Limits...
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.

Show MeSH

Related in: MedlinePlus

Simulated distributions of synaptic weights. (a) Distribution for 1,000 independent clusters with Ncl⁡ = 10. Black trace, histogram with 80 bins illustrating an approximately log-normal distribution of the 10,000 weights. Each bin is equal in width in natural log units. Red curve, a log-normal distribution (mean at 0.0131, standard deviation of 0.9341), fitted by MATLAB, that approximately reproduces the histogram. The histogram was constructed after 50,000 simulated days to ensure a steady state. (b) Black and red traces, similar to (a), except the mean and standard deviation of LTP, parameters a1 and sd1, are fixed at 0.16 and 0.04, respectively. Blue trace, the histogram of W is shifted to much lower values when a1 is decreased by 2%. (c) Weight dynamics without regeneration of synapses. The histogram of the active synapses shifts to much greater values (black trace). ~45% of synapses are silent, unable to regenerate, and not included in the histogram. This histogram is an approximate steady state, although with no regeneration, all synapses would become silent after a much longer time. Red curve, normal distribution from (a).
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4402204&req=5

fig2: Simulated distributions of synaptic weights. (a) Distribution for 1,000 independent clusters with Ncl⁡ = 10. Black trace, histogram with 80 bins illustrating an approximately log-normal distribution of the 10,000 weights. Each bin is equal in width in natural log units. Red curve, a log-normal distribution (mean at 0.0131, standard deviation of 0.9341), fitted by MATLAB, that approximately reproduces the histogram. The histogram was constructed after 50,000 simulated days to ensure a steady state. (b) Black and red traces, similar to (a), except the mean and standard deviation of LTP, parameters a1 and sd1, are fixed at 0.16 and 0.04, respectively. Blue trace, the histogram of W is shifted to much lower values when a1 is decreased by 2%. (c) Weight dynamics without regeneration of synapses. The histogram of the active synapses shifts to much greater values (black trace). ~45% of synapses are silent, unable to regenerate, and not included in the histogram. This histogram is an approximate steady state, although with no regeneration, all synapses would become silent after a much longer time. Red curve, normal distribution from (a).

Mentions: For each time step, the LTP and LTD amplitudes are proportional, respectively, to Gaussian random variables r1 and r2. These variables have respective means a1 and a2, and sd1 and sd2 are the standard deviations. a1 and a2 are substantially larger, by a fixed factor of 4, than are sd1 and sd2. Thus r1 and r2 are very rarely negative, but if either becomes negative it is reset to zero. A synapse is “strong” if its weight is above a threshold Tst. The average LTP amplitude a1 is a decreasing function of the number of strong synapses in a given cluster, denoted as Nst. With Ncl⁡ the total number of synapses in a cluster, the average LTP amplitude a1 decreases linearly with Nst, from a maximum amplitude x2 (for Nst = 0) to a minimum x1 (for Nst = Ncl⁡). For the simulation of Figure 2(b) with this amplitude decrease removed, a1 and thus sd1 are fixed parameters. For comparison, simulations were also carried out in which r1 and r2 were drawn from exponential distributions. With exponential distributions r1 and r2 are always nonnegative, with probability densities that peak at 0 and decay exponentially for increasing positive values. The corresponding decay rate constants were varied independently within the range [0.5,3.0].


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

Smolen P - Neural Plast. (2015)

Simulated distributions of synaptic weights. (a) Distribution for 1,000 independent clusters with Ncl⁡ = 10. Black trace, histogram with 80 bins illustrating an approximately log-normal distribution of the 10,000 weights. Each bin is equal in width in natural log units. Red curve, a log-normal distribution (mean at 0.0131, standard deviation of 0.9341), fitted by MATLAB, that approximately reproduces the histogram. The histogram was constructed after 50,000 simulated days to ensure a steady state. (b) Black and red traces, similar to (a), except the mean and standard deviation of LTP, parameters a1 and sd1, are fixed at 0.16 and 0.04, respectively. Blue trace, the histogram of W is shifted to much lower values when a1 is decreased by 2%. (c) Weight dynamics without regeneration of synapses. The histogram of the active synapses shifts to much greater values (black trace). ~45% of synapses are silent, unable to regenerate, and not included in the histogram. This histogram is an approximate steady state, although with no regeneration, all synapses would become silent after a much longer time. Red curve, normal distribution from (a).
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4402204&req=5

fig2: Simulated distributions of synaptic weights. (a) Distribution for 1,000 independent clusters with Ncl⁡ = 10. Black trace, histogram with 80 bins illustrating an approximately log-normal distribution of the 10,000 weights. Each bin is equal in width in natural log units. Red curve, a log-normal distribution (mean at 0.0131, standard deviation of 0.9341), fitted by MATLAB, that approximately reproduces the histogram. The histogram was constructed after 50,000 simulated days to ensure a steady state. (b) Black and red traces, similar to (a), except the mean and standard deviation of LTP, parameters a1 and sd1, are fixed at 0.16 and 0.04, respectively. Blue trace, the histogram of W is shifted to much lower values when a1 is decreased by 2%. (c) Weight dynamics without regeneration of synapses. The histogram of the active synapses shifts to much greater values (black trace). ~45% of synapses are silent, unable to regenerate, and not included in the histogram. This histogram is an approximate steady state, although with no regeneration, all synapses would become silent after a much longer time. Red curve, normal distribution from (a).
Mentions: For each time step, the LTP and LTD amplitudes are proportional, respectively, to Gaussian random variables r1 and r2. These variables have respective means a1 and a2, and sd1 and sd2 are the standard deviations. a1 and a2 are substantially larger, by a fixed factor of 4, than are sd1 and sd2. Thus r1 and r2 are very rarely negative, but if either becomes negative it is reset to zero. A synapse is “strong” if its weight is above a threshold Tst. The average LTP amplitude a1 is a decreasing function of the number of strong synapses in a given cluster, denoted as Nst. With Ncl⁡ the total number of synapses in a cluster, the average LTP amplitude a1 decreases linearly with Nst, from a maximum amplitude x2 (for Nst = 0) to a minimum x1 (for Nst = Ncl⁡). For the simulation of Figure 2(b) with this amplitude decrease removed, a1 and thus sd1 are fixed parameters. For comparison, simulations were also carried out in which r1 and r2 were drawn from exponential distributions. With exponential distributions r1 and r2 are always nonnegative, with probability densities that peak at 0 and decay exponentially for increasing positive values. The corresponding decay rate constants were varied independently within the range [0.5,3.0].

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