Introduction

In Chapter 3 the Lapicque model, in which a lumped circuit consisting of a resistance and capacitance in parallel, was employed to represent the entire nerve cell. Though that simple model is not without usefulness, when we cast our minds back to the anatomical facts we reviewed concerning motoneurons in Chapter 1, we realize that we must extend the model if we wish to incorporate the realities of neuronal structure.

For example, we might ask what is the relative effectiveness of synapses close to the soma, compared to those of the same strength on distal parts of the dendritic tree. Or we might wish to inquire how branching affects the integration of various inputs. The model developed in this chapter will help us answer these kinds of questions within a mathematical framework, which is not conceptually difficult, though it has a cumbersome nature when the geometry of the cell is complicated. The various portions of the dendritic tree and the axon are now regarded as passive nerve cylinders and the equations satisfied by the electric potential are the partial differential equations of linear cable theory. (The term passive here means that the membrane conductance is fixed.)

We will here bridge the gap between the simple lumped-circuit model of Chapter 3 and the more complicated Hodgkin–Huxley model considered later. It must be emphasized that in this chapter and the next we deal only with subthreshold responses: that is, levels of excitation less than those required to generate action potentials.

The central nervous system

Our brains and spinal cords contain specialized cells called nerve cells or neurons, which are collectively referred to as the central nervous system (CNS). At one time it was thought that the nervous system was continuous, but it is now firmly established that the neuron is the fundamental discrete unit of the CNS. The nervous system is extremely complex and estimates of the number of nerve cells in the human brain are on the order of 10 billion (i.e., 1010). In addition, there are closely associated cells, as numerous or more so, called glial cells or glia, that seem to play an important regulatory role. They have several properties in common with neurons but are nevertheless quite distinguishable from them.

From location to location in the CNS, nerve cells differ in their properties and functions. It is convenient, however, to envisage a paradigm, or typical nerve cell, with four basic components (see Figure 1.1). The components and their usual roles are as follows.

Cell body or soma

This is the focal part from which branching structures emanate. It roughly delineates the input or information-gathering parts of the cell from the output or information-transmitting parts.

Dendrites

There are usually several dendrites that may branch several times to form treelike structures–the dendritic trees. Over the dendrites occur many contacts from other cells at specialized sites called synapses, though these are also often found on the cell body.

Introduction

In the preceding chapter we showed how, in the framework of cable theory, the steady-state depolarization could be found either in a nerve cylinder or a whole neuron composed of soma, dendritic tree, and axon. To achieve that, we had to solve ordinary differential equations with given boundary conditions at terminals and branch points.

The steady-state solutions are of interest when they can be related to experimental results and can provide some relatively quick insights into the effects of various input patterns and various neuronal geometries. In the natural activity of a nerve cell, however, steady-state conditions will never prevail. In order to understand the dynamic behavior of nerve cells, we must therefore examine the time-dependent solutions.

To obtain the time-dependent solutions, we must solve the partial differential equation (4.25), or the dimensionless version (4.59), for the depolarization V(x, t) at position x at time t. The inclusion of the time variable makes obtaining solutions more difficult, though it may be said that if we are using the linear cable model, there is no problem that we cannot, in principle, solve.

We will begin by showing the usefulness of the Green's function method of solution for nerve cylinders. This extends the approach we used in the previous chapter, and the technique can be used for any spatio–temporal input pattern. We will then look at the case of a nerve cylinder with time-dependent current injection at a terminal.

Introduction

One fundamental principle in neural modeling is that one should use the simplest model that is capable of predicting the experimental phenomena of interest. A nerve-cell model must necessarily contain parameters that admit of physical interpretation and measurement, so that it is capable of predicting the different quantitative behaviors of different cells.

The model we will consider in this chapter is very simple and leads only to first-order linear differential equations for the voltage. However, when we employ the model in many situations of neurophysiological interest, we find that the mathematical analysis becomes quite difficult, due mainly to the nonlinearities introduced by the imposition of a firing threshold. This will become even more apparent in Chapter 9, where we consider stochastic versions of this model.

The model will be called the Lapicque model after the neurophysiologist who first employed it in the calculation of firing times (Lapicque 1907). Other names for this model, which have recently appeared in the literature are the leaky integrator or the forgetful integrate and fire model.

According to Eccles (1957) the resting motoneuron membrane can be represented by the circuit shown in Figure 3.1A. A battery with a potential difference equal to that of the resting membrane potential maintains that potential across the membrane circuit elements consisting of a resistor and capacitor in parallel. We call this a lumped model or a point model to indicate that the whole cell (with attention focused on the soma and dendrites) is lumped together into one representative circuit.

This is the first of two volumes dealing with theories of the dynamical behavior of neurons. It is intended to be useful to graduate students and research workers in both applied mathematics and neurobiology. It would be suitable for a one-quarter or one-semester course in quantitative methods in neurobiology.

The book essentially contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the last 30 years. Chapter 1, however, contains a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical development. A number of suggestions are made for further reading for the reader whose training has been primarily mathematical.

