State Based Model of Long-Term Potentiation and Synaptic Tagging and
                    Capture
It is widely believed that synaptic potentiation , as demonstrated by the, physiological phenomenon of long-term potentiation ( LTP ) , plays an important, rôle in memory formation in the brain 1 , 2 ., This has triggered a, vast number of experiments in which this phenomenon has been recorded , both, in vivo and in vitro ., Typically , LTP can be, elicited in a population of CA1 neurons by placing an electrode into an input, pathway in the stratum radiatum , and applying a burst of high-frequency stimulation ., One major result that has emerged is that there are at least two distinct, “phases” of LTP , see 3 for a review ., Firstly ,, there is an “early” , transient phase ( e-LTP ) that can be induced, by a single , brief ( ) , burst of high-frequency stimulation ( weak HFS ) ., The lifetime of, this phase is around three hours in slice experiments , and its expression does not, require protein synthesis 4–6 ., Secondly , there is, late-phase LTP ( ) , which is stable for at least the eight hour time-span of a, typical slice experiment , but which can last up to months in vivo, 7–9 ., can be induced by repeated ( typically three ) bursts of HFS ,, separated by 10 minute intervals ( strong HFS ) ., Thus , notably , more stimulation does, not increase the amount of synaptic weight change at individual synapses ( as often, assumed in models ) , but rather increases the duration of weight enhancement ., It has, been shown that protein synthesis is triggered at the time of induction and is, necessary for, 4 , 5 , although, a more complicated rôle for protein synthesis in LTP has been implied 10 , 11 ., Interestingly , e-LTP at one synapse can be converted to if repeated bursts of HFS are given to other inputs of the same, neuron during a short period before or after the induction of e-LTP at the first, synapse 12–14 ., This discovery led to, the hypothesis that HFS initiates the creation of a “synaptic, tag” at the stimulated synapse , which is thought to be able to capture, plasticity-related proteins ( PRPs ) ., The PRPs are believed to be synthesized in the, cell body , although recent data suggest they may be manufactured more locally in, dendrites 15 ., The general framework for these hetero-synaptic, effects is called “synaptic tagging and capture” ( STC ) ., Which, proteins are involved in each stage of STC has not been fully elucidated yet ., Current data suggest that , at least in apical dendrites ,, calcium/calmodulin-dependent kinase II ( CaMKII ) is specifically involved in, signaling the tag in LTP induction 15 and protein kinase ( ) is involved in the late maintenance of potentiated synapses 6 , 16 ., The counterpart of LTP , long-term depression ( LTD ) , can be induced by stimulating CA1, hippocampal neurons with low-frequency stimulation ( LFS ) 17 , 18 ., LTD, states appear to have analogous properties to the LTP states discussed above ., The, early phase , which we call e-LTD , lasts around three hours , is not dependent on, protein synthesis , and can be induced by weak LFS , consisting of , for example , 900, stimuli at 1 Hz ., For induction of the late phase , , a stronger form of LFS is required , for example 900 bursts of, three stimuli at 20 Hz , with an inter-burst interval of one second 19 ., Like , is stable for the duration of most experiments and is protein, synthesis dependent 20 ., Moreover , e-LTD of one synapse can be converted, to if strong LFS is given to a second synapse of the same neuron, within an interval of around one hour 19 ., The setting of LTD, tags appears to be mediated by mitogen-activated protein kinases 15 , but, no specific PRP is yet known ., It turns out that LTP and LTD are not independent processes and that an interaction, known as “cross-capture” can occur between synapses tagged for, LTP and synapses tagged for LTD 19 ., Thus 1 ) e-LTD of one synapse can be converted to by giving inducing strong HFS to a second synapse shortly before or after, the induction of e-LTD at the first synapse; 2 ) e-LTP can be converted to in an analogous manner ., Cross-capture suggests that strong HFS and, strong LFS both trigger synthesis of both proteins and proteins ., A separate strand of research has put forward the idea that plasticity protocols, cause synapses to make discrete jumps between weak and strong states 21 , 22 ., Discrete synapses have a number of interesting theoretical properties , for example:, 1 ) old memories become at risk of being erased as new ones are stored , ( e . g . 