Two components of long-term memory

Piotr A. woiniak1, Edward J. ~orzela6cz~k~ and Janusz A. ~urakowski~

1.2~aboratoryof the Applied Research at the Department of Nursing and Health Sciences, Karol Marcinkowski Medical Academy, 79 Dqbrowski St., 60-529 Pornali Poland; 3~epartmentof Physics and Astronomy, University of Delaware, Newark, DE 19716, USA

Abstract. The existence of two independent components of long-term memory has been demonstrated by the authors. The evidence has been derived from the authors' findings related to the optimum spacing of repetitions in paired-associate learning. The two components are sufficient to explain the optimum spacing of repetitions as well as the spacing effect. Although the molecular counterparts of the two components of memory are not known, the authors provide a collection of guidelines that might facilitate identification of such counterparts.

to whom correspondence Key words: memory, learning, paired-associate learning, spacing should be addressed repetitions, synapse, long-term potentiation, spacing effect 302 P.A. Woiniak et al.

It has been found in earlier research that the op- out the spacing effect, a large number of repetitions timum spacing of repetitions in paired-associate in a very short period of time might increase the op- learning, understood as the spacing which takes a timum inter-repetition interval to an excessive minimum number of repetitions to indefinitely value, far beyond the period in which the learned as- maintain a constant level of knowledge retention sociation is important for the conditioned individ- (e.g. 95%), can roughly be expressed using the fol- ual. lowing formulae (Woiniak and Gorzelanczyk Because of a deeply-rooted evolutionary signi- 1994). ficance of the increasing interval paradigm in con- solidating long-term memories, the authors postulate the universal applicability of their find- ings on optimum spacing of repetition to a wide range of learning tasks in mammals, and probably beyond. where: The molecular correlates underlying the regular Ii - inter-repetition interval after the i-th repeti- nature of the optimum spacing of repetitions have tion not yet been identified. C1 - length of the first interval (dependent on the The majority of publications on mechanisms of chosen knowledge retention, and usually equal memory introduce the ill-defined term "strength of to several days) memory", which at the molecular level is used sy- C2 - constant that denotes the increase of inter- nonymously with the term "synaptic potentiation". -repetition intervals in subsequent repetitions Strength of memory is usually understood as the (dependent on the chosen knowledge retention, parameter of the memory system whose value, and the difficulty of the remembered item) which determines the ease of recall, increases with The above formulae have been found for human repetitive actions accompanying learning. subjects using computer optimization procedures It has been widely assumed that the study of employed to supervise the process of self-paced long-term potentiation (LTP) in CA1 cells of the learning of word-pairs using the active recall drop- hippocampus may shed light on at least some mech- out technique. anisms underlying consolidation of memory in hu- The length of an optimum inter-repetition inter- mans (Aronica et al. 199 1, Bliss and Collingridge val computed using Eqns. (I) and (2) is determined 1993). This area of study has recently abounded in by the following factors: identifying molecular factors correlated with - interval must be short enough to prevent forget- strength of memory or synaptic potentiation in the ting wake of conditioning. At different points in time, - interval must be long enough to prevent the ne- these include: activation of glutamate NMDA re- gative impact of the spacing effect (Hintzman 1974, ceptors (Bliss and Lynch 1988), elevation of cyto- Glenberg 1977). solic calcium (Lisman and Goldring 1988), The evolutionary value of forgetting and the activation of metabotropic glutamate receptor spacing effect may be to optimize the use of limited (Bashir et al. 1993), activation of phospholipase C, memory storage for preserving the most relevant increased levels of diacylglycerol (DAG) and ino- and useful engrams. Forgetting probably serves as sit01 triphosphate (IP3) (Nahizaka 1989), increased a garbage collection mechanism that is used to levels of nitric oxide (NO) (Bruchwyler et al. 1993), remove the least relevant memory traces and to pre- increased levels of arachidonic acid (AA) (Bliss and vent storage overflow. On the other hand, the spac- Collingridge 1993), increased levels of pre- and ing effect might prevent conserving memories that postsynaptic CAMP and cGMP (Mork and Geisler are relevant only in a limited period of time. With- 1989, Wood et al. 1990), increased activity of mem- Components of long term memory 303 brane-bound protein kinase C (Alkon 1989, Olds et 2. Just at the onset of the i-th repetition, r=0, al. 1989, Spieler et al. 1993), etc. Also, after a longer while si> si-1>0 (si denotes s right at the onset of the period of time, the following changes can be ob- i-th repetition). This indicates that there is no func- served: synthesis of some transcription factors tion gi such that s=gi(r), i.e. s cannot be a function (Kaczmarek 1993), gene expression (Matthies of r only. 1989), increased number of various glutamate re- 3. During the inter-repetition interval, r(tl)or(t2) ceptors (Lynch 1984), etc. if ti<>t2 (t denotes time and r(t) denotes rat the mo- As it will be shown below, however, the widely ment t). On the other hand, s(tl)=s(t2) (s(t) denotes investigated strength of memory (or synaptic poten- s at the moment t). This shows that there is no func- tiation) does not suffice to account for the regular tion g2 such that r=g2(s), or we would have: pattern of optimum repetition spacing. r(ti)=g2(s(tl))=g2(~(t2))=r(t2), which leads to a con- Consider the following illustrative example, if tradiction. r cannot be a function of s only. (1) the probability of recalling a piece of informa- 4. In Steps 2 and 3 we have shown that r and s tion from memory is 97% at a given point in time are independent, as there are no functions gl and g2 following the first repetition, and (2) the same