A model for long-term potentiation and depression

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.

Effect of the initial synaptic state on the probability to induce long-term potentiation and depression

Long-term potentiation (LTP) and long-term depression (LTD) are the two major forms of long-lasting synaptic plasticity in the mammalian neurons, and are directly related to higher brain functions such as learning and memory. Experimentally, they are characterized by a change in the strength of a synaptic connection induced by repetitive and properly patterned stimulation protocols. Although many important details of the molecular events leading to LTP and LTD are known, experimenters often report problems in using standard induction protocols to obtain consistent results, especially for LTD in vivo. We hypothesize that a possible source of confusion in interpreting the results, from any given experiment on synaptic plasticity, can be the intrinsic limitation of the experimental techniques, which cannot take into account the actual state and peak conductance of the synapses before the conditioning protocol. In this article, we investigate the possibility that the same experimental protocol may result in different consequences (e.g., LTD instead of LTP), according to the initial conditions of the stimulated synapses, and can generate confusing results. Using biophysical models of synaptic plasticity and hippocampal CA1 pyramidal neurons, we study how, why, and to what extent the phenomena observed at the soma after induction of LTP/LTD reflects the actual (local) synaptic state. The model and the results suggest a physiologically plausible explanation for why LTD induction is experimentally difficult to obtain. They also suggest experimentally testable predictions on the stimulation protocols that may be more effective.

Realistic modeling of neurons and networks: towards brain simulation

Realistic modeling is a new advanced methodology for investigating brain functions. Realistic modeling is based on a detailed biophysical description of neurons and synapses, which can be integrated into microcircuits. The latter can, in turn, be further integrated to form large-scale brain networks and eventually to reconstruct complex brain systems. Here we provide a review of the realistic simulation strategy and use the cerebellar network as an example. This network has been carefully investigated at molecular and cellular level and has been the object of intense theoretical investigation. The cerebellum is thought to lie at the core of the forward controller operations of the brain and to implement timing and sensory prediction functions. The cerebellum is well described and provides a challenging field in which one of the most advanced realistic microcircuit models has been generated. We illustrate how these models can be elaborated and embedded into robotic control systems to gain insight into how the cellular properties of cerebellar neurons emerge in integrated behaviors. Realistic network modeling opens up new perspectives for the investigation of brain pathologies and for the neurorobotic field.

Quantifying altered long-term potentiation in the CA1 hippocampus

Long-term potentiation (LTP) of synaptic transmission is a widely accepted model of learning and memory. In vitro brain slice techniques were used to investigate the effects of cortical-spreading depression and picrotoxin, an antagonist of the gamma-aminobutyric acid A (GABA(A)) receptor, on the tetanus-induced long-term potentiation of field excitatory postsynaptic potentials. Cortical-spreading depression is involved in glutamate desensitization; on the other hand, GABA(A) antagonists could increase postsynaptic excitability. This study shows that picrotoxin effectively induced long-term potentiation with 142.25 ± 4.18% of the baseline in the picrotoxin group (n = 8) versus 134.36 ± 2.35% of the baseline in the control group (n = 10). In group with picrotoxin applied to CSD, we obtained the smallest magnitude of LTP (120.15 ± 3.73% of the baseline, n = 8). These results suggest that picrotoxin could increase hippocampal activity and LTP; on the contrary, CSD reduced LTP magnitude. In addition, the results also suggest that the decay rate of post-tetanic potentiation has a direct relationship with LTP. Moreover, data were interpreted by nonlinear least squares quantifying, and LTP could also be quantified. The nonlinear attribute of LTP had an influence on the fitting, with respect to increasing the accuracy of the parameters and the compatibility of combination of stimuli that produce LTP.

Postsynaptic signal transduction models for long-term potentiation and depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models.