23 ) ; 2 ), synaptic saturation , important in preventing run-away activity , is automatically, included , while storage capacity can be high 24 ., There have been several biochemical models that posit binary synapses 25–31 ., Induction and, maintenance of activity-dependent plasticity has been successfully incorporated into, a recent study 31 , and the longevity of evoked synaptic changes has, been investigated 28 , 29 ., There is however great divergence between most, network-level plasticity models and the experimental observations outlined above ., Network models typically ignore interaction between synapses , use graded weights ,, and assume that the stimulus only determines the amount of weight change and not its, longevity ., Given the limited knowledge of the processes involved , a detailed model seems at, present out of reach ., Instead , the model we present in this paper aims to integrate, the key results from experiments on induction , maintenance and STC together into a, concise model , whilst remaining simple enough to be useful for neural network, modeling ., The model posits a set of possible physical states in which a synapse can, exist , including , in particular , states with a tag present ., The states are, characterized by their synaptic strength , and also by their resistance to, potentiation and depression ., These characteristics are assumed to be determined by, the number of AMPA receptors present in the membrane 32 , and by the, configuration of proteins within the post-synaptic density ( PSD ) 33 ., In our, model , a synapse existing in one state will evolve by making stochastic transitions, between the different states , the probability per unit time of any given transition, being specified explicitly by the model ., High- or low-frequency stimulation is, assumed to change these transition probabilities ., The model does not , at this stage , include the complete biochemical machinery, involved in the induction , expression and maintenance of synaptic plasticity ., Instead , for reasons of computational efficiency , we develop a high-level model that, abstracts these processes and concentrates on the quantities important for network, behavior , namely the induction protocols and the resulting weight changes ., The model, reproduces sufficient agreement with real data to render it useful in exploring, further the functional consequences of STC in network modeling ., We have used our model to simulate several electrophysiology experiments with, multiple populations of synapses ., More specifically , we consider stimulation of, multiple independent synaptic inputs to the same neuronal population in CA1 ,, such that a protein synthesis-triggering stimulus ( i . e . , strong HFS or strong, LFS ) to one input affects all populations of synapses , and leads to STC, interactions between populations ., The stimulation protocol for the experiment, sets the transition rates for synaptic state transitions within each population ., In all cases we assume that at time there have been no recent stimulation protocols , and that the, system is in equilibrium ., Thus , initially , all transition rates are at their, resting values , and all synapses occupy one of the basal states ., Moreover ,, within each population , 80% of the synapses occupy the weak , as, opposed to the strong , basal state ( see Results ) ., Note though , that in a real, experiment , not all synapses will be in basal states , because they might have, experienced strong stimuli already , earlier in life ., As a result , some synapses, may already be in the or state before the experiment is started ., These will however, remain in these states throughout the experiment , and not interfere with other, synapses , so they can be ignored ., However , the presence of such synapses would, reduce the observed amount of LTP/D , both in model and experiment ., The actual number of synapses measured in experiments using extra-cellular, recordings is not known and probably varies considerably between experiments ., The results we obtain come from taking 1000 synapses in each population ., Starting from the initial equilibrium condition , we update state occupancy, numbers at each time-step by random sampling in accordance with the transition, rates ., Then , for each population , we can find the relative field excitatory post-synaptic, potential by expressing the summed synaptic weight at time as a percentage of the initial summed synaptic weight: ( 1 ) where denotes , for population , the occupancy number of state at time , with the states numbered as in Figure 1 ., Furthermore , we used that the, weight of states 4 , 5 , 6 was , twice that of states 1 , 2 , 3 ., In addition to stochastically simulating experiments , it is possible to calculate, mean results as well as the inter-trial standard deviation for each experiment, we simulate ., Let us consider a single population of synapses within an, experiment ., Let denote the probability that a particular synapse is in state at time ., Then the time evolution equation