Introduction

Kin recognition, especially the failure to recognize close relatives, is a commonly occurring theme in the history and literature of western civilization. Sophocles' tragic tale of Oedipus is perhaps the best known example of kin recognition gone awry. Oedipus followed the inadvertent murder of his father (Laius) by unknowingly marrying his own mother (Jocasta). According to the Old Testament (Genesis 27:27) an error in kin discrimination enabled Jacob to cheat his older brother Esau out of his birthright. By disguising himself as Esau, Jacob deceived their father (Isaac) into granting him the final blessing and inheritance intended for the first born son. Similarly, the fate of Odysseus (Ulysses) was ultimately decided by his inability to identify one of his offspring. On his final voyage, Odysseus launched an attack against Telegonus – his son born of the goddess Circe. Only after being mortally wounded by the younger man did the hero of Homer's saga learn of their relationship.

Despite such long-held fascination with the consequences of kin recognition errors, humans are evidently quite proficient at recognizing family members (as well as other individuals). Nonetheless, there is little knowledge of the scope of human kin recognition capabilities or the underlying bases of this form of social discrimination. As recently pointed out by Wells (1987), in comparison to research with various non-human species, there have been relatively few empirical studies of kin recognition in our own species.

Introduction

The complex societies of wasps, ants and bees constitute a special problem for the Darwinian theory of evolution. This did not escape the attention of Charles Darwin. He considered these insects to represent ‘one special difficulty, which at first appeared to me insuperable, and actually fatal to my whole theory’ (The Origin of Species, Chap. VII, p. 236). If we accept that natural selection operates at the level of individual organisms, it is difficult to comprehend just how it could occur in species like those of eusocial insects, where the majority of individuals are almost always excluded from reproduction because of morphological specializations which generally involve sterility. Darwin conceived of an explanation which allowed him to reconcile the existence of insect societies with his theory of natural selection (‘This difficulty, though appearing insuperable, is lessened, or, as I believe, disappears, when it is remembered that selection may be applied to the family, as well as to the individual …’: ibid., p. 237). This interpretation led eventually to a significant step forward, when an analogy was drawn between the multicellular organism and the insect society, which was conceptualized as a ‘superorganism’ (Wheeler, 1911; Emerson, 1952). After being neglected for some years, this theory has recently been rehabilitated (Lumsden, 1982; Jaisson, 1985; Wilson, 1985). This mode of thinking helps to resolve the difficulties in understanding the functioning of natural selection in insect societies. It suggests that the social group, as a unit, can be influenced by selective pressures, and that there is a relationship between the reproductive caste and the sterile worker caste comparable to that between the soma and the germ plasm of a multicellular organism.

This chapter concerns our methods. How do we translate the available data on the cellular physiology of the CA3 region into a useful model of the circuitry? By “model,” we mean here a computer program. We must then consider how to organize and construct the computer program.

Specifically, we must decide the following: How many cells should we include, and of what types? How are the cells arranged in space? How can the communication between different cells be described? This last question is particularly complex, because it includes both functional and structural aspects. Functionally, we must model the transduction of soma membrane potential into axonal action potentials and axon conduction delays, and the transformation of arriving presynaptic impulses into postsynaptic conductance changes. Structurally, we must specify how the axonal outputs of each type of cell are distributed in space and how many synaptic inputs of each type (excitatory, GABAA, GABAB) each cell should have. We shall discuss these fundamentally physiological issues in turn and then analyze briefly how our simulation program actually works.

Cells

Types of cells. We use three basic types of cells: pyramidal cells (or e cells, for “excitatory cells”); inhibitory cells whose postsynaptic effect resembles that mediated by perisomatic GABAA receptors (i1 cells); a inhibitory cells whose postsynaptic effect represents that mediated by dendritic GABAB receptors (i2 cells).

There are three general issues to consider in developing an electrophysiological model of a neuron. First, how should one describe the passive electrical features, independent of synaptic inputs and voltage-dependent channels? This issue is addressed by anatomical study of detailed neuronal architecture, by examining the theoretical and experimental responses of neurons to injection of subthreshold currents, and by applying certain of the methods of mathematical physics. Second, how should one describe synaptic inputs? Third, how should one simulate voltage-dependent and calcium-dependent currents? We shall discuss each of these general issues in turn, and then present the particular computer model that we use for a pyramidal cell. The behavior of the model will be compared to the behavior of actual hippocampal pyramidal cells. We shall then present a critique of the model. In the Appendix, we review Hodgkin-Huxley theory, the foundation for our simulation of voltage-dependent currents.

Passive properties, cable theory

Approach to modeling the passive properties of neurons. The goal here is to obtain a quantitative description of membrane potential in a single cell as a function of space and time. This is a necessary step for an understanding of the subthreshold behavior of a neuron and the integration of different synaptic inputs that impinge onto various membrane locations. First we divide the cell into its component pieces: the axon, cell body, and the dendrites.