prob- such that s=gl(r) or r=g2(s). This obviously does not ability is equal to 97% at another moment after the mean that there exists no parameter x and functions second repetition, then (3) the state of memory in ys and yr such that s=y,(x) and r=yr(x). these two moments of time must be different. On 5. It can be shown that r and s suffice to compute one hand, there must be a mechanism that deter- the optimum spacing of repetitions (cf. Eqns. (1) mines that the probability of recall is 97% and not and (2)). Let us first assume that the two following otherwise. On the other, the memory system after functions fr and fs are known in the system involved the point in time following the first repetition will in memory storage: ri=fr(si) and si=fs(si-l). In our manifest a much faster decline in the recall prob- case, these functions have a trivial form fr: ri=si and ability than in the moment following the second fs: ~i=si-l*C2(where C2 is the constant from Eqn. repetition (note, that optimum inter-repetition inter- (2)). In such a case, the variables r and s are suffi- vals increase with each successive repetition). In cient to represent memory at any moment t in opti- other words, though the recall probability is 97% in mum spacing of repetitions. Here is a repetition both cases, the stability of memories is higher in the spacing algorithm which shows this to be true: latter case. The conclusion is that more than one in- 1. assume that the variables ri and si describe the dependent memory process must underlie the regu- state of memory after the i-th repetition larities implied by Eqns. (I) and (2). 2. let there elapse ri time Let us have a slightly more formal look at the 3. let there be a repetition above observation. 4. let the function fs be used to compute the new 1. We want to determine the set of (molecular) value of si+l from si variables involved in storing memory traces that 5. let the function fr be used to compute the new will suffice to account for the optimum spacing of value of ri+l from si+l repetitions. Let us, initially, assume two correlates 6. i:=i+l of these variables in learning that is subject to opti- 7. got0 2 mum spacing as expressed by Eqns. (1) and (2): The above reasoning shows that variables r and r - time which remains from the present moment s form a sufficient set of independent variables until the end of the current optimum interval (op- needed to compute the optimum spacing of repeti- timum interval is the interval at the end of which tions. Obviously, using a set of transformation func- the retention drops to the previously defined tions of the form r=Tr(r) and s=Ts(s), one can level, e.g. 95%) conceive an infinite family of variable pairs r-s that s - length of the current optimum interval. could describe the status of the memory system. A 304 P.A. Woiniak et al. difficult choice remains to choose such a pair r-s where: that will most conveniently correspond with mole- i - number of the repetition in question cular phenomena occurring at the level of the sy- t - time since the i-th repetition napse. Ri(t) - retrievability after the time t passing since The following terminology and interpretation is the i-th repetition in optimum spacing of repeti- proposed by the authors in a memory system invol- tions ving the existence of the r-s pair of variables: the C1 and C2 - constants from Eqns. (1) and (2) variable R, retrievability, determines the prob- K - retention of knowledge equal to 0.95 (it is im- ability with which a given memory trace can be in- portant to notice that the relationship expressed voked at a given moment, while the variable S, by Eqn. (7) may not be true for retention higher stability of memory, determines the rate of decline than 0.95 due to spacing effect resulting from of retrievability as a result of forgetting, and conse- shorter intervals) quently the length of inter-repetition intervals in the For the proposed interpretation of variables R optimum spacing of repetitions. and S, they should exhibit the following set of Assuming the negatively exponential decrease properties in accordance with the known properties of retrievability, and the interpretation of stability as of memory: an inverse of the retrievability decay constant, we 1. R should be related to the probability of recall- might conveniently represent the relationship be- ing a given memory engram; forgetting should tween R and S using the following formula (t denotes be understood as the decrease in R time) : 2. R should reach a high value as early as after the first repetition, and decline rapidly in the matter of days (the average optimum inter-repetition in- terval for retention 95% equals several days) The transformation functions from the pair r-s 3. S determines the rate of decline of R (the higher used in Steps 1-5 of the reasoning, to the proposed the stability of memories, the slower the decrease interpretation R-S will look as follows (assuming of retrievability) the definition of the optimum inter-repetition inter- 4. with each repetition, as S gets higher, R declines val as the interval that produces retention of knowl- at a slower rate (stability of memory increases edge K=0.95): with successive repetitions) 5. S should assume a high value only after a larger number of repetitions (stability of memories is positively correlated with the amount of train- ing) 6. S should not change (significantly) during the The relationship between the stability after the i- inter-repetition interval th repetition (Si) and the constants Ci and C2 deter- 7. if the value of R is high, repetitions do not affect mining the optimum spacing of repetitions as defined S significantly (spacing effect) by Eqns. (1) and (2) can therefore be written as: 8. R and S increase only as a result of an effective repetition (i.e, repetition that takes place after a sufficiently long interval) As shown above, if high levels of retrievability and finally, retrievability in the optimum spacing of prevent the increase in stability, the two presented repetitions can be expressed as: components of long-term memory suffice to ac- count not only for the optimum spacing of repeti- tion, but for the spacing effect as well. Components of long term memory 305

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