for the is given by ( 2 ) where the matrices are defined by ( 3 ) and denotes the transition rate from state to state at time ( with the convention that the ) ., Using equations ( 2 ) and ( 3 ) , and the fact that at all times, the occupancy numbers follow a multinomial distribution with parameters , it is straightforward to obtain the following equations for, the moments of the : ( 4 ) ( 5 ) ( 6 ) From these equations , together with equation ( 1 ) , we obtain ( 7 ) ( 8 ) where is the weight associated with state i , , ., Numerical integration of equations ( 4 ) , ( 7 ) and ( 8 ) , from, appropriate initial conditions , enables us to plot the mean and the standard, deviation of ., Using the equilibrium multinomial distribution , the appropriate initial conditions are and ., Our model is designed to reproduce as much pre-existing electrophysiological data, on long-term plasticity and STC as possible , whilst at the same time remaining, as simple as possible for its purpose ., In drawing up a list of states , a, trade-off must be made between having few states and complicated transition rate, dynamics or having lots of states and simple transition rate dynamics ., Our, convention is to say that states are distinct if they differ either in their, synaptic strength or in the expected time it will take them to potentiate or, depress in the absence of any plasticity protocols ., This leads us to a six state, model , containing three weak and three strong states: weak basal , strong basal ,, e-LTD , e-LTP , and ., The reactions that are triggered by plasticity protocols are, incorporated via time-variable transition rates between these six states ., Figure 1 shows schematic, drawings of the synaptic states of the model , together with the allowed, transitions between states ., The rate parameter associated with the transition, from one state to another state gives the probability per unit time of a synapse in state making the transition ., Equivalently , the inverse of the rate, parameter is the average time it takes the synapse to make the transition, ( assuming no other transition is available ) ., In our simulations we model, populations of synapses , with each individual synapse behaving independently, with respect to making transitions between states ., In mathematical terms , our, model is a stochastic Markov process ., Effects of stimulation protocols are, modeled by transient changes to the transition rates ., To model STC , certain, stimulation protocols given to just one population of synapses can affect the, transition rates of multiple populations ., These hetero-synaptic effects reflect, the capturing component of STC ., In the absence of stimuli , synapses fluctuate between a weak and a strong basal, state ., The weak basal state is assigned an arbitrary synaptic weight , whilst the strong basal state is taken to have synaptic, weight ., These could correspond to the two states probed in the, experiments of Ref ., 22 , in which it was found that the pairing of a, brief steady current injection with an appropriate depolarization led to, switch-like approximate doubling or halving of synaptic efficacy ., The difference, in efficacy between the two states is assumed to come about from AMPA receptor, insertion/deletion ., The transition rate for changes from weak to strong efficacy is set to , whilst that for changes from strong to weak efficacy , , is set to ., The values of these parameters are chosen, ( a ) to fit the, observation that 80% of synapses occupy the weak basal state when the, population is in equilibrium 22;, ( b ) for the model to reproduce data on, e-LTP/D decay to good agreement ( via decay from the e-LTP/D state followed by, equilibration between the two basal states ) ., These rates are comparable with, AMPA receptor recycling times 34 ., The other strong synaptic states are the e- and states ., They have the same efficacy as the strong basal state ,, but are considered potentiated states due to their increased resistance to, depression ., Choosing all potentiated states to have the same weight is motivated, by the data which shows that in experiments all LTP forms exhibit very similar, amounts of weight change ., This is actually surprising given the wide variety of, mechanisms that underlie the different forms of LTP ., Transitions into the, potentiated states only occur during intervals following certain stimulation, protocols , which we discuss below ., Once a synapse enters the e-LTP state it will, decay back into the strong basal state , with transition rate , unless it has the opportunity to move into the state ., The motivation for this decay rate comes from, experimental results on e-LTP decay ., Furthermore , it is assumed there is a tag, present in the e-LTP state since data suggest synapses in an e-LTP state convert, to