In this chapter and the next we shall analyze the interactions that take place between CA3 neurons in a large population (thousands of cells). The cardinal issues are these: Under what conditions does population firing become synchronized? What factors regulate the extent of synchronization? At one extreme, all cells might fire nearly simultaneously (complete synchrony), or alternatively small subsets of neurons might discharge at the same time (partial synchrony). How can one cell, or a small group of cells, influence the rest of the population? If synchronization is partial, rather than complete, what factors determine which selected cells participate?

It is well to consider why we so emphasize synchronization. After all, in principle, the firing pattern in any particular cell might resemble a Poisson process, and the correlation between firing patterns in different cells either might be weak or might assume some particularly complicated form. In that case, we would focus not on synchronization but on factors that, say, regulate the mean firing throughout the population. However, neuronal firing in the hippocampus in vivo (theta rhythm and sharp waves, described in Chapter 1) and in vitro (epileptiform population bursts and synchronized synaptic potentials, described in Chapter 3 and later in this chapter) tends to aggregate into (more or less) discrete “events” or waves. Thus, synchronization of population activity may represent a basic signaling mechanism.

In this chapter we review data on unitary synaptic interactions between hippocampal neurons necessary to construct a model of the CA3 neuronal network. First, the properties of excitatory and inhibitory synapses between hippocampal neurons are described. We then show that the properties of single synapses allow certain details of the operation of simple recurrent circuits to be deduced. Finally, we consider how activity occurring in multiple parallel circuits is integrated into the summed activity of a large neuronal network. These matters will be further expanded in later chapters.

Our current knowledge of synaptic function has been derived from only a few synapses, such as neuromuscular junctions in frog (Katz, 1969) and crayfish (Atwood and Wojtowicz, 1986), the giant synapse of the squid stellate ganglion (Llinás and Nicholson, 1975), synapses on goldfish Mauthner cells (Korn and Faber, 1987), and Ia afferents terminating on spinal motoneurons (Rail, 1967; Redman and Walmsley, 1983). Are these synapses useful models for understanding connections between cortical cells? Clearly, cortical synapses must be studied directly to provide appropriate information. Such studies have proliferated with the increasing use of isolated preparations. From these studies, values are emerging for several critical parameters of cortical synaptic function. We shall give current estimates from connections between hippocampal neurons.

First, what is the amplitude of postsynaptic potentials evoked by a single presynaptic excitatory or inhibitory neuron?

Thus far, we have concentrated on collective neuronal behaviors in which the only interactions have been mediated by chemical synapses. Another type of neuronal interaction is clearly of importance during hyperexcitable states and may exert at least subtle influences even under normal conditions. Influences between neurons may be mediated by the flow of transmembrane current through the extracellular medium: field effects (Dudek and Traub, 1989). Field effects provide a means for the synchronization of action potentials in different neurons on a time scale of about 1 ms. Slow or DC extracellular fields can also bias a large population of neurons, rendering them all more excitable. The general subject of electrical field effects in the brain has been reviewed by Faber and Korn (1989). We shall restrict our attention here to the hippocampus.

There are several structural features and electrophysiological observations suggesting that field effects might be important in the hippocampus. First, there is the large amplitude of extracellular population spikes that can be obtained after synchronized stimulation of an afferent pathway. Amplitudes of 5–10 mV or more are not unusual in the stratum pyramidale during epileptiform activity in vitro, and population spikes of 20 mV and more in vivo are not unusual (Somjen et al., 1985). These extracellular negative potentials would be expected to produce transmembrane positivities.

In this chapter we ask how hippocampal neurons translate their synaptic inputs into an output signal sent toward other neurons. This basic question has two aspects. First, what are the firing patterns for pyramidal cells and interneurons? Neuronal firing patterns determine both how cells respond to synaptic inputs and the timing of synaptic events that they elicit in other cells. Second, what are the detailed physiological mechanisms, such as electrotonic properties or ionic-channel density and kinetics, that determine how and why a neuron responds as it does? We wish to know how a neuron functions as a device that processes its inputs that are distributed in space and time. A model of a neuron (Chapter 4) must capture the phenomenology correctly; preferably, the model will accurately represent underlying mechanisms to achieve that objective.

Before expanding on these themes, let us first consider the preparations that are used for cellular neurophysiology, with some of their advantages and disadvantages. In vivo studies are the sine qua non for understanding the normal repertoire of neuronal firing patterns and synaptic inputs and how these are correlated with behavioral states. However, stable intracellular recording is very difficult when animals are moving, such as during exploration-associated theta rhythm. Voltage-clamping cells in vivo is likely to be extraordinarily difficult.

Review of anatomy

In this chapter we shall review some aspects of the anatomy and physiology of the hippocampus, considering the hippocampus as only one component of the whole brain. We shall discuss also some clinical consequences of abnormal hippocampal function (epilepsy, amnestic states). Our purpose is to provide a biological background for the more detailed physiological and mathematical material to follow. We wish to define some of the relevant questions that can be answered in brain slices and in computer models of brain slices. We shall move freely between observations of the hippocampus from many different species (rodents, nonhuman primates, humans, and so on), assuming that the same general principles apply to all of them.

