Some thoughts about neural coding and spike trains

Transcription

1 BioSystems 58 (2000) Some thoughts about neural coding and spike trains José Pedro Segundo *,1 Departamento de Biomatemática, Facultad de Clenclas, Monte ideo, Uruguay Abstract This communication introduces the topic. Foundations: Core concepts: Codings are relations summarized by rules or codes. Special codings are neural, natural (in everyday life), experimental (in laboratories), conditional (to partner restrictions), etc. Partial aspects are mechanisms, what partners say about each other, etc. Critical experimental issues: Trains are e aluated by when spikes occur: i.e. as point processes and timings. Trains and point process representations become synonyms. Any code must: (i) be a number (rate) cod and an interval cod ; and (ii) include referent, train covariations involving steady states with overall averages and fluctuations with patterns (dispersions, sequences). Seminal findings. Early data proved trains participated in codings; this is accepted unanimously. Inevitably, though accepted less readily, codings included rates, intervals, averages and patterns. Literature highlights. (1) Confirmed the seminal finding (2.2.) over vast domains; (2) Demonstrated both general and synaptic codings (referents, respectively, sensory, states, etc. and trains in directly connected neurons); (3) Revealed overlap between general and synaptic coding features. Overlap allows train participation in network dynamics; (4) Introduced natural formal contexts. (Point Process Mathematics, Communication. Information and Dynamical Systems Theories); (5) Includes confused opinions: (i) Opposition between rates and intervals; (ii) claims that averages are meaningful but patterns irrelevant. Both, overlooking foundations and evidence, are untenable Published by Elsevier Science Ireland Ltd. All rights reserved. Keywords: Neural coding; Point processes; Coding roles of spike trains; Foundations and evidence 1. Introduction This communication is intended as no more than a simple introduction to a Workshop, that, * Present address: Department of Neurobiology, University of California, Los Angeles, CA , USA. Tel.: ; fax: address: segundo@neurobio.medsch.ucla.edu (J.P. Segundo). 1 Supported by Trent H. Wells jr. Inc. as the one in Osaka in 1999, is on neural coding and spike trains. Its primary goal is to identify the topic s foundations (Section 2). This is complemented by listing the salient overall highlights of the relevant data base (Section 3). Keeping both (Section 2) and (Section 3) in mind is indispensable for strict consideration of neural coding and spike trains. This kind of purpose can be served acceptably, it is felt, by a succinct, almost telegraphic text and by citations reduced to a bare minimum /00/$ - see front matter 2000 Published by Elsevier Science Ireland Ltd. All rights reserved. PII: S (00)

2 4 J.P. Segundo / BioSystems 58 (2000) Foundations Foundations are the notions upon which the topic stands and is supported (e.g. Perkel and Bullock, 1968; Segundo, 1970). They jointly include the topics core concepts (Section 2.1) and two critical experimental issues (Section 2.2) Core concepts (and definitions) A coding or encoding is a relation R between two entities (variables messages etc.); the relation R is such that it can be summarized by rules, and these constitute its code (Segundo, 1970). Relatio has the elementary sense of a pair of objects in a definite order (Stoll, 1961); one-to-oneness is not required. Coding therefore has the sense used by Khinchine (1957) when referring to the conversion of source output alphabets to channel input alphabets. Association, mapping, representation, transformation, correspondence etc. are acceptable synonyms. Codings can be summarized by codes, and thus are not random relations. A random relation is one that, in the rigorous sense defined by Chaitin (1975) allows no abbreviation (or, inpractice, only limited ones): this sense judiciously formalizes the everyday meaning of lacking plan or purpose. Codings imply bonds of some kind between the variables which, therefore, covary significantly. The fact of the coding includes the entities that participate, the variables that pertain to those entities, the states and/or changes matched experimentally, as well as the rules that, inferred from the data, tell us how the partner variables covary and thus compose the code. The pertinent literature is quite clear in that codings are considered relations with bonds. The existence of a relation with a bond is, in fact, the indispensable take-off point, that which justifies interests in the