The remainder of the book is a mathematical treatment of nerve-cell properties and responses. From Chapter 2 onward, there is a steady increase in mathematical level. An attempt has been made to explain some of the essential mathematics as it is needed, although some familiarity with differential equations and linear algebra is desirable. It is hoped that physiologists will benefit from this method of presentation. Biophysicists, engineers, physicists, and psychologists who are interested in theoretical descriptions of neurons should also find this book useful.

From Chapter 2 onward, the theme is the systematic development of mathematical theories of the dynamical behavior of neurons. The fundamental observation is of the resting membrane potential. Hence Chapter 2 is mainly concerned with the passive properties of cells and is an exposition of the classical theory of membrane potentials (i.e., the Nernst–Planck and Poisson equations).

• MEASURING THE NEED FOR POWER

Practically every Student of personality, from Freud to McDougall to Murray and Cattell, has found that human beings are characterized by a need for power, aggression, or domination. Anthropologists, biologists, and philosophers like Nietzsche have all been impressed by human beings' aggressive urges.

The story of how a measure for the motive involved here was finally derived is considerably more complicated than it was for the achievement motive. An early measure patterned after the scoring System for n Achievement was discovered to have some limitations and was eventually modified, expanded, and refined into the measure generally used today. The account of its development illustrates how science proceeds by trial and correction and, once again, how crucial precise measurement is in science.

The original coding System for n Power was derived by Veroff (1957) from examining the content of stories written by Student candidates for office while they were waiting for election returns to be counted. The idea was that students seeking office would be more likely than others to want power and that their power need would be more apt to be aroused while they were waiting to see if they would get power than under more neutral conditions.

For historical reasons, as explained in Chapter 3, academic psychologists first conceived of motives as efforts to avoid discomfort and to reduce strong Stimulation, whether caused by hunger, thirst, pain, electric shock, conflict, or frustration. They found it easy to observe the effects of such strong Stimulation on their favorite subjects—namely, animals in the laboratory—and they believed that psychoanalysts working with patients had confirmed their view that anxiety reduction was a kind of master motive. From this point of view it did not make much sense to think in terms of different kinds of avoidance motives: Individuals simply learned different ways of reducing their anxiety, and these might be as varied as the number of people studied. Thus, one person might reduce his or her anxiety by chewing gum, another by jogging, and a third by going to the movies.

It did not make sense to try to define and measure a gum-chewing motive, a jogging motive, or a movie-going motive, so not much attention has been given to sophisticated measurement in this area such as has characterized the work on measuring n Achievement or n Power. In the beginning, scholars were satisfied with simple reports by individuals as to how anxious they felt.

• HOW NATURAL INCENTIVES INFLUENCE THE DEVELOPMENT OF THE HUNGER MOTIVE

Much has been learned about the factors that affect eating in animals and humans. The purpose of this chapter is not to review all this knowledge, but to learn from it as much as we can about the way motives develop out of sign Stimuli and the behavior they release, or what we have called natural incentives. The advantage of using hunger as the model for this purpose is that everyone agrees that some of the sign Stimuli involved produce innate affects and that enough research has been done on eating in animals and humans to show how motives might develop out of these innate affects through learning.

To oversimplify somewhat, three types of sign Stimuli influence eating: (1) sign Stimuli arising from nutritional deficiency, particularly low levels of available blood sugar (Mayer, 1955; Mayer & Marshall, 1956), which increase eating; (2) sign Stimuli arising from the palatability or tastiness of food; and (3) sign Stimuli arising from satiety, such as a full stomach or high blood sugar level, which decrease eating. Ordinarily the mechanisms involved operate automatically to make sure the body has enough energy (represented as available blood sugar) to do its work.

• ANALYZING THE REASONS FOR THE GROWTH AND DECLINE OF CIVILIZATIONS

Cultures, like individuals, differ greatly not only from each other, but from themselves at different moments in time. Some are peaceful, others aggressive; some rich, some poor; some expansive and mobile, others stay-at-home. Anthropologists, historians, economists, political scientists, and philosophers have often tried to figure out why. Why were the Romans such geniuses at military and civic organization, and the Greeks not? Why were the Greeks so successful economically for some hundreds of years before Christ only to disappear for a time as a nation of importance in world history? Why did the Roman Empire rise and fall? When a second flowering of civilization occurred on the Italian peninsula during the Renaissance, why was it in the arts rather than in military science, as at a much earlier period? What caused the British Empire to expand over the entire face of the globe in the nineteenth Century and to decline almost equally rapidly in the twentieth? Why were the British more successful than any other European nation?

Answers by historians to such questions tend to be given in terms of particular events in history, such as a battle that was won or lost, suddenly favorable terms of trade, or the discovery of a new economic resource to exploit.

Ever since psychologists observed that motivated people or animals learn faster, they have been interested in how motives combine with other variables to increase the probability that a response will occur. In more general terms the question is, What factors in what combinations will best predict what response will be made, or if made, how often and how strongly it will be made?

