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Modeling maintenance of long-term potentiation in clustered synapses: long-term memory without bistability.

Smolen P - Neural Plast. (2015)

Bottom Line: A unimodal weight distribution results.For stability of this distribution it proved essential to incorporate resource competition between synapses organized into small clusters.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.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Origin, Department of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas Medical School at Houston, Houston, TX 77030, USA.

ABSTRACT
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. 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 (>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.

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Distributions of the magnitude of synaptic weight change. (a) Black trace, histogram with 80 bins illustrating the steady-state distribution of weight update amplitudes for the active synapses in Figure 2(a). These amplitudes consist of all the synchronous weight updates for the 9,482 active synapses (out of 10,000 total), at a given time step. Red curve, a normal distribution (mean 0.0, standard deviation 0.07) that approximates the histogram excepting the sharp peak for update amplitudes near zero. (b) A histogram of ΔW versus W shows a slightly increasing, relatively linear trend. 80 bins for W are equally spaced on a log scale. Black trace, mean values of ΔW. Red traces, mean ± 1 standard deviation.
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fig4: Distributions of the magnitude of synaptic weight change. (a) Black trace, histogram with 80 bins illustrating the steady-state distribution of weight update amplitudes for the active synapses in Figure 2(a). These amplitudes consist of all the synchronous weight updates for the 9,482 active synapses (out of 10,000 total), at a given time step. Red curve, a normal distribution (mean 0.0, standard deviation 0.07) that approximates the histogram excepting the sharp peak for update amplitudes near zero. (b) A histogram of ΔW versus W shows a slightly increasing, relatively linear trend. 80 bins for W are equally spaced on a log scale. Black trace, mean values of ΔW. Red traces, mean ± 1 standard deviation.

Mentions: Simulation of the Pearson correlation coefficient R was done as follows. Let Xi denote the total set of n synaptic weights at a reference time, with i the indexing variable from 1 to n. For 1,000 10-synapse clusters, n = 10, 000. Let Yi denote the set of n weights at any later time step. As t increases from the reference time, Yi will evolve and R will decline from 1. Let , denote the means of Xi, Yi. The standard equation was used:(7)R=∑i=1nXi−X−Yi−Y−∑i=1nXi−X−2∑i=1nYi−Y−2.Standard parameter values, used in all simulations unless stated otherwise, are as follows:(8)Ncl⁡=10,  Wreset=0.4,  Twk=0.08,Tst=0.8,  vhi=4.0,  vlo=0.2,Wmed=0.4,  x1=0.144,  x2=0.18,a2=0.16,  khi=0.05,  Whi=20.0,  Pbas=0.1.In Supplementary Material (available online at http://dx.doi.org/10.1155/2015/185410), a Java program is given that executes simulations from Figures 2–4.


Modeling maintenance of long-term potentiation in clustered synapses: long-term memory without bistability.

Smolen P - Neural Plast. (2015)

Distributions of the magnitude of synaptic weight change. (a) Black trace, histogram with 80 bins illustrating the steady-state distribution of weight update amplitudes for the active synapses in Figure 2(a). These amplitudes consist of all the synchronous weight updates for the 9,482 active synapses (out of 10,000 total), at a given time step. Red curve, a normal distribution (mean 0.0, standard deviation 0.07) that approximates the histogram excepting the sharp peak for update amplitudes near zero. (b) A histogram of ΔW versus W shows a slightly increasing, relatively linear trend. 80 bins for W are equally spaced on a log scale. Black trace, mean values of ΔW. Red traces, mean ± 1 standard deviation.
© Copyright Policy - open-access
Related In: Results  -  Collection

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fig4: Distributions of the magnitude of synaptic weight change. (a) Black trace, histogram with 80 bins illustrating the steady-state distribution of weight update amplitudes for the active synapses in Figure 2(a). These amplitudes consist of all the synchronous weight updates for the 9,482 active synapses (out of 10,000 total), at a given time step. Red curve, a normal distribution (mean 0.0, standard deviation 0.07) that approximates the histogram excepting the sharp peak for update amplitudes near zero. (b) A histogram of ΔW versus W shows a slightly increasing, relatively linear trend. 80 bins for W are equally spaced on a log scale. Black trace, mean values of ΔW. Red traces, mean ± 1 standard deviation.
Mentions: Simulation of the Pearson correlation coefficient R was done as follows. Let Xi denote the total set of n synaptic weights at a reference time, with i the indexing variable from 1 to n. For 1,000 10-synapse clusters, n = 10, 000. Let Yi denote the set of n weights at any later time step. As t increases from the reference time, Yi will evolve and R will decline from 1. Let , denote the means of Xi, Yi. The standard equation was used:(7)R=∑i=1nXi−X−Yi−Y−∑i=1nXi−X−2∑i=1nYi−Y−2.Standard parameter values, used in all simulations unless stated otherwise, are as follows:(8)Ncl⁡=10,  Wreset=0.4,  Twk=0.08,Tst=0.8,  vhi=4.0,  vlo=0.2,Wmed=0.4,  x1=0.144,  x2=0.18,a2=0.16,  khi=0.05,  Whi=20.0,  Pbas=0.1.In Supplementary Material (available online at http://dx.doi.org/10.1155/2015/185410), a Java program is given that executes simulations from Figures 2–4.

Bottom Line: A unimodal weight distribution results.For stability of this distribution it proved essential to incorporate resource competition between synapses organized into small clusters.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.

View Article: PubMed Central - PubMed

Affiliation: Laboratory of Origin, Department of Neurobiology and Anatomy, W. M. Keck Center for the Neurobiology of Learning and Memory, The University of Texas Medical School at Houston, Houston, TX 77030, USA.

ABSTRACT
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. 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 (>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.

Show MeSH
Related in: MedlinePlus