible regime. Finally, we argue how the emerging connectivity may minimize the metabolic cost for maintaining a network structure that rapidly transmits stimulus information despite sparse input and output connectivity.

Dendritic spines change their size and shape spontaneously, but the function of this remains unclear. Here, we address this in a biophysical model of spine fluctuations, which reproduces experimentally measured spine fluctuations. For this, we characterize size- and shape fluctuations from confocal microscopy image sequences using autoregressive models and a new set of shape descriptors derived from circular statistics. Using the biophysical model, we extrapolate into longer temporal intervals and find the presence of 1/f noise. When investigating its origins, the model predicts that the actin dynamics underlying shape fluctuations self-organizes into a critical state, which creates a fine balance between static actin filaments and free monomers. In a comparison against a non-critical model, we show that this state facilitates spine enlargement, which happens after LTP induction. Thus, ongoing spine shape fluctuations might be necessary to react quickly to plasticity events.

Summary It is known that dendritic spines change their size and shape spontaneously and sometimes to a large degree, but the function of this remains unclear. Here, we quantify these changes using time-series analysis of confocal data and demonstrate that spine size can follow different autoregressive integrated moving average (ARIMA) models and that shape- and size-changes are not correlated. We capture this behavior with a biophysical model, based on the spines’ actin dynamics, and find the presence of 1 /f noise. When investigating its origins, the model predicts that actin in the dendritic spines self-organizes into a critical state, which creates a fine balance between static actin filaments and free monomers. We speculate that such a balance might be functionally beneficially to allow a spine to quickly reconfigure itself after LTP induction.

Dendritic spines are the morphological basis of excitatory synapses in the cortex and their size and shape correlates with functional synaptic properties. Recent experiments show that spines exhibit large shape fluctuations that are not related to activity-dependent plasticity but nonetheless might influence memory storage at their synapses. To investigate the determinants of such spontaneous fluctuations, we propose a mathematical model for the dynamics of the spine shape and analyze it in 2D --- related to experimental microscopic imagery --- and in 3D. We show that the spine shape is governed by a local imbalance between membrane tension and the expansive force from actin bundles that originates from discrete actin polymerization foci. Experiments have shown that only few such polymerization foci co-exist at any time in a spine, each having limited life time. The model shows that the momentarily existing set of such foci pushes the membrane along certain directions until foci are replaced and other directions may now be affected. We explore these relations in depth and use our model to predict shape and temporal characteristics of spines from the different biophysical parameters involved in actin polymerization. Approximating the model by a single recursive equation we finally demonstrate that the temporal evolution of the number of active foci is sufficient to predict the size of the model-spines. Thus, our model provides the first platform to study the relation between molecular and morphological properties of the spine with a high degree of biophysical detail.

The distributional hypothesis states that the meaning of a concept is defined through the contexts it occurs in. In practice, often word co-occurrence and proximity are analyzed in text corpora for a given word to obtain a real-valued semantic word vector, which is taken to (at least partially) encode the meaning of this word. Here we transfer this idea from text to images, where pre-assigned labels of other objects or activations of convolutional neural networks serve as context. We propose a simple algorithm that extracts and processes object contexts from an image database and yields semantic vectors for objects. We show empirically that these representations exhibit on par performance with state-of-the-art distributional models over a set of conventional objects. For this we employ well-known word benchmarks in addition to a newly proposed object-centric benchmark.

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.

The connectivity of the brain is continuously adjusted to new environmental influences by several activity-dependent adaptive processes. The most investigated adaptive mechanism is activity-dependent functional or synaptic plasticity regulating the transmission efficacy of existing synapses. Another important but less prominently discussed adaptive process is structural plasticity, which changes the connectivity by the formation and deletion of synapses. In this review, we show, based on experimental evidence, that structural plasticity can be classified similar to synaptic plasticity into two categories: (i) Hebbian structural plasticity, which leads to an increase (decrease) of the number of synapses during phases of high (low) neuronal activity and (ii) homeostatic structural plasticity, which balances these changes by removing and adding synapses. Furthermore, based on experimental and theoretical insights, we argue that each type of structural plasticity fulfills a different function. While Hebbian structural changes enhance memory lifetime, storage capacity, and memory robustness, homeostatic structural plasticity self-organizes the connectivity of the neural network to assure stability. However, the link between functional synaptic and structural plasticity as well as the detailed interactions between Hebbian and homeostatic structural plasticity are more complex. This implies even richer dynamics requiring further experimental and theoretical investigations.