All psychologists except a few association theorists like Guthrie (1935) assume that motives, rewards, or reinforcers are one of the determinants of response strength, and that there are also several other determinants that need to be taken into account. To begin with, the environmental Situation is obviously important. A hungry rat will run faster through a maze or learn the correct turns more quickly than a satiated rat, but only if there is food in the goal box, and only if the rat can get into the maze. In other words, if one is interested in predicting the strength of the maze-running response, it is helpful not only to know how hungry the rat is, but also that the rat has access to the maze and that there is food available at the end of it. Response strength is jointly determined by a motivational variable in the organism and certain environmental variables.

More than most textbooks in psychology, this book reflects the work, the life, and the personality of its author. After forty prolific years of boldly original research and theorizing on the topic of human motivation, David McClelland has not produced a conservative, homogenized, and middle-of-the-road review of the literature. Like Personality, McClelland's classic textbook on personality psychology written over thirty years ago, this text takes some risks. First, the book does not aim to review all of the important literature on human motivation; rather, it seeks to explore in some detail a selected set of critical and intriguing motivational issues. Second, the book does not merely summarize theories, methods, and research findings pertaining to the scientific study of human motivation; rather, it attempts a theoretical synthesis of its own based on the author's particular perspective on human motivation—a perspective that has developed through a number of stages during the last forty years.

David Winter (1982)—a Student and colleague of McClelland—has recently traced McClelland's intellectual biography as a psychologist through six stages. From his rigorous training within the behaviorist tradition of Clark Hull at Yale and his early research on verbal discrimination learning, McClelland moved to the study of thematic measurement of psychological motives (such as the achievement motive) in the late 1940s.

• MOTIVES AS ONE OF THREE MAJOR DETERMINANTS OF BEHAVIOR

What is the subject matter of motivation? From the commonsense point of view, motivation refers on one hand to conscious intents, to such inner thoughts as, I wish I could play the piano, I want to be a doctor, and I am trying hard to solve this problem. On the other hand, looking at behaviors from the outside, motivation refers to inferences about conscious intents that we make from observing behaviors. Thus, if we see a young girl perform a connected series of acts such as walking into a room, drawing up the piano stool, getting out some music, opening the piano, and starting to play, we infer that she wants to play the piano. If she stops playing after a while, we infer that she no longer wants to play the piano. As Marshall Jones (1955) put it in introducing the annual volumes of the Nebraska Symposium on Motivation, the subject matter of motivation has to do with “how behavior gets started, is energized, is sustained, is directed, is stopped.” Put another way, motivation has to do with the why of behavior, as contrasted with the how or the what of behavior. We can observe what the girl is doing, that is, playing the piano. Or we can observe how she is doing it, that is, what motor skills she is using to play the piano. Or we can try to determine why she is doing what she is doing.

The psychology of motivation is a broad and loosely defined field. It covers everything from detailed investigations of the physiological mechanisms involved in animal drives to elaborate analyses of the unconscious motives behind abnormal or symptomatic acts in a person to factor analyses of the motives people assign to themselves to explain their behavior. Different textbooks and different courses have been organized around these different areas of investigation. In this book we will draw on all these sources of information and attempt to provide an integrated view of the field by narrowing somewhat the focus of attention.

The book emphasizes how motives differ from other determinants of action and how they relate to other motivation-type variables such as emotions, incentives, values, causal explanations, and conscious and unconscious intents. It examines how motives are acquired, where they come from, and on what they are based. Biological sources of human motives are reviewed, and this review introduces the topic of natural incentives, or what is sometimes called intrinsic motivation. Some selectivity is necessary in reviewing the large field of animal research on motivation in order to focus on biological sources of individual differences in human motive strength. Social sources of differences in motive strength are also considered, including everything from the way parents rear their children to educational interventions designed to change peoples' motives. Such studies contribute not only practical information on how to develop motives, but also theoretical information on the nature of motives and how they differ from other characteristics.

• THORNDIKE'S STUDIES OF ANIMAL MOTIVATION

At the very moment Freud was discovering the motives behind the dreams of his patients in Vienna, psychologists in the United States were pursuing a radically different approach to understanding motivation. They felt that reports of inner states of mind were unreliable and therefore could never form the basis of an objective science of psychology patterned after the natural sciences. The idea is nicely expressed in a recent physiology textbook (Vander, Sherman, & Luciano, 1975): “Conscious experiences are difficult to investigate because they can be known only by verbal report. Such studies lack objectivity … in an attempt to bypass these difficulties scientists have studied the behavioral correlates of mental phenomena in other animals.”

It was this line of reasoning that led the U.S. psychologist Edward L. Thorndike to begin studies of motivation and learning in kittens, dogs, and chickens in the 1890s. He placed animals in boxes made out of orange crate slats with a door that opened when a string was pulled or a button inside was turned from the vertical to the horizontal position.