The Formation of Multi-synaptic Connections by the Interaction of Synaptic and Structural Plasticity and Their Functional Consequences

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.Author Summary: The connectivity between neurons is modified by different mechanisms. On a time scale of minutes to hours one finds synaptic plasticity, whereas mechanisms for structural changes at axons or dendrites may take days. One main factor determining structural changes is the weight of a connection, which, in turn, is adapted by synaptic plasticity. Both mechanisms, synaptic and structural plasticity, are influenced and determined by the activity pattern in the network. Hence, it is important to understand how activity and the different plasticity mechanisms influence each other. Especially how activity influences rewiring in adult networks is still an open question.