The hippocampus is a cortical structure that is necessary for the formation of new memories. The detailed mechanisms by which this function is accomplished are not well understood. The hippocampus in rodents contains cells that respond to spatial location (“place cells”). It generates characteristic EEG rhythms that depend on the behavioral state of animal. The hippocampus readily produces seizures in experimental contexts, and epileptic seizures originating in or near the hippocampus pose an important clinical problem.

The hippocampus forms a rather large part of the rodent brain (Paxinos and Watson, 1986). There is one hippocampus on each side of the brain. In humans, there is a hippocampus in each of the two medial temporal lobes.

Our approach to modeling the brain

What makes the brain so difficult to understand? This question has no simple answer. Many aspects of brain structure obviously contribute to its complexity. There are the large numbers of cells that have different shapes and electrical properties. There are the bewildering connection patterns within and between hundreds of nuclear regions. Dozens of neurotransmitters and modulators exist, each with its own repertoire of receptors and synaptic actions. Data on all of these issues are being and will continue to be pursued with tenacity and persistence, yet, in our opinion, there persists a nagging uncertainty as to what underlying principles, if any, are at work in the brain.

Our doubt exists because the function and behavior of the brain are clearly dependent on the simultaneous activities of many, perhaps all, of its elements. How can activity in so many cells be measured and understood when most experimental techniques allow access to only a few? Just as compelling, what conceptual framework is appropriate for thinking about the simultaneous, coupled activities of large populations of neurons?

In this monograph we shall describe our own approach to a small part of this imposing problem. No single aspect of our approach is mysterious or unique, yet the different aspects may provide new insight into the functioning of the mammalian cortex. We are interested in neuronal population activities generated within small networks of cortical neurons.

Oscillatory synchronous neuronal population behaviors are generated in many parts of the mammalian brain. Such behaviors underlie rhythmical EEG waves in the cortex. Some other brain regions wherein repeating population events occur, with many of the cells firing synchronously, include the brain-stem respiratory pattern generator (Feldman and Ellenberger, 1988), various brain-stem nuclei during pontine-geniculooccipital waves (PGO waves, an EEG correlate of REM sleep) (Steriade et al., 1989), the thalamus during spindle waves (Steriade and Llinás, 1988), and pools of motoneurons during swimming (Wallen et al., 1985) or during eye movements.

It is important to understand population oscillations, for several reasons. First, rhythmic population activities form the background “blackboard” on which afferent, associative, and motor activities must be written (Arieli and Grinvald, 1988; Eckhorn et al., 1988; Gray and Singer, 1989); see also the section on theta rhythm in Chapter 1. Understanding the initiation and synchronization of waves of activity in any one of these cases may shed light on underlying mechanisms in the others. Second, we would like to know the factors that determine the amplitude and period of the oscillation. Does each cell oscillate at the same frequency as the population? Can the frequency of the population behavior be inferred from the intrinsic properties of the cells (Llinás, 1988), or is population rhythmicity an emergent property that cannot be inferred from a single cell?

Our primary goals in this book have been two. The first has been to determine if our current experimental data concerning cellular physiology and synaptic connections suffice to account for various types of collective phenomena exhibited by the in vitro CA3 region. The answer here is yes, up to a point. Many details concerning the quantitative electrophysiology of single neurons, the spatial structure of synaptic connections, and the events required to elicit synaptic plasticity remain to be elucidated, as do the implications of such details for population behavior. The second goal has been to obtain insight into the hippocampus as a (perhaps) novel physical system. Is a particular collective behavior analogous to a well-understood physical paradigm, such as a chain reaction or a time-dependent percolation? Or are there, alternatively, interesting new principles at work, perhaps pertinent to basic questions of brain function? Here again, the answer is yes, up to a point. Synchronized bursts in the presence of picrotoxin appear analogous to a chain reaction, and the ideas of percolation have proved helpful intuitively, if not yet quantitatively. Hippocampal physiology and mathematical physics may yet prove to have something to offer each other. It is our view that “conventional” neural network models, layered neural networks, and symmetric spin-glass models are not appropriate for description of the CA3 region of the hippocampus, although modified, more complex “spin models” may well prove to be helpful.

The structural features of our hippocampal model are motivated by and largely supported by physiological experiments. In many ways the model works, generating cellular and neuronal population responses that look realistic. Nevertheless, the model is complicated. It involves a number of different parameters, simulations of the model use large amounts of computer time, and there is no obvious way to represent the model in a tractable set of equations. Can we simplify things and make a reduced model that retains “essential features” while gaining in physical or mathematical intuition? (This can be a dangerous game: Essential features may end up being defined as just those features that the reduced model exhibits.)

One approach was discussed briefly in Chapter 7 in the section on chaos: to take one signal generated by the model that represents its average behavior such as the number of pyramidal cells firing as a function of time. We then ask if this output has a small “dimension” (specifically, the correlation dimension). If it does, we might be able to construct a simple system to generate an output indistinguishable from the complex output. Such a system might have less than 15 or 20 variables or “degrees of freedom,” as compared with the thousands of variables in the original system. This approach is intriguing (Babloyantz and Destexhe, 1986; Babloyantz et al, 1985). We need to emphasize that the results for the hippocampal model are extremely preliminary.