topic and without which conceptually no issue relevant to it can exist and make sense. This must be, therefore, the natural and intuitive sense wherein neuroscientists perceive the notion Special codings The coding R is a general abstraction that embraces all conceivable ways in which each partner can be described, and all conceivable situations in which partners can be matched. Subsets of R constitute special codings. Each subset is defined with a particular restrictive criterion; different special codings can overlap. Codings are neural when one partner at least involves the nervous system; only codings involving spike trains are dealt with here. The other partner is called the referent (see Section 3.2). (i) The natural coding R L is operant during the animal s natural life; (ii) The experimental coding R E is that inferred experimentally: it includes only particular features and particular situations (e.g. interval histograms, respiration and phrenic neurons); (iii) Conditional codings (R N/ m* or R M/n* ) arise when a particular conditioning event (or class of events) in the space of one partner is chosen and its associations in the other space are considered. R may involve stimuli to the skin and trains in certain neurons, respectively, events m in space M and n in N. One conditional coding associates prospectively a particular stimulus (event m*) and all trains (n) it could elicit; another one associates retrospectively a particular train (event n*) and all stimuli (m) that could elicit it. Similarly, conditional codings arise in motor and other functions Partial aspects All relations, and therefore all codings, exhibit partial aspects which inherent to them, must always be present. Such aspects can be highly significant functionally. Understandably, papers generally tackle preferentially one aspect and pay at best superficial attention to others. Using a single partial aspect to define coding is restrictive and thus not appropriate. Thus, the present author differs with his friends and colleagues Perkel and Bullock (1968) and Perkel (1970) who defined coding as the representation and transformation of information. As pointed out, many papers tackle preferentially aspects other than those dealing with information. Some partial aspects follow: (i) Underlying

3 J.P. Segundo / BioSystems 58 (2000) mechanisms. These are the basic processes that allow the coding (e.g. those in receptors, neurons, synapses or effectors); (ii) Operational roles. These imply how the coding participates in each special network and function (e.g. in some spinal circuit or in vision); (iii) Reciprocal knowledge. The expression refers to the fact that, because of the coding, each partner has something to say about the other (e.g. sensory stimuli and the associated trains). Reciprocal knowledge can be quantified in several ways, for example using cross-statistics (e.g. correlations, spectra); it is quantified more precisely and exhaustively, using the specific measure called mutual information. It is necessary to keep in mind that valid investigator-centered issues raised in R may differ from meaningful neuron-centered ones participating in R L Critical experimental issues Two experimental issues contribute to the topics foundations. One is the cardinal criterion used for evaluating spike trains (Section 2.2.1); the other is a finding that became seminal (Section 2.2.2) The cardinal criterion for e aluating spike trains Spontaneously and instinctively, neuroscientists evaluate individual trains by recognizing spikes individually and then noting when they occur: i.e. noting how whether spikes are many and packed or few and dispersed evolves as time advances and more spikes appear. Thus, the indices of the cell s activity are the numbers of spikes it generates and the intervals between them, and both are pursued together as they unfold. In other words, neuroscientists spontaneously and instinctively evaluate trains as series of events along time assimilating them to realizations of point processes (Cox and Lewis, 1966; Cox and Isham, 1980): the point process is the set of instants t I when spikes occur called timing. The nomenclature used here was proposed by Segundo et al. (1968). In this context, therefore, a train, its point process description and its timing become synonyms and are indistinguishable. Accordingly, any statement about a spike train so evaluated must imply both constitutional variables of all point processes: namely, numbers (or counts) translating into rates and intervals. Because of this, it also is unavoidable that any putative code involving trains so evaluated must comply with