an state whenever PRPs become available for capture 12 , 13 ., Although we do not model the biochemistry explicitly , we suggest that when a, synapse is in the e-LTP state , the CaMKII in the synapse is in a phosphorilated, state 15 ., When a synapse enters the state , it becomes very stable , as the only transition is very, slow decay to the strong basal state , with a rate of ., Synapses in the state are assumed to have captured PRPs , such as, 6 , 16 ., Although there is some evidence that decay, from the state is an active process rather than passive decay 8 , 35 , detailed knowledge of this is still lacking ,, so we did not attempt to include this ., The given decay rate is not intended to, be precise , but is intentionally of a smaller order of magnitude than the other, time-constants of the model ., Finally , the model is symmetric in potentiation and, depression , and so the LTD states are analogous to the LTP states ., The model has ten transitions in total , however setting some rates identical, leaves a total of seven transition rate parameters , Figure 1 . We have so far mentioned and which are responsible for fluctuations between the basal, states , as well as and which are the decay rates for e-LTP/D and respectively ., In addition , there are three further parameters , , and , for transitions into e-LTP/D and states ., These are only switched on following a, plasticity-inducing protocol ., Note that of these seven parameters , only and are constant; , , , and change transiently after stimulation ., In this section and the next we discuss the effects of LTP-inducing protocols on, the transition rates; the effect on synaptic weight dynamics is discussed in, later sections ., We model induction in a direct way , focusing on the effects of, specific plasticity-inducing stimuli rather than introducing additional stimulus, parameters ( such as strength , frequency or duration ) ., Specifically , we consider, 1 ) for e-LTP , a single one second burst of HFS ( weak HFS ) ;, 2 ) for , three repeated bursts of HFS , separated by 10 minute, time-intervals ( strong HFS ) ., The time courses for the transition rates have been, chosen so that the model matches the electrophysiological data that the model, aims to reproduce ., After any burst of HFS is applied , the following two changes occur ., Firstly , the, rate from the weak to strong basal state increases to some very, large value for a short period , before returning to its original value ., Mathematically , we use for a stimulus at time ., This , in effect , moves all synapses occupying the weak basal, state into the strong basal state ., This rapid switching is motivated by the, above-mentioned observations at the single synapse level 22 , and is assumed to, come about from AMPA receptor insertion ., Secondly , transitions from the strong basal state into the e-LTP state are, transiently turned on ., Following a stimulus at time , the rate of these transitions is given by an alpha-function ., Thus the rate takes a few minutes to grow to a significant level , peaks at a, value of , ten minutes after stimulation , and then decays back toward, zero , Figure 2 ., Alpha-functions arise naturally in chemical reaction dynamics ., In general , a, chain of first-order reactions will lead to a difference of exponentials , while, two subsequent reactions with identical rates will yield an alpha-function ., Here, the alpha-function is assumed to arise from the biochemical induction process in, the PSD ., The time-course for is motivated from evidence that a synaptic tag takes a few, minutes to form 36 ., Biophysically , the transitions to the e-LTP state might correspond to the, phosphorilation of serine-831 of the GluR1 AMPA receptor sub-units during LTP, induction 33 , which is higher 30 minutes after LTP induction, than immediately post-stimulus 2 ., Serine-831, phosphorilation is driven by CaMKII phosphorilation which happens on a faster, time-scale than that of tag stabilization 36 ., A highly, simplified model of this cascade would yield an alpha-function ., Alternatively ,, the CaMKII phosphorilation itself might correspond to tag formation and the, transition to e-LTP ., In addition to evoking the rate changes described above , a synapse subject to, strong HFS must incur additional changes resulting from the triggering of, protein synthesis and diffusion 4 , 5 ., This translates in our model to the, triggering of the transition rate from the e-LTP state into the state ., As discussed above this might correspond to the capture, of ., We assume that for the second burst of HFS crosses the threshold for protein, synthesis and the rate begins to change ., Simulations are not sensitive to the precise, course takes , nor is this tightly constrained by experimental data ., We assume the plausible form