Arbor is a software library designed for efficient simulation of large-scale networks of biological neurons with detailed morphological structures. It combines customizable neuronal and synaptic mechanisms with high-performance computing, supporting multi-core CPU and GPU systems. In humans and other animals, synaptic plasticity processes play a vital role in cognitive functions, including learning and memory. Recent studies have shown that intracellular molecular processes in dendrites significantly influence single-neuron dynamics. However, for understanding how the complex interplay between dendrites and synaptic processes influences network dynamics, computational modeling is required. To enable the modeling of large-scale networks of morphologically detailed neurons with diverse plasticity processes, we have extended the Arbor library to support simulations of a large variety of spike-driven plasticity paradigms. To showcase the features of the extended framework, we present examples of computational models, beginning with single-synapse dynamics, progressing to multi-synapse rules, and finally scaling up to large recurrent networks. While cross-validating our implementations by comparison with other simulators, we show that Arbor allows simulating plastic networks of multi-compartment neurons at nearly no additional cost in runtime compared to point-neuron simulations. In addition, we demonstrate that Arbor is highly efficient in terms of runtime and memory use as compared to other simulators. Using the extended framework, as an example, we investigate the impact of dendritic structures on network dynamics across a timescale of several hours, finding a relation between the length of dendritic trees and the ability of the network to efficiently store information. By our extension of Arbor, we aim to provide a valuable tool that will support future studies on the impact of synaptic plasticity, especially, in conjunction with neuronal morphology, in large networks.

Ripples are a typical form of neural activity in hippocampal neural networks associated with the replay of episodic memories during sleep as well as sleep-related plasticity and memory consolidation. The emergence of ripples has been observed both dependent as well as independent of input from other brain areas and often coincides with dendritic spikes. Yet, it is unclear how input-evoked and spontaneous ripples as well as dendritic excitability affect plasticity and consolidation. Here, we use mathematical modeling to compare these cases. We find that consolidation as well as the emergence of spontaneous ripples depends on a reliable propagation of activity in feed-forward structures which constitute memory representations. This propagation is facilitated by excitable dendrites, which entail that a few strong synapses are sufficient to trigger neuronal firing. In this situation, stimulation-evoked ripples lead to the potentiation of weak synapses within the feed-forward structure and, thus, to a consolidation of a more general sequence memory. However, spontaneous ripples that occur without stimulation, only consolidate a sparse backbone of the existing strong feed-forward structure. Based on this, we test a recently hypothesized scenario in which the excitability of dendrites is transiently enhanced after learning, and show that such a transient increase can strengthen, restructure and consolidate even weak hippocampal memories, which would be forgotten otherwise. Hence, a transient increase in dendritic excitability would indeed provide a mechanism for stabilizing memories.

Synapses in the brain are highly noisy, which leads to a large trial-by-trial variability. Given how costly synapses are in terms of energy consumption these high levels of noise are surprising. Here we propose that synapses use noise to represent uncertainties about the somatic activity of the postsynaptic neuron. To show this, we developed a mathematical framework, in which the synapse as a whole interacts with the soma of the postsynaptic neuron in a similar way to an agent that is situated and behaves in an uncertain, dynamic environment. This framework suggests that synapses use an implicit internal model of the somatic membrane dynamics that is being updated by a synaptic learning rule, which resembles experimentally well-established LTP/LTD mechanisms. In addition, this approach entails that a synapse utilizes its inherently noisy synaptic release to also encode its uncertainty about the state of the somatic potential. Although each synapse strives for predicting the somatic dynamics of its postsynaptic neuron, we show that the emergent dynamics of many synapses in a neuronal network resolve different learning problems such as pattern classification or closed-loop control in a dynamic environment. Hereby, synapses coordinate themselves to represent and utilize uncertainties on the network level in behaviorally ambiguous situations.

In many situations it is behaviorally relevant for an animal to respond to co-occurrences of perceptual, possibly polymodal features, while these features alone may have no importance. Thus, it is crucial for animals to learn such feature combinations in spite of the fact that they may occur with variable intensity and occurrence frequency. Here, we present a novel unsupervised learning mechanism that is largely independent of these contingencies and allows neurons in a network to achieve specificity for different feature combinations. This is achieved by a novel correlation-based (Hebbian) learning rule, which allows for linear weight growth and which is combined with a mechanism for gradually reducing the learning rate as soon as the neuron's response becomes feature combination specific. In a set of control experiments, we show that other existing advanced learning rules cannot satisfactorily form ordered multi-feature representations. In addition, we show that networks, which use this type of learning always stabilize and converge to subsets of neurons with different feature-combination specificity. Neurons with this property may, thus, serve as an initial stage for the processing of ecologically relevant real world situations for an animal.

The maintenance of synaptic changes resulting from long-term potentiation (LTP) is essential for brain function such as memory and learning. Different LTP phases have been associated with diverse molecular processes and pathways, and the molecular underpinnings of LTP on the short, as well as long time scales, are well established. However, the principles on the intermediate time scale of 1-6 hours that mediate the early phase of LTP (E-LTP) remain elusive. We hypothesize that the interplay between specific features of postsynaptic receptor trafficking is responsible for sustaining synaptic changes during this LTP phase. We test this hypothesis by formalizing a biophysical model that integrates several experimentally-motivated mechanisms. The model captures a wide range of experimental findings and predicts that synaptic changes are preserved for hours when the receptor dynamics are shaped by the interplay of structural changes of the spine in conjunction with increased trafficking from recycling endosomes and the cooperative binding of receptors. Furthermore, our model provides several predictions to verify our findings experimentally.

Neural networks in the brain are dominated by sometimes more than 60% feedback connections, which most often have small synaptic weights. Different from this, little is known how to introduce feedback into artificial neural networks. Here we use transfer entropy in the feed-forward paths of deep networks to identify feedback candidates between the convolutional layers and determine their final synaptic weights using genetic programming. This adds about 70% more connections to these layers all with very small weights. Nonetheless performance improves substantially on different standard benchmark tasks and in different networks. To verify that this effect is generic we use 36000 configurations of small (2-10 hidden layer) conventional neural networks in a non-linear classification task and select the best performing feed-forward nets. Then we show that feedback reduces total entropy in these networks always leading to performance increase. This method may, thus, supplement standard techniques (e.g. error backprop) adding a new quality to network learning.

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.

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.

Memory storage in the brain relies on mechanisms acting on time scales from minutes, for long-term synaptic potentiation, to days, for memory consolidation. During such processes, neural circuits distinguish synapses relevant for forming a long-term storage, which are consolidated, from synapses of short-term storage, which fade. How time scale integration and synaptic differentiation is simultaneously achieved remains unclear. Here we show that synaptic scaling - a slow process usually associated with the maintenance of activity homeostasis - combined with synaptic plasticity may simultaneously achieve both, thereby providing a natural separation of short- from long-term storage. The interaction between plasticity and scaling provides also an explanation for an established paradox where memory consolidation critically depends on the exact order of learning and recall. These results indicate that scaling may be fundamental for stabilizing memories, providing a dynamic link between early and late memory formation processes.

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.