Coding by neuronal populations
There is a yet more profound aspect of spatial ensemble averaging to be considered. Spatial integration is the mechanism by which neurons in a local neighborhood corresponding to a cortical "column" make their own spatial ensemble average, and thereby establish the basis for cooperative collective action. Spatial integration occurs continually in each neuron as its dendrites converge and sum the waves of current that are generated by its synapses upon axonal pulse input. It also occurs as each neuron transmits to many others in the surround and then receives their transmissions back again. In many if not all areas of cortex the excitatory neurons excite each other (but not themselves), and the cooperative interaction is the basis for the emergence of the local mean field and the population neighborhood. Receptors cannot form a population in this sense because they are not synaptically connected, and they are not globally interactive in other ways. Spatial integration also occurs between cortical areas, as for example in the divergence of the axon projection from the bulb to the olfactory cortex, which is important for the readout of the population (see "Readout of percepts"), but divergence alone and parallel action alone are not sufficient. There must be feedback, as indicated by feedback within the transmitting population and by the "centrifugal" connections (Figure 1) from the target populations back to the transmitter population.
The macroscopic activity of the population is difficult to observe in the pulse activity of the individual neurons, because a large amount of random variation exists in the intervals between pulses in the "spontaneous" background activity of each cell. From some indirect measures it is estimated that in the cortex only one part in 1,000 to 10,000 of the total variance in the activity of the individual neurons in the population is covariant with the activity of the population. Because time ensemble averaging destroys the endogenous components, the minimum for detecting population activity would require simultaneous recording from 1000 to 10,000 cells. At present the experimental limit for recording "units" simultaneously is from about 100 individual cells.
Nature, however, provides easy access to cortical spatial ensemble averages. This comes about because the same dendritic currents that determine the firing rates of single neurons at trigger zones flow across the tissue resistance, and their ohmic potentials add as the currents pass through the tissue (Figure 8). When the extracellular field potential is properly recorded, it provides a basis to estimate the strength of the local mean field activity in the neighborhood of the neuronal population from the amplitude of its EEG. Multiple simultaneously recorded EEGs from an array of electrodes placed on the cortical surface at suitable spacings provide a basis for observing the spatial AM patterns of cortical activity (Figure 6). Other methods currently under development include measurement of cortical electric fields with voltage-sensitive dyes and optical recorders, (T'so et al., 1990) or with magnetic sensors to measure the magnetic components of the fields of dendritic current (Williamson and Kaufmann, 1989; Llinas et al., 1991). At present their instrumental noise levels are so high that they cannot be used without time ensemble averaging or narrow band pass filtering, so the use of these methods is restricted to measuring time ensemble averaged evoked potentials and not the unaveraged traces.
Simultaneous recordings of EEGs from 60 to 64 electrodes in rectangular arrays placed surgically on the olfactory bulb or cortex reveal a substantial degree of spatial coherence of the activity at all times. In contrast, the time series recorded at each electrode is highly irregular. The wave form from each electrode is as non-reproducible as a freehand scrawl, but the simultaneous recordings always contain the same scrawl (Figure 6). To be sure, there are local differences in the amplitudes and peak latencies (Figure 7) of the scrawl, but the same peaks and troughs occur everywhere, and the instantaneous frequency of the EEG traces tends to be the same.
The commonality is often difficult to see in the visual, auditory and olfactory cortexes, because the EEG reflects the sum of electric currents from multiple sources, many of them unknown, and the common wave form comprises only half to three quarters of the total variance of the activity in the traces (Freeman and Viana di Prisco, 1986; Freeman and Grajski, 1987). The common wave form is extracted by computing a spatial ensemble average from each set of EEG traces, in much the way that the cortex extracts the bulbar output (see "Readout of percepts"). This commonality of wave form extends over the entire bulb. Similarly other common wave forms cover the entire olfactory cortex (Bressler, 1987) and much if not all of the primary visual (Freeman and van Dijk, 1987) and auditory (Pantev et al., 1991) cortexes. In contrast to lower frequencies such as the alpha (8-12 Hz) and theta (3-7 Hz) rhythms these time series appear to be self-organized within the cortexes and not imposed by pacemakers lying in the basal ganglia or brainstem.
What makes these spatial AM patterns interesting is the fact that that they contain behavioral information as demonstrated experimentally by conditioning. After an animal is trained to discriminate and respond to an odorant (Figure 9), a unique spatial AM pattern reappears in the EEG of the bulb whenever the animal inhales that odorant. If it inhales another odorant that it can discriminate, a different reproducible pattern emerges. The common oscillatory activity constitutes a "carrier" wave, and the information about an odorant is expressed by the spatial AM pattern of the carrier in the wave packet independently of its wave forms, frequencies, or latency patterns.
These findings suggest that olfactory coding resembles the frames in a movie film. The light is a fluctuating energy or carrier (wave form) that bursts on and off with each frame. The information in each frame (sniff) is given by the intensity of the light (amplitude of the wave) at each pixel (local neighborhood), and it is held for the duration of the frame. If the same scene is shown in sequential frames, the spatial pattern of the carrier amplitude is reproduced in each frame. If a new scene appears, a new spatial pattern is seen. This analogy may suggest the intermittent flow of perceptual information in the olfactory system by a process known as chaotic itinerancy (Tsuda, 1991).
To recapitulate, microscopic coding is found in its clearest form in the peripheral nervous system and in the sensory and motor relays to and from the cerebral cortex. The information is carried in the pulse trains of a selected subset of neurons. Observers extract it statistical time series analysis of point processes using time ensemble averaging on the recorded data, because each pulse sharply defines the time and place of its piece of information in terms of the time interval from the last preceding pulse at that trigger zone. The pulse frequency gives the intensity of the stimulus, and the origin of the axon determines the quality of the stimulus. Stimulus parameters are modified by cellular mechanisms that control receptor sensitivity, but they are not changed by associative learning. Macroscopic coding is found most clearly in cerebral cortex, co-existing with the microscopic activity that is injected into the cortex by afferent axons. This information is spatially distributed over the entire population comprising an area of cortex, but it is parsed into time segments. Within those segments it is stationary in the form of an amplitude modulation of a common carrier. The patterns are self-organized, not topographically related to input, and strongly dependent on modifications by near and remote experience that has been incorporated into the cortex by learning.