when the second burst of HFS comes at time ., The maximum value of is reached at time ., The precise conditions for protein synthesis are not known ., The strong HFS protocol described here is not the only protocol that leads to ; sometimes a strong , single burst of HFS is used 11 ., In that instance , we would need to assume that protein synthesis starts sooner ., In general , this could be achieved by integrating the stimulation and, thresholding it ., The rate also governs transitions from the e-LTD to the state , which enables the model to describe, “cross-capture” , whereby e-LTD of one synapse by weak LFS, can be converted to by applying strong HFS to a different synapse 19 ., We discuss this further in the section “Modeling synaptic tagging and, capture” ., Figure 2, summarizes the effects of weak and strong HFS on the transition rates in our, model , including their courses ., The effects of LFS are analogous to those of HFS ., Both weak and strong LFS affect, the rate from the strong basal to the weak basal state , and the rate from the weak basal to the e-LTD state in the same way that, HFS affects the rates and , respectively ., The only difference is that is held very high ( at ) for the extended period of four minutes , to reflect the, longer duration of an LFS protocol ., The rate follows the time-course , with being the time at stimulus onset ., This transition could, correspond to the de-phosphorilation of serine S-845 33 ., As mentioned above , the rate from the e-LTD state to the state is given by the same parameter as the rate from the e-LTP state to the state ., Strong LFS triggers this parameter in the same way as, strong HFS , i . e . , following strong LFS starting at time ., ( This can be taken to start at stimulus onset since the, strong LFS we consider consists of triple pulses separated by just one second, intervals ., This is in contrast to our strong HFS protocol , for which the bursts, are separated by 10 minute time-intervals ., ) In the above discussion , we have focused on stimulation of a single population of, synapses ., However STC relates to interactions between different populations of, synapses ., In our model , transitions from the weak basal state to the strong, basal state ( ) , or from the strong basal state to the e-LTP state ( ) reflect synapse-specific changes; namely changes in the, number of AMPA receptors , and configurational changes in the PSD 32 , 33 ., The transition rates and are only modified in stimulated synapses , and hence weak HFS, only affects synapses to which it is applied ., However , transition from the e-LTP, to the state results in cell-wide changes , i . e . , protein synthesis ., Thus , after one population of synapses has received strong HFS ,, many populations of synapses will see a change in the rate of these transitions ., Consistent with experiments , synapses in, an unstimulated population have little chance of being in the e-LTP state , and, will not be affected by the strong HFS; no tags are present ., But if another, population of synapses has received weak HFS and move into the tagged ( e-LTP ), state , then they have a chance to move into the state; proteins are captured by tags ., The STC process for LTD, is analogous to that for LTP ., Note that there is evidence that the STC interaction has limited range , and can, not occur between far away synapses , such as between a basal dendrite synapse, and an apical dendrite synapse 15 , 37 ., In this work we assume that when two different, populations within the same neuron are stimulated , they are close enough to, interact via STC ., However , extension to compartmentalized STC is possible ( see, Discussion ) ., As we demonstrate below , the model also accounts for, “cross-capture” in a straightforward way by using the same, parameter for transitions from the e-LTP state to the state and from the e-LTD state to the state ., Thus , for example , after one, population of synapses has received strong HFS , synapses from a, second population that find themselves in the tagged e-LTD, state will have a chance to change into the state as a result of LTD tags capturing proteins ., In addition to reproducing single-trial experiments , the model makes novel, predictions about the theoretical mean and inter-trial standard deviation of the, fEPSP ., Figure 7A and 7B, illustrate this for populations of 1000 synapses given weak HFS and weak LFS ,, whilst graphs C+D illustrate this for strong HFS and strong LFS ., We see, that when e-LTP is established the standard deviation is greater than at, baseline , whilst when e-LTD is established the standard deviation is less , Figure 7B ., In the former case ,, the increase is a result of variability in the number of synapses that make it, into the e-LTP state ., Although all synapses are initially