Optimal learning rules for discrete synapses

There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity

Evidence against AMPA receptor-lacking glutamatergic synapses in the superficial dorsal horn of the rat spinal cord

Pure NMDA receptor (NMDAr)-mediated EPSCs, thought to correspond to "silent" glutamatergic synapses that lack AMPA receptors (AMPArs), have been observed in superficial spinal dorsal horn of neonatal but not adult rats. Recent anatomical studies suggest that AMPArs are present at virtually all glutamatergic synapses in this region in adults. We used antigen retrieval to examine colocalization of AMPArs and PSD-95 (a marker for glutamatergic synapses) in laminae I–II of neonatal and adult rats. We found a high degree of colocalization in all cases, which suggests that AMPArs are present in the great majority of glutamatergic synapses even in neonatal animals. We therefore reexamined evidence for silent synapses by performing blind whole-cell recordings from superficial dorsal horn neurons in slices from neonatal or adult rats, with focal stimulation to activate glutamatergic synapses. On some occasions in both neonatal (10 of 109, 9%) and adult (9 of 77, 12%) slices, NMDAr-mediated EPSCs were observed when the holding potential was raised to +50 mV at a stimulus strength that had failed to evoke AMPAr-mediated EPSCs. However, in all cases tested, AMPAr-mediated EPSCs were then observed when the cell was returned to –70 mV; this and other properties of the EPSCs suggest that they do not represent genuine silent synapses. When compared with previous findings, our results indicate that the appearance of silent synapses depends on experimental protocol. This suggests that pure NMDAr-mediated EPSCs seen in previous studies do not correspond to AMPAr-lacking synapses but result from another mechanism, for example, loss of labile AMPArs from recently formed synapses

Adenosine A1 receptor activation mediates the developmental shift at layer 5 pyramidal cell synapses and is a determinant of mature synaptic strength

During the first postnatal month glutamatergic synapses between layer 5 pyramidal cells in the rodent neocortex switch from an immature state exhibiting high probability of neurotransmitter release, large unitary amplitude and synaptic depression to a mature state with decreased probability of release, smaller unitary amplitude and synaptic facilitation. Using paired recordings, we demonstrate that the developmental shift in release probability at synapses between rat somatosensory layer 5 thick-tufted pyramidal cells is due to a higher and more heterogeneous activation of presynaptic adenosine A1 receptors. Immature synapses under control conditions exhibited distributions of CV, failure rate and release probability that were almost coincident with the A1 receptor blocked condition; however, mature synapses under control conditions exhibited much broader distributions that spanned those of both the A1 receptor agonised and antagonised conditions. Immature and mature synapses expressed A1 receptors with no observable difference in functional efficacy and therefore the heterogeneous A1 receptor activation seen in the mature neocortex is due to increased adenosine concentrations that vary between synapses. Given the central role demonstrated for A1 receptor activation in determining synaptic amplitude and the statistics of transmission between mature layer 5 pyramidal cells, the emplacement of adenosine sources and sinks near the synaptic terminal could constitute a novel form of long-term synaptic plasticity

Multifaceted Changes in Synaptic Composition and Astrocytic Involvement in a Mouse Model of Fragile X Syndrome.

Fragile X Syndrome (FXS), a common inheritable form of intellectual disability, is known to alter neocortical circuits. However, its impact on the diverse synapse types comprising these circuits, or on the involvement of astrocytes, is not well known. We used immunofluorescent array tomography to quantify different synaptic populations and their association with astrocytes in layers 1 through 4 of the adult somatosensory cortex of a FXS mouse model, the FMR1 knockout mouse. The collected multi-channel data contained approximately 1.6 million synapses which were analyzed using a probabilistic synapse detector. Our study reveals complex, synapse-type and layer specific changes in the neocortical circuitry of FMR1 knockout mice. We report an increase of small glutamatergic VGluT1 synapses in layer 4 accompanied by a decrease in large VGluT1 synapses in layers 1 and 4. VGluT2 synapses show a rather consistent decrease in density in layers 1 and 2/3. In all layers, we observe the loss of large inhibitory synapses. Lastly, astrocytic association of excitatory synapses decreases. The ability to dissect the circuit deficits by synapse type and astrocytic involvement will be crucial for understanding how these changes affect circuit function, and ultimately defining targets for therapeutic intervention