Coupled phosphatase and kinase switches produce the tristability required for long-term potentiation and long-term depression

Studies of long-term potentiation (LTP) and long-term depression (LTD) strongly suggest that individual synapses can be bidirectionally modified. A central question is the biochemical mechanisms that make LTP and LTD persistent. Previous theoretical models have proposed that the autophosphorylation properties of CaMKII could underlie a bistable molecular switch that maintains LTP, and there is experimental support for this mechanism. In contrast, there has been comparatively little theoretical or experimental work regarding the mechanisms that maintain LTD. Several lines of evidence indicate that LTD is not simply a reversal of previous LTP but rather involves separate biochemical reactions. These findings indicate that a minimal model of the synapse must involve a tristable system. Here, we describe a phosphatase (PP2A) switch, which together with a kinase switch form a tristable system. PP2A can be activated by a Ca(2+)-dependent process but can also be phosphorylated and inactivated by CaMKII. When dephosphorylated, PP2A can dephosphorylate itself. We show that these properties can lead to a persistent increase in PP2A during LTD (as reported experimentally), thus forming a phosphatase switch. We show that the coupled PP2A and CaMKII switches lead to a tristable system in which the kinase activity is high in the LTP state; the PP2A activity is high in the LTD state, and neither activity is high in the basal state. Our results provide an explanation for the recent finding that inhibition of PP2A prevents LTD induction.

Convergence among non-sister dendritic branches: an activity-controlled mean to strengthen network connectivity

The manner by which axons distribute synaptic connections along dendrites remains a fundamental unresolved issue in neuronal development and physiology. We found in vitro and in vivo indications that dendrites determine the density, location and strength of their synaptic inputs by controlling the distance of their branches from those of their neighbors. Such control occurs through collective branch convergence, a behavior promoted by AMPA and NMDA glutamate receptor activity. At hubs of convergence sites, the incidence of axo-dendritic contacts as well as clustering levels, pre- and post-synaptic protein content and secretion capacity of synaptic connections are higher than found elsewhere. This coupling between synaptic distribution and the pattern of dendritic overlapping results in ‘Economical Small World Network’, a network configuration that enables single axons to innervate multiple and remote dendrites using short wiring lengths. Thus, activity-mediated regulation of the proximity among dendritic branches serves to pattern and strengthen neuronal connectivity.

Spike-driven synaptic plasticity for learning correlated patterns of mean firing rates

Long term synaptic changes induced by neural spike activity are believed to underlie learning and memory. Spike-driven long-term synaptic plasticity has been investigated in simplified situations in which the patterns of mean rates to be encoded were statistically independent. An additional regulatory mechanism is required to extend the learning capability to more complex and natural stimuli. This mechanism can be provided by those effects of the action potentials that are believed to be responsible for spike-timing dependent plasticity. These effects, when combined with the dependence of synaptic plasticity on the post-synaptic depolarization, produce the non-monotonic learning rule needed for storing correlated patterns of mean rates.

Long-term potentiation and depression induced by a stochastic conditioning of a model synapse

Protracted presynaptic activity can induce long-term potentiation (LTP) or long-term depression (LTD) of the synaptic strength. However, virtually all the experiments testing how LTP and LTD depend on the conditioning input are carried out with trains of stimuli at constant frequencies, whereas neurons in vivo most likely experience a stochastic variation of interstimulus intervals. We used a computational model of synaptic transmission to test if and to what extent the stochastic fluctuations of an input signal could alter the probability to change the state of a synapse. We found that, even if the mean stimulation frequency was maintained constant, the probability to induce LTD and LTP could be a function of the temporal variation of the input activity. This mechanism, which depends only on the statistical properties of the input and not on the onset of additional biochemical mechanisms, is not usually considered in the experiments, but it could have an important role to determine the amount of LTP/LTD induction in vivo. In response to a change in the distribution of the interstimulus intervals, as measured by the coefficient of variation, a synapse could be easily adapted to inputs that might require immediate attention, with a shift of the input thresholds required to elicit LTD or LTP, which are restored to their initial conditions as soon as the input pattern returns to the original temporal distribution.

Possible roles of retrograde messengers on LTP, LTD, and associative memory

There are still no clear biophysical models for Associative Long-Term Potentiation (LTP) and Depression (LTD) in the hippocampus, where two populations of synapses targeted to the same receptive field are involved. Here we propose a model that allows an interpretation of the experiments in terms of the molecular processes that may be involved in associative memory. The model suggests that retrograde messengers could have a critical role in the induction and maintenance of associative LTP and LTD, by controlling the coupling between the two populations of synapses.