moved into the strong, basal state by the HFS , ( resulting briefly in zero fEPSP variability ) , while the, tag-forming reaction in the PSD is still incomplete , a variable number of, synapses drop into the weak basal state from where they can no longer access the, e-LTP state , Figure 1 ., Although an analogous process occurs during the onset of e-LTD , the standard, deviation remains less in this case since the transition rate from the weak to, strong basal state ( ) is much less than that from the strong to weak basal state ( ) ., The standard deviation is also less when is established , Figure 7D ., This is because strong HFS/LFS enables almost all the, synapses to enter , first the e-LTP/D state , and then the state , in which the weight becomes stable ., The theoretical predictions above can be used in a similar way to the noise, analysis technique used to extract properties of voltage- and ligand-gated, channels from measurements of their mean current and current fluctuations 39 ., In, all cases the transition matrix determines not only the evolution of the mean, but also the fluctuations around the mean ., In principle this means that a more, accurate estimate of the transition matrix can be obtained by fitting both the, mean and the fluctuations ., In analogy with standard noise analysis , here the, fluctuations in the basal state are inversely proportional to the number of, synapses , the spectrum of the fluctuations can be used to determine the rate, constants , and changes to the fluctuations as compared to baseline can be used, to calculate how many synapses have made a transition ., Although we have, attempted to perform this type of analysis on data recorded by Roger Redondo , we, found that too many additional noise sources , as well as non-stationarity , makes, this analysis currently unsuitable ., We have presented a model of synaptic plasticity at hippocampal synapses which, reproduces several slice experiments ., It contains just six distinct states , yet, gives rise to a rich set of electrophysiological properties ., The model incorporates, the two observed flavors of LTP and LTD , namely the early and late phases , and, de-potentiation , as well as the interaction between these two phases , known commonly, as synaptic tagging and capture ., The model has a number of key features: Because all three LTP and all three LTD states have the same weight associated to, them ( and , respectively ) , a given synapse has a binary weight ., This is, reminiscent of a number of models that have proposed bistable synapses to stabilize, memories , often using CaMKII as a switch 25–31 ., In, the current model , synapses have three levels of stability ( basal , early-phase and, late-phase ) , with the early- and late-phase being stable up to hours ., It is likely, that on a biochemical level , bistable switches underlie these more stable states and, slow down the transition rates , consistent with those earlier models ., Another key postulate of the model is the existence of a single state that, corresponds both to the synapse exhibiting e-LTP and the presence of an tag , ( and similarly for LTD ) ., They go hand in hand; under natural, conditions there is no mechanism by which an tag can be removed , whilst still retaining e-LTP , or indeed, vice-versa , Figure 6 . If tag, formation is incomplete , de-potentiation ( from LFS ) can occur and tag formation, halted , but if tag formation is complete , de-potentiation can not occur and the tag, can not be destroyed , consistent with data in 36 ., Pharmacological, 15 and genetic manipulations ( reviewed in 40 ) can, interfere with tag setting and capture ., The reverse , tag setting without e-LTP , has, not ( yet ) been observed ., Finally , the model makes predictions about the noise level in the fEPSP during a, period of potentiation ( or depression ) followed by a return to baseline value ., In, particular , it predicts that the noise level increases during a period of e-LTP , but, decreases during a period of e-LTD , or , Figure 7 . The, source of this noise is purely the random nature of the transitions between states ., As experimental noise is not taken into account by the model , a test of these, predictions would require systematic removal of experimental noise from a data set ., The reason for the decreased variability during is that many synapses occupy a state that is immune to weight, change ., An alternative , more complicated model would allow for the possibility of a, synapse in a “strong” state to become even stronger , say by, insertion of even more AMPA receptors ., If this were the case , then a greater level, of noise could occur during as a result of synapses fluctuating between the state of our current model and an extra “even, stronger” state ., Note however that this would be