Rapid, learning-induced inhibitory synaptogenesis in murine barrel field

The structure of neurons changes during development and in response to injury or alteration in sensory experience. Changes occur in the number, shape, and dimensions of dendritic spines together with their synapses. However, precise data on these changes in response to learning are sparse. Here, we show using quantitative transmission electron microscopy that a simple form of learning involving mystacial vibrissae results in approximately 70% increase in the density of inhibitory synapses on spines of neurons located in layer IV barrels that represent the stimulated vibrissae. The spines contain one asymmetrical (excitatory) and one symmetrical (inhibitory) synapse (double-synapse spines), and their density increases threefold as a result of learning with no apparent change in the density of asymmetrical synapses. This effect seems to be specific for learning because pseudoconditioning (in which the conditioned and unconditioned stimuli are delivered at random) does not lead to the enhancement of symmetrical synapses but instead results in an upregulation of asymmetrical synapses on spines. Symmetrical synapses of cells located in barrels receiving the conditioned stimulus also show a greater concentration of GABA in their presynaptic terminals. These results indicate that the immediate effect of classical conditioning in the "conditioned" barrels is rapid, pronounced, and inhibitory

Modeling Maintenance of Long-Term Potentiation in Clustered Synapses, Long-Term Memory Without Bistability

Memories are stored, at least partly, as patterns of strong synapses. Given molecular turnover, how can synapses maintain strong for the years that memories can persist? Some models postulate that biochemical bistability maintains strong synapses. However, bistability should give a bimodal distribution of synaptic strength or weight, whereas current data show unimodal distributions for weights and for a correlated variable, dendritic spine volume. Bistability of single synapses has also never been empirically demonstrated. Thus it is important for models to simulate both unimodal distributions and long-term memory persistence. Here a model is developed that connects ongoing, competing processes of synaptic growth and weakening to stochastic processes of receptor insertion and removal in dendritic spines. The model simulates long-term (in excess of 1 yr) persistence of groups of strong synapses. A unimodal weight distribution results. For stability of this distribution it proved essential to incorporate resource competition between synapses organized into small clusters. With competition, these clusters are stable for years. These simulations concur with recent data to support the clustered plasticity hypothesis, which suggests clusters, rather than single synaptic contacts, may be a fundamental unit for storage of long-term memory. The model makes empirical predictions, and may provide a framework to investigate mechanisms maintaining the balance between synaptic plasticity and stability of memory.Comment: 17 pages, 5 figure

Storage Capacity of Extremely Diluted Hopfield Model

The storage capacity of the extremely diluted Hopfield Model is studied by using Monte Carlo techniques. In this work, instead of diluting the synapses according to a given distribution, the dilution of the synapses is obtained systematically by retaining only the synapses with dominant contributions. It is observed that by using the prescribed dilution method the critical storage capacity of the system increases with decreasing number of synapses per neuron reaching almost the value obtained from mean-field calculations. It is also shown that the increase of the storage capacity of the diluted system depends on the storage capacity of the fully connected Hopfield Model and the fraction of the diluted synapses.Comment: Latex, 14 pages, 4 eps figure

Postsynaptic protein organization revealed by electron microscopy.

Neuronal synapses are key devices for transmitting and processing information in the nervous system. Synaptic plasticity, generally regarded as the cellular basis of learning and memory, involves changes of subcellular structures that take place at the nanoscale. High-resolution imaging methods, especially electron microscopy (EM), have allowed for quantitative analysis of such nanoscale structures in different types of synapses. In particular, the semi-ordered organization of neurotransmitter receptors and their interacting scaffolds in the postsynaptic density have been characterized for both excitatory and inhibitory synapses by studies using various EM techniques such as immuno-EM, electron tomography of high-pressure freezing and freeze-substituted samples, and cryo electron tomography. These techniques, in combination with new correlative approaches, will further facilitate our understanding of the molecular organization underlying diverse functions of neuronal synapses