Introduction
Two salient facts about neurons are that each functional part of the brain contains uncountably large numbers of them, and that each neuron forms synaptic connections to and from uncountably large numbers of other neurons (Braitenberg and Schutz, 1991). Statistical sampling is used. Estimates of the number of neurons in a cubic millimeter of cortex range from 104 to 106, and for the number of synaptic connections on each dendritic tree from 103 to 105. The typical sensory input for a conditioned stimulus is carried by a parallel array of an uncountably large number of receptor axons, and the motor outflow for a typical conditioned response a fraction of a second later is carried in parallel by an uncountably large number of motor axons. Every goal-directed response involves stupendous numbers of neurons in multiple brain parts.
Much of what is understood about the functions of these massive numbers of neurons comes from recording the activity of neurons one at a time with microelectrodes. Networks of model neurons are constructed by induction that represent the actions of a small subset of neurons, on the implicit assumption that what the other (unobserved) neurons are doing during a perceptual act or a conditioned reflex is not important for the activity of the observed subset. This approach might be called a statistical mechanics (Wilson and Cowan, 1972; Amari, 1974; Amari and Maginu, 1988; Hansel and Sompolinsky, 1990) of brain function, comparable to the study of molecules in an ideal gas in terms of their kinetic energy, position, collision rates, etc.
A different approach is to conceive not individual neurons but interactive populations of neurons. The weak interactions among uncountable numbers can be predicted to give rise to cooperative properties, which can only be accessed by measuring local mean field quantities constituting observable macroscopic variables for the masses. This alternative approach might be called a thermodynamics of brain function, by which the equivalents are sought for the temperature, pressure, viscosity, etc. of an ideal gas. However, physical analogs on their face are inappropriate and have led many physicists astray. Neurons are not molecules in a gas, so a fresh beginning must be made for a new brain science (Skarda and Freeman, 1987).
Neural populations come into play significantly during animal behavior, and their properties cannot be understood from studies of isolated neural preparations in vitro or in brains under anesthesia. Therefore this new approach is introduced in the context of acts of animal perception, and in particular the perception of odors through the olfactory system (Figure 1), because it is the simplest and best known at present, and because there is good reason to propose (Herrick, 1948) that it is the phylogenetic prototype for the algorithms by which all sensory systems operate in perception, and indeed for all instances of behaviorally related interactions of cortex within itself and with subcortical nuclei and the far reaches of the brainstem and spinal cord.
Consideration is restricted here to acts of pre-attentive perception that do not require inspection or combining successive stimuli over time. Such acts occur in each sensory system independently of other senses on first arrival, but by the time to the next heartbeat, eye movement, or inhalation, all the senses are involved. This takes place by convergence from the several sensory cortexes into the limbic and motor systems of the brain (Figure 1). These acts of perception occur in all vertebrates and perhaps in all animals. The acts are rapid in onset, short in duration, reliable, and reproducible. In animals they are easily controlled by standard techniques for conditioning. For these reasons a rabbit that has been trained to sniff an odorant is an optimal subject for the study of the neurobiology of perception in the olfactory system, with the hope that what is learned about perceptual coding will hold for all other senses as well (Freeman and van Dijk, 1987; Tsuda, 1991).
It is known from lesion studies, in which the damage is caused by disease or experimental surgery, that the neural activities sustaining these acts of pre-attentive perception take place in the outer shell of the brain, the cerebral cortex. From behavioral experiments with trained animals it is known that each act takes place just after some sensory input has been transmitted to each of the sensory cortexes in the brain, and that it takes place then within a few tenths of a second of stimulus arrival, before any decision is taken on what to do next. Response latency measurements show that it happens in the time needed for a sniff or a saccade (a twinkling of the eye). These findings show exactly where and when to look for the behaviorally related physiological process in the brain that sustains a percept.
Previous studies in neuronal physiology (e.g. Shepherd, 1983) have shown how sensory stimuli are analyzed, not how percepts are synthesized in the brain From studies combining theory and experiment it is known how sensory stimuli are transduced by receptor neurons in a two-stage process. First the stimulus is converted to a loop current with its energy source in the membrane at or near the site of action of the stimulus and its effective action at the initial segment of the sensory axon, where its amplitude is re-expressed by the frequency of a train of action potentials. The loop current flows inside the cell in one direction and outside the cell in the other direction across the tissue resistance, giving rise to a "generator potential", which for the olfactory receptors in the nose is called (Figure 2) the electroolfactogram. This two-stage operation also serves as a model for the function of cortical neurons. They receive action potentials ("units") at the synapses on their dendrites and convert them to dendritic loop currents. The currents are summed at the initial segments of their axons (the "trigger zones") where the net amplitude determines the frequency of axonal firing. The dendritic currents cause oscillating waves of electrical potentials to appear in and around cortex (Basar, 1980) called the electroencephalogram (EEG). Thus there are two main state variables by which neural activity is carried: pulses on axons, and waves on dendrites.
These sensory stimuli are pre-analyzed in both the pulse and wave modes at intermediate stations. In the visual system which is the best known in regard to pre-processing, there are complex operations in the retina and the lower brain called "adaptation", "range compression", "contrast enhancement", "motion detection", and so on. Sensory stimuli in the cortex selectively activate neurons that are called "feature extractors", such as "line" or "bug" detectors, "face" or "hand" cells, or the archetypal "grandmother cells" that are conceived to fire whenever that person appears. Comparable operations have been described for the auditory and somatic cortexes as well. Typically the neurons in these cortexes receive input axons that are organized in parallel arrays to provide the anatomical basis for topographic mapping onto the brain from receptor arrays in a body surface such as the retina, skin and ear. The alignment of input axons side by side provides the anatomical basis for extracting spatial and temporal derivatives of input for edge and motion detection and for contrast enhancement.
Similar pre-analysis also takes place in the olfactory system, but the processing is far less complicated and largely consists of dynamic range compression and signal normalization (Freeman, 1975), though some degree of contrast enhancement may take place (Shepherd, 1983). The simplicity makes easier the task of finding percepts. The olfactory system has a rough topographic map from its receptor neurons in the nose into the receiving sheet of cortical tissue, the olfactory bulb (Figure 3). Roughly 50 million olfactory receptors in the rabbit transmit their output by unbranched axons to half a million neurons in the bulb. As is typical for sensory systems a large number of receptors converges to a small number of bulbar neurons, the convergence ratio here being about a thousand to one.
The axons of the bulbar neurons that carry pulses to the olfactory cortex do not form a topographic map. Each output axon has many branches that diverge widely over the cortex. Conversely, each cortical neuron receives input from neurons that are widely dispersed throughout the bulb, thereby performing not only temporal integration but spatial integration as well. This divergence is an important property which will repeatedly referred to in this review (see Section on "Readout of percepts"). This type of divergent connection may in fact be much more common in cortical connections than is the topographic map.
The studies in olfaction will now be used to answer the question of how, within a few tenths of a second, an act of pre-attentive perception is accomplished, that is, how relevant sensory input is (a) extracted from the environment by a sniff, (b) globally integrated by arrays of cortical neurons, and (c) combined with pertinent past experience and expectancy of future events into a space-time pattern of cortical activity. That pattern is called a "wave packet" in its physical aspect and a "percept" in its behavioral or functional aspect (Freeman, 1975). The answer will be expressed in the language of nonlinear dynamics of neural populations.