inconsistent with, experimental evidence that synapses have only two stable levels of efficacy , e . g ., 2 , 22 ., Next , we discuss shortcomings and potential extensions of the model ., In general , it, is likely that adding extra states and more complex dynamics would refine the, agreement with experimental data ., However , doing this incurs the cost of making the, model more cumbersome to fit and computationally more expensive ., Extra states could ,, for example , enable us to incorporate the biochemistry of the PSD , leading to a more, realistic description of the flow from the basal states into the LTP and LTD states, 41 ., A recent model of LTP by Smolen 42 indeed incorporates continuous variables for the, state of the tag and for protein expression , together with modeling of calcium, dynamics ., Protein synthesis probably plays a more subtle rôle in LTP than our model, incorporates ., For example , immunity to de-potentiation does not require protein, synthesis in our model , even though some data suggest it does 43 ., Other data suggest that ,, at high levels of synaptic activation , protein synthesis can be involved in e-LTP as, well as in, 10 ., We, have not considered such regimes of reduced protein synthesis in which there could, be competition for the capture of proteins available 44 ., To reduce the level, of protein synthesis , one could simply decrease the post-strong stimulus growth and, peak of the transition rate , ( the rate corresponding to the availability of PRPs ) ., Competition, could then be incorporated by reducing the value of further every time a synapse makes the transition into a state ., Both these effects would reduce the number of synapses that, enter the states and the long term change in the fEPSP would be reduced ., Another extension would involve specifying the distances of the site of protein, synthesis from the two stimulated populations ., Our results are not sensitive to the, precise time-course of the transition rate , and so our model does not make predictions about this ., The, time-course for could however be made to reflect the distance of the site of, protein synthesis from the stimulated synapses ., For very local protein synthesis , would grow faster and larger than for more distant protein, synthesis ., In particular , if different populations were at different distances from, the site of protein synthesis , then the rate would differ between the two populations ., For example , suppose, protein synthesis took place near a population of synapses given strong HFS ., Then a, second popu
Recent data indicate that plasticity protocols have not only synapse-specific but, also more widespread effects ., In particular , in synaptic tagging and capture, ( STC ) , tagged synapses can capture plasticity-related proteins , synthesized in, response to strong stimulation of other synapses ., This leads to long-lasting, modification of only weakly stimulated synapses ., Here we present a biophysical, model of synaptic plasticity in the hippocampus that incorporates several key, results from experiments on STC ., The model specifies a set of physical states in, which a synapse can exist , together with transition rates that are affected by, high- and low-frequency stimulation protocols ., In contrast to most standard, plasticity models , the model exhibits both early- and late-phase LTP/D ,, de-potentiation , and STC ., As such , it provides a useful starting point for, further theoretical work on the role of STC in learning and memory .
It is thought that the main biological mechanism of memory corresponds to, long-lasting changes in the strengths , or weights , of synapses between neurons ., The phenomenon of long-term synaptic weight change has been particularly well, documented in the hippocampus , a crucial brain region for the induction of, episodic memory ., One important result that has emerged is that the duration of, synaptic weight change depends on the stimulus used to induce it ., In particular ,, a certain weak stimulus induces a change that lasts for around three hours ,, whilst stronger stimuli induce changes that last longer , in some cases as long, as several months ., Interestingly , if separate weak and strong stimuli are given, in reasonably quick succession to different synapses of the same neuron , both, synapses exhibit long-lasting change ., Here we construct a model of synapses in, the hippocampus that reproduces various data associated with this phenomenon ., The model specifies a set of abstract physical states in which a synapse can, exist as well as probabilities for making transitions between these states ., This, paper provides a basis for further studies into the function of the described, phenomena .
computational biology/computational neuroscience, neuroscience/theoretical neuroscience