two conditions: (a) In the first place, that code must jointly be a number (count) or rate code and an interval code. Theoretically, for a particular train one can obtain the statistics and distributions of counts given those of intervals, and vice-versa. For example, the average rate and the average interval are reciprocals and interchangeable, providing, of course, that they are estimated under identical conditions. This does not mean that the restricted descriptions obtained in practice necessarily are always equivalent; (b) in the second place, any such code must jointly include covariation of referent steady states with train overall averages, and covariation of referent fluctuations with train dispersions and sequences. A train s dispersion and sequence are called its pattern : patterns are quantified by innumerable rate and interval statistics. Logically, accepting the functional significance of average rates and their differences under some conditions, necessarily lead to accepting the functional significance of patterns and their differences under the same or other conditions. Indeed, assume that in some coding over a span (0, S] the average rates r 1 and r 2 differ functionally and that patterns are irrelevant; necessarily, then, over (0, 2S] at the same average (r 1 +r 2 )/2, the patterns r 1 /(0, S], r 2 /(S, 2S] versus r 2 /(0, S], r 1 /(S, 2S] must differ functionally The seminal finding Experimentally, electrophysiologists proved early that spike trains viewed as embodiments of point processes often covaried with functional referents, in other words often participated inneural codings. This, acknowledged immediately, opened the field. Nowadays, it is accepted unanimously, and almost unthinkingly taken for granted. Covariations, i.e. codings, includednumbers (counts, rates), intervals, averages and patterns (dispersions, sequences). This, which could not

4 6 J.P. Segundo / BioSystems 58 (2000) 3 7 have been otherwise (Section 2.2.1), is accepted less readily (Section 3.5). The above statements and conclusions are based on either logic or inferential rules: they are, therefore, comprehensive and of a general nature. This does not imply they must hold also in every particular observation, regardless of where, when and how monitored and evaluated, i.e. rates and patterns will participate somehow in every coding, but each coding may well include local observations where one or both do not participate. 3. Highlights of the data base The following will first underscore what are considered the highlights of, i.e. the main conclusions inferred from, the relevant experiments (Section 3.1, Section 3.2, Section 3.3). This is followed by statements that involve facts as perceived, as well as value judgements about them (Section 3.4, Section 3.5). All are stated telegraphically Confirmation o er a ast domain of the seminal finding (Section 2.2.2) that spike trains as point processes and timings participate in neural codings Particular instances of functionally meaningful codings matched spike trains with referents in practically all fields explored (see Section 3.2). As could not be otherwise (Section 2.2.1), all codings included numbers (counts rates) intervals, averages and patterns Demonstration of general and of synaptic codings, each with characteristic kinds of referents General codings Referents are sensory or effector parameters, normal or abnormal states, etc. (e.g. tactile stimuli, respiratory patterns, sleep states, seizures) Synaptic codings Referents are trains in neurons having direct synaptic connections with the first. Connections are at either the input or output side of the targeted neuron: the latter acts simultaneously as, respectively, post or presynaptic partner. They provide the operational unit for nervous systems conceived as networks of neurons that generate spikes and interact via synapses. Synaptic codings imply issues and notions whose recognition and dissection are critical for understanding network dynamics (e.g. Bullock, 1961; Segundo and Perkel, 1969; Segundo, 1970). For example, in synaptic codings, the postsynaptic cell adjusts its output trains to the input presynaptic spike trains: it can thus be said to perform as an analyser device for the former. When dissimilar arriving trains associate with dissimilar output trains, the fact of a difference is preserved: the postsynaptic neuron thus reads that difference discriminating between trains. The essence of integration is that pre and postsynaptic trains, though related, are different (excepted are special cases such as neuromuscular synapses). Moreover, the postsynaptic neuron unceasingly resolves