Cortical connectivity emerges from the permanent interaction between neuronal activity and synaptic as well as structural plasticity. An important experimentally observed feature of this connectivity is the distribution of the number of synapses from one neuron to another, which has been measured in several cortical layers. All of these distributions are bimodal with one peak at zero and a second one at a small number (3-8) of synapses. In this study, using a probabilistic model of structural plasticity, which depends on the synaptic weights, we explore how these distributions can emerge and which functional consequences they have. We find that bimodal distributions arise generically from the interaction of structural plasticity with synaptic plasticity rules that fulfill the following biological realistic constraints: First, the synaptic weights have to grow with the postsynaptic activity. Second, this growth curve and/or the input-output relation of the postsynaptic neuron have to change sub-linearly (negative curvature). As most neurons show such input-output-relations, these constraints can be fulfilled by many biological reasonable systems. Given such a system, we show that the different activities, which can explain the layer-specific distributions, correspond to experimentally observed activities. Considering these activities as working point of the system and varying the pre- or postsynaptic stimulation reveals a hysteresis in the number of synapses. As a consequence of this, the connectivity between two neurons can be controlled by activity but is also safeguarded against overly fast changes. These results indicate that the complex dynamics between activity and plasticity will, already between a pair of neurons, induce a variety of possible stable synaptic distributions, which could support memory mechanisms.

Most of the excitatory cortical synapses reside on dendritic spines. Although these spines undergo a remarkably high turnover [1,2], they have been shown to be involved in learning and long-term memory. Along this line, it is unclear how information is preserved while its substrate (synapses or spines) is permanently changing. Here, we use a simple stochastic model of structural plasticity to investigate this phenomenon : We assume a certain number of potential synaptic locations from one neuron to another. At those locations, synapses (spines) are created with a constant probability and removed with a probability depending on the number of existing synapses and the stimulation of the neurons. From these two probabilities, the stationary distribution of the number of synapses between two neurons can be calculated. Experimental measurements of these stationary probability distributions in the cortex show that the majority of connections has either zero or multiple synapses while one or two contacts are very improbable [e.g., [3-5]]. Using information theoretic measures we show that, in our model, such bimodal distributions enable information storage over time scales many orders of magnitudes higher than the involved probabilities. Thus, in this system the conflict of rapid spine turnover (probabilities) and long-term memory is resolved by storing the information collaboratively in multiple synapses. In the following, we will consider the bimodal stationary distributions as the working point of the system. Then, we can model external signals, as, e.g., increased or decreased activities during learning, as changes of the removal probabilities and stationary distributions (e.g., mediated by synaptic plasticity [6]). For instance, for learning signals resulting to unimodal stationary distributions (only connected or only unconnected), we find that learning is orders of magnitude faster than forgetting. Along this line, we observe that retraining a task does not induce an increased overturn rate as during initial training, which has been similarly observed for dendritic spines in vivo [1,2]. Our results clearly relate the difference in time scales to the shape of the stationary distribution and therefore reveal the functional advantage of the bimodal distribution found in experiment.

A long-standing problem is how memories can be stored for very long times despite the volatility of the underlying neural substrate, most notably the high turnover of dendritic spines and synapses. To address this problem, here we are using a generic and simple probabilistic model for the creation and removal of synapses. We show that information can be stored for several months when utilizing the intrinsic dynamics of multi-synapse connections. In such systems, single synapses can still show high turnover, which enables fast learning of new information, but this will not perturb prior stored information (slow forgetting), which is represented by the compound state of the connections. The model matches the time course of recent experimental spine data during learning and memory in mice supporting the assumption of multi-synapse connections as the basis for long-term storage.

The continuous turnover of synapses observed in cortical networks poses a severe problem for storing long-term memory in the connectivity of these networks. Yet, in this chapter, we demonstrate that this can be resolved by considering connections consisting of multiple synapses. We show that, under certain conditions, the interaction of synaptic and structural plasticity induces a collective dynamics across all synapses between two neurons with stable states at zero and at multiple synapses. This dynamics leads to experimentally observed connectivity and enables long-term information storage despite synaptic turnover. Furthermore, the resulting connectivity can be controlled by external stimulations: very low or high stimulation levels quickly drive the neurons to become connected with zero or multiple synapses, respectively. Using this to actively store information on multisynaptic connections entails that information storage can be orders of magnitude faster than information retention under intermediate stimulation levels.