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The formation of multi-synaptic connections by the interaction of synaptic and structural plasticity and their functional consequences.

Fauth M, Wörgötter F, Tetzlaff C - PLoS Comput. Biol. (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Georg-August University Göttingen, Third Institute of Physics, Bernstein Center for Computational Neuroscience, Göttingen, Germany.

ABSTRACT
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.

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The BCM rule feedforward connection shows a hysteresis in pre- and postsynaptic stimulation.(A) The predicted probability distributions p[S] (in colour-code) for the system from Fig. 4A is strongly influenced by varying the postsynaptic stimulation. Black lines indicate the values of S (treated as continuous variable) for which synapse creation and deletion are equally probable. These points correspond to stable (continuous line) or unstable (dashed line) fixed points of the dynamical system following the net probability flow of our system and indicate the existence of local extrema in the long-term equilibrium probability distribution. Two bifurcations lead to an appearance and disappearance of a bistability, which indicates a possible hysteresis. (B) The same applies for varying the presynaptic activity, although the second bifurcation on the right hand side does not reveal for continuous S, but takes place in the discrete case as both sign changes happen between two consecutive states. (C) Simulation reveals the predicted hysteresis: postsynaptic stimulation was increased stepwise such that vi(S = 0) increased by steps of 0.01 until it reached 1.0 and then decreased again. For each stimulation, the average number of synapses was calculated separately for the in- and decreasing direction and later averaged over all stimulation cycles (see Methods). The blue curve depicts the average number of synapses in the increasing and the green curve the decreasing direction. (D) Altering presynaptic activity in the same way also yields a hysteresis loop. (Parameters: BCM rule with synaptic scaling with μ = 0.2, θ = 0.08; υtss = 0.1; κ = 9.0, structural plasticity P = 12; ln pbuild = −16, a = 2.0, ρ = 0.125, in A, C: vj = 0.656, in B, D: vi(S = 0) = 0.2975)
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pcbi.1004031.g007: The BCM rule feedforward connection shows a hysteresis in pre- and postsynaptic stimulation.(A) The predicted probability distributions p[S] (in colour-code) for the system from Fig. 4A is strongly influenced by varying the postsynaptic stimulation. Black lines indicate the values of S (treated as continuous variable) for which synapse creation and deletion are equally probable. These points correspond to stable (continuous line) or unstable (dashed line) fixed points of the dynamical system following the net probability flow of our system and indicate the existence of local extrema in the long-term equilibrium probability distribution. Two bifurcations lead to an appearance and disappearance of a bistability, which indicates a possible hysteresis. (B) The same applies for varying the presynaptic activity, although the second bifurcation on the right hand side does not reveal for continuous S, but takes place in the discrete case as both sign changes happen between two consecutive states. (C) Simulation reveals the predicted hysteresis: postsynaptic stimulation was increased stepwise such that vi(S = 0) increased by steps of 0.01 until it reached 1.0 and then decreased again. For each stimulation, the average number of synapses was calculated separately for the in- and decreasing direction and later averaged over all stimulation cycles (see Methods). The blue curve depicts the average number of synapses in the increasing and the green curve the decreasing direction. (D) Altering presynaptic activity in the same way also yields a hysteresis loop. (Parameters: BCM rule with synaptic scaling with μ = 0.2, θ = 0.08; υtss = 0.1; κ = 9.0, structural plasticity P = 12; ln pbuild = −16, a = 2.0, ρ = 0.125, in A, C: vj = 0.656, in B, D: vi(S = 0) = 0.2975)

Mentions: As predicted by the confidence regions, the shape of the distributions are altered strongly by these changes: If pre- or postsynaptic influences are weak, there is only one probability maximum at S = 0 (Fig. 7A for pre- and Fig. 7B for postsynaptic influence). For higher influences, the second peak emerges and for even stronger influences the probability mass shifts to the upper peak until the peak at S = 0 eventually vanishes.