the alternative of firing or not firing, thus acting as a decision-making element. Its decisions are based on happenings within a bounded recent epoch. Within this period, a veritable memory, the postsynaptic neuron evaluates the rate and interval averages and patterns of recent pre and postsynaptic spikes. Epochs and spikes therein have been alluded to as integration period and influential events, respectively Disclosure of a remarkable o erlap between the train features that participate in general codings and the features seen in synaptic codings Because of this agreement, networks can use trains as tools in their ongoing dynamics; its importance is, therefore, paramount Introduction of neural coding and spike trains into its natural formal contexts Contexts are, say, Point Process Mathematics, Communication and Information Theory and Dynamical Systems Theory. An increasing number of sophisticated publications based on these formal constructs has contributed greatly to the appropriateness of our approaches and comprehen-

5 J.P. Segundo / BioSystems 58 (2000) sion. The present Workshop will add significantly to it. In particular, the general concepts of Communication and Information Theories apply to all systems formed by interacting entities (e.g. Segundo, 1970; Rieke et al., 1997). This includes neural codings individually, as well as entire nervous systems composed by endless numbers of such codings. Application of those concepts to particular cases has not always been as fruitful as one could wish: this is because of two main reasons. One, that our often limited knowledge of neural function hinders pursuing what Shannon called semantic and effectiveness issues; these issues are self-evident in sensory and motor neurons where main roles are, respectively, identifying stimuli and eliciting particular contractions. Another reason is that precise quantifications using entropies and mutual informations demand knowing all outcomes and having reliable estimates of all probabilities: this often requires very large data sets Untenable hypothesis On the negative side, a measure of confusion arises from a tendency to overlook the topic s foundations (Section 2.1, Section 2.2) notions, experimental issues plus the evidence made available subsequently (Section 3.1, Section 3.2, Section 3.3), as well as their logical frameworks and the guidelines from them derived. This neglect characterizes two opinions, currently expressed or implied. Namely: (i) the trenchant opposition between rate and interval statistics; and (ii) the exclusive significance of overall average rates plus the irrelevance of intervals and of local rate patterns. Both opinions clash with foundations and evidence, and thus are untenable; opinion (ii) also is inconsistent intrinsically (see Section 2.2.1). Publications espousing such credos preserve a façade of verisimilitude by practicing biased citation policies whereby references espousing them are accepted and all others purged. Their not negligible support probably reflects issues emerging from the Sociology of Science. References Bullock, T.H., The problem of recognition in an analyzer made of neurons. In: Rosemblith, W.A. (Ed.), Sensory Communication. Wiley, New York, pp Chaitin, G.J., Randomness and mathematical proof. Scientific American 232, Cox, D.R., Isham, V., Point processes. Chapman and Hill, London and New York. Cox, D.R., Lewis, P.A.W., The Statistical Analysis of Series of Events. John Wiley and Sons, New York. Khinchine, A.I., Mathematical Foundations of Information Theory. Dover Publications Inc, New York. Perkel, D.H., Spike trains as carriers of information. In: Quarton, G.C., Melnechuk, T, Schmitt, F.O. (Eds.), The Neurosciences. Second Study Program. Rockefeller University Press, New York, pp Rieke, F., Warland, D., de Ruyter, van Steveninck, Bialek, W., Spikes. Exploring the Neural Code. The MIT Press, Cambridge, MA. Segundo, J.P., Communication and coding by nerve cells. In: Quarton, G, Melnechuk, T., Schmitt, F.O. (Eds.), The Neurosciences. Second Study Program. Rockefeller University Press, New York, pp Segundo, J.P., Perkel, D.P., The nerve cell as an analyzer of spike trains. In: Brazier, M.B.A. (Ed.), The Interneuron, UCLA Forum in Medical Sciences, No. 11. University of California Press, Berkeley and Los Angeles, pp Segundo, J.P., Perkel, D.P., Wyman, H., Hegstad, H., Moore, G.P., Input-output relations in computer-simulated nerve cells. Influence of the statistical properties, number and interdependence of excitatory pre-synaptic terminals. Kybernetik 4, Stoll, R.R., Sets, Logic, Axiomatic Theories. W.H. Freeman and Co, San Francisco..