Synapses and Memory Storage

The synapse is the functional unit of the brain. During the last several decades we have acquired a great deal of information on its structure, molecular components, and physiological function. It is clear that synapses are morphologically and molecularly diverse and that this diversity is recruited to different functions. One of the most intriguing findings is that the size of the synaptic response in not invariant, but can be altered by a variety of homo- and heterosynaptic factors such as past patterns of use or modulatory neurotransmitters. Perhaps the most difficult challenge in neuroscience is to design experiments that reveal how these basic building blocks of the brain are put together and how they are regulated to mediate the information flow through neural circuits that is necessary to produce complex behaviors and store memories. In this review we will focus on studies that attempt to uncover the role of synaptic plasticity in the regulation of whole-animal behavior by learning and memory.The idea that learning results from changes in the strength of the synapse was first suggested by Santiago Ramon y Cajal (1894) based on insights from his anatomical studies. That modulation of synaptic connectivity is a critical mechanism of learning was incorporated into more refined models by Hebb in the 1940s and 1950s. The experimental investigation of these intriguing conjectures required the development of behavioral systems in which one could examine changes in the neuronal components of a specific behavior during or after the modification of that behavior with learning (Kandel and Spencer 1968).     

Multi-input Synapses,but Not LTP-Strengthened Synapses,Correlate with Hippocampal Memory Storage in Aged Mice

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Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.     

Memory Maintenance in Synapses with Calcium-Based Plasticity in the Presence of Background Activity

Most models of learning and memory assume that memories are maintained in neuronal circuits by persistent synaptic modifications induced by specific patterns of pre- and postsynaptic activity. For this scenario to be viable, synaptic modifications must survive the ubiquitous ongoing activity present in neural circuits in vivo. In this paper, we investigate the time scales of memory maintenance in a calcium-based synaptic plasticity model that has been shown recently to be able to fit different experimental data-sets from hippocampal and neocortical preparations. We find that in the presence of background activity on the order of 1 Hz parameters that fit pyramidal layer 5 neocortical data lead to a very fast decay of synaptic efficacy, with time scales of minutes. We then identify two ways in which this memory time scale can be extended: (i) the extracellular calcium concentration in the experiments used to fit the model are larger than estimated concentrations in vivo. Lowering extracellular calcium concentration to in vivo levels leads to an increase in memory time scales of several orders of magnitude; (ii) adding a bistability mechanism so that each synapse has two stable states at sufficiently low background activity leads to a further boost in memory time scale, since memory decay is no longer described by an exponential decay from an initial state, but by an escape from a potential well. We argue that both features are expected to be present in synapses in vivo. These results are obtained first in a single synapse connecting two independent Poisson neurons, and then in simulations of a large network of excitatory and inhibitory integrate-and-fire neurons. Our results emphasise the need for studying plasticity at physiological extracellular calcium concentration, and highlight the role of synaptic bi- or multistability in the stability of learned synaptic structures.     

Multi-Stability and Pattern-Selection in Oscillatory Networks with Fast Inhibition and Electrical Synapses

A model or hybrid network consisting of oscillatory cells interconnected by inhibitory and electrical synapses may express different stable activity patterns without any change of network topology or parameters, and switching between the patterns can be induced by specific transient signals. However, little is known of properties of such signals. In the present study, we employ numerical simulations of neural networks of different size composed of relaxation oscillators, to investigate switching between in-phase (IP) and anti-phase (AP) activity patterns. We show that the time windows of susceptibility to switching between the patterns are similar in 2-, 4- and 6-cell fully-connected networks. Moreover, in a network (N = 4, 6) expressing a given AP pattern, a stimulus with a given profile consisting of depolarizing and hyperpolarizing signals sent to different subpopulations of cells can evoke switching to another AP pattern. Interestingly, the resulting pattern encodes the profile of the switching stimulus. These results can be extended to different network architectures. Indeed, relaxation oscillators are not only models of cellular pacemakers, bursting or spiking, but are also analogous to firing-rate models of neural activity. We show that rules of switching similar to those found for relaxation oscillators apply to oscillating circuits of excitatory cells interconnected by electrical synapses and cross-inhibition. Our results suggest that incoming information, arriving in a proper time window, may be stored in an oscillatory network in the form of a specific spatio-temporal activity pattern which is expressed until new pertinent information arrives.     

Flexible Memory Networks

Networks of neurons in some brain areas are flexible enough to encode new memories quickly. Using a standard firing rate model of recurrent networks, we develop a theory of flexible memory networks. Our main results characterize networks having the maximal number of flexible memory patterns, given a constraint graph on the network’s connectivity matrix. Modulo a mild topological condition, we find a close connection between maximally flexible networks and rank 1 matrices. The topological condition is H ₁(X;ℤ)=0, where X is the clique complex associated to the network’s constraint graph; this condition is generically satisfied for large random networks that are not overly sparse. In order to prove our main results, we develop some matrix-theoretic tools and present them in a self-contained section independent of the neuroscience context.     

Plasticity at Thalamo-amygdala Synapses Regulates Cocaine-Cue Memory Formation and Extinction

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Invariant Features of Memory Capacity

Our purpose in these experiments was to study short-term (immediate) and long-term memory in the memorization of the same subject matter. By memory capacity is meant the number of units a person is able to reproduce in one repetition, or on an average in one repetition. In short-term reception and full reproduction of the material to be memorized, short-term memory capacity is commensurate with the number of units reproduced. Long-term memory capacity reflects the ability to accumulate as well as to retain information. When the material to be remembered exceeds the short-term memory capacity, the first reproduction is incomplete, and multiple presentation and repetition of the information are necessary for error-free and complete reproduction. In this case the memory capacity is equal to the number of units contained in the presented material divided by the number of repetitions.     

Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.     

The Molecular Biology of Memory Storage: A Dialog Between Genes and Synapses

The biology of learning, and short-term and long-term memory, as revealed by Aplysia and other organisms, is reviewed.     

Stochastic Resonance Crossovers in Complex Networks

Here we numerically study the emergence of stochastic resonance as a mild phenomenon and how this transforms into an amazing enhancement of the signal-to-noise ratio at several levels of a disturbing ambient noise. The setting is a cooperative, interacting complex system modelled as an Ising-Hopfield network in which the intensity of mutual interactions or “synapses” varies with time in such a way that it accounts for, e.g., a kind of fatigue reported to occur in the cortex. This induces nonequilibrium phase transitions whose rising comes associated to various mechanisms producing two types of resonance. The model thus clarifies the details of the signal transmission and the causes of correlation among noise and signal. We also describe short-time persistent memory states, and conclude on the limited relevance of the network wiring topology. Our results, in qualitative agreement with the observation of excellent transmission of weak signals in the brain when competing with both intrinsic and external noise, are expected to be of wide validity and may have technological application. We also present here a first contact between the model behavior and psychotechnical data.     

Evolution of Cooperation on Stochastic Dynamical Networks

Cooperative behavior that increases the fitness of others at a cost to oneself can be promoted by natural selection only in the presence of an additional mechanism. One such mechanism is based on population structure, which can lead to clustering of cooperating agents. Recently, the focus has turned to complex dynamical population structures such as social networks, where the nodes represent individuals and links represent social relationships. We investigate how the dynamics of a social network can change the level of cooperation in the network. Individuals either update their strategies by imitating their partners or adjust their social ties. For the dynamics of the network structure, a random link is selected and breaks with a probability determined by the adjacent individuals. Once it is broken, a new one is established. This linking dynamics can be conveniently characterized by a Markov chain in the configuration space of an ever-changing network of interacting agents. Our model can be analytically solved provided the dynamics of links proceeds much faster than the dynamics of strategies. This leads to a simple rule for the evolution of cooperation: The more fragile links between cooperating players and non-cooperating players are (or the more robust links between cooperators are), the more likely cooperation prevails. Our approach may pave the way for analytically investigating coevolution of strategy and structure.     

具有时滞的双向联想记忆神经网络的全局渐近稳定性

双向联想记忆模型是两层异联想网络,本文讨论了具有轴突信号传输时滞的双向联想记忆神经网络的全局渐近稳定性,得出了保证神经网络平衡点稳定的几个充分条件,所得到的结论对于具有时滞的连续双向联想记忆神经网络的设计和应用都是很有意义的。     

Stochastic Simulation of Biomolecular Networks in Dynamic Environments

Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate—using decision-making by a large population of quorum sensing bacteria—that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.     

Estimating the Stochastic Bifurcation Structure of Cellular Networks

High throughput measurement of gene expression at single-cell resolution, combined with systematic perturbation of environmental or cellular variables, provides information that can be used to generate novel insight into the properties of gene regulatory networks by linking cellular responses to external parameters. In dynamical systems theory, this information is the subject of bifurcation analysis, which establishes how system-level behaviour changes as a function of parameter values within a given deterministic mathematical model. Since cellular networks are inherently noisy, we generalize the traditional bifurcation diagram of deterministic systems theory to stochastic dynamical systems. We demonstrate how statistical methods for density estimation, in particular, mixture density and conditional mixture density estimators, can be employed to establish empirical bifurcation diagrams describing the bistable genetic switch network controlling galactose utilization in yeast Saccharomyces cerevisiae. These approaches allow us to make novel qualitative and quantitative observations about the switching behavior of the galactose network, and provide a framework that might be useful to extract information needed for the development of quantitative network models.     

一类BAM随机神经网络的稳定性

对于一类双向联想记忆（BAM）随机神经网络。研究其全局稳定性和指数稳定性,利用Schwarz积分不等式和Ito积分性质,给出其稳定性判定的充分性条件．     

关于一类具有时滞的双向联想记忆神经网络的收敛性

研究了一类具有时滞的双层双向联想记忆模型的收敛性,给出了平衡点的存在性、唯一性、全局渐近稳定性的充分条件．     

Thermal Memory in Self-Assembled Collagen Fibril Networks

Collagen fibrils form extracellular networks that regulate cell functions and provide mechanical strength to tissues. Collagen fibrillogenesis is an entropy-driven process promoted by warming and reversed by cooling. Here, we investigate the influence of noncovalent interactions mediated by the collagen triple helix on fibril stability. We measure the kinetics of cold-induced disassembly of fibrils formed from purified collagen I using turbimetry, probe the fibril morphology by atomic force microscopy, and measure the network connectivity by confocal microscopy and rheometry. We demonstrate that collagen fibrils disassemble by subunit release from their sides as well as their ends, with complex kinetics involving an initial fast release followed by a slow release. Surprisingly, the fibrils are gradually stabilized over time, leading to thermal memory. This dynamic stabilization may reflect structural plasticity of the collagen fibrils arising from their complex structure. In addition, we propose that the polymeric nature of collagen monomers may lead to slow kinetics of subunit desorption from the fibril surface. Dynamic stabilization of fibrils may be relevant in the initial stages of collagen assembly during embryogenesis, fibrosis, and wound healing. Moreover, our results are relevant for tissue repair and drug delivery applications, where it is crucial to control fibril stability.