The formation of multi-synaptic connections by the interaction of synaptic and structural plasticity and their functional consequences.

Fauth M, Wörgötter F, Tetzlaff C - PLoS Comput. Biol. (2015)

The BCM rule feedforward connection shows a hysteresis in pre- and postsynaptic stimulation.(A) The predicted probability distributions p[S] (in colour-code) for the system from Fig. 4A is strongly influenced by varying the postsynaptic stimulation. Black lines indicate the values of S (treated as continuous variable) for which synapse creation and deletion are equally probable. These points correspond to stable (continuous line) or unstable (dashed line) fixed points of the dynamical system following the net probability flow of our system and indicate the existence of local extrema in the long-term equilibrium probability distribution. Two bifurcations lead to an appearance and disappearance of a bistability, which indicates a possible hysteresis. (B) The same applies for varying the presynaptic activity, although the second bifurcation on the right hand side does not reveal for continuous S, but takes place in the discrete case as both sign changes happen between two consecutive states. (C) Simulation reveals the predicted hysteresis: postsynaptic stimulation was increased stepwise such that vi(S = 0) increased by steps of 0.01 until it reached 1.0 and then decreased again. For each stimulation, the average number of synapses was calculated separately for the in- and decreasing direction and later averaged over all stimulation cycles (see Methods). The blue curve depicts the average number of synapses in the increasing and the green curve the decreasing direction. (D) Altering presynaptic activity in the same way also yields a hysteresis loop. (Parameters: BCM rule with synaptic scaling with μ = 0.2, θ = 0.08; υtss = 0.1; κ = 9.0, structural plasticity P = 12; ln pbuild = −16, a = 2.0, ρ = 0.125, in A, C: vj = 0.656, in B, D: vi(S = 0) = 0.2975)
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pcbi.1004031.g007: The BCM rule feedforward connection shows a hysteresis in pre- and postsynaptic stimulation.(A) The predicted probability distributions p[S] (in colour-code) for the system from Fig. 4A is strongly influenced by varying the postsynaptic stimulation. Black lines indicate the values of S (treated as continuous variable) for which synapse creation and deletion are equally probable. These points correspond to stable (continuous line) or unstable (dashed line) fixed points of the dynamical system following the net probability flow of our system and indicate the existence of local extrema in the long-term equilibrium probability distribution. Two bifurcations lead to an appearance and disappearance of a bistability, which indicates a possible hysteresis. (B) The same applies for varying the presynaptic activity, although the second bifurcation on the right hand side does not reveal for continuous S, but takes place in the discrete case as both sign changes happen between two consecutive states. (C) Simulation reveals the predicted hysteresis: postsynaptic stimulation was increased stepwise such that vi(S = 0) increased by steps of 0.01 until it reached 1.0 and then decreased again. For each stimulation, the average number of synapses was calculated separately for the in- and decreasing direction and later averaged over all stimulation cycles (see Methods). The blue curve depicts the average number of synapses in the increasing and the green curve the decreasing direction. (D) Altering presynaptic activity in the same way also yields a hysteresis loop. (Parameters: BCM rule with synaptic scaling with μ = 0.2, θ = 0.08; υtss = 0.1; κ = 9.0, structural plasticity P = 12; ln pbuild = −16, a = 2.0, ρ = 0.125, in A, C: vj = 0.656, in B, D: vi(S = 0) = 0.2975)
Mentions: As predicted by the confidence regions, the shape of the distributions are altered strongly by these changes: If pre- or postsynaptic influences are weak, there is only one probability maximum at S = 0 (Fig. 7A for pre- and Fig. 7B for postsynaptic influence). For higher influences, the second peak emerges and for even stronger influences the probability mass shifts to the upper peak until the peak at S = 0 eventually vanishes.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Georg-August University Göttingen, Third Institute of Physics, Bernstein Center for Computational Neuroscience, Göttingen, Germany.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus