What Tolhurst et al. (1981) and Dean (1981) found, therefore, was that at the level of action potential generation, cortical neurons could be described as essentially stochastic. This was a surprising result at the time, and it has been widely confirmed (Rieke et al. 1997, Shadlen & Newsome 1998). What then is the source of this apparent stochasticity, and would a more detailed biophysical analysis of the spike generation mechanism reveal an underlying deterministic process that would yield this apparent indeterminacy?

To examine one possible answer to that question, Mainen & Sejnowski (1995) sought to determine whether the biophysical process that actually generates action potentials in response to changes in membrane voltage was determinate...

They found that the spike-generating mechanism was fully deterministic. A given pattern of membrane voltage gave rise to exactly the same pattern of action potentials no matter how many times it was injected into the cell.

On the one hand, this was a reassuring result. At base, the pattern of action potential generation was found to be governed by a determinate device. However, on the other hand, it was puzzling. Spike rates are not determinate in this sense. Tolhurst et al. and Dean’s work indicates that spike rates are distributed in a Poisson-like fashion, and there clearly is nothing about the spike generator within each cell that produces this pattern. The Mainen & Sejnowski (1995) data indicate that the apparent randomness in spike patterns must be a function of apparent randomness in the underlying membrane voltages. What then are the sources of these Poisson-like fluctuations in membrane voltage?

We know that membrane voltages are governed, ultimately, by the pattern of synaptic activations that a cell receives from the neurons that impinge upon it. Each cortical neuron receives about 10,000 synapses from the tissue that surrounds it. The fact that about half of these synapses are excitatory and half are inhibitory is also important. It means that net excitation and inhibition are largely balanced in an active neuron and small shifts in this balance cause the membrane voltage to rise and fall, and thus cause action potentials to be generated. Together, these observations make a clear suggestion. The source of the apparent stochasticity in the membrane voltage either is a determinate pattern of synaptic activations that carefully sculpts the membrane voltage to yield an apparently indeterminate pattern of action potentials for reasons we do not yet understand or the process of synaptic activation is itself apparently indeterminate.

A number of groups have investigated this latter possibility by studying the activity of single synapses (see Auger & Marty 2000, Stevens 2003 for reviews of this literature). The basic approach taken by these groups has been to activate a neuron and then monitor the rate at which individual synaptic vesicles are released into the synaptic cleft. Before these experiments were undertaken one could have speculated that synapses were simple determinate mechanisms: When an action potential invades the presynaptic region, it might be presumed that synaptic vesicles of neurotransmitter were deterministically released into the synaptic cleft. Modern studies of this process seem to contradict this view, however. Current evidence indicates that when an action potential invades the presynaptic terminal, the chance that a single synaptic vesicle will be released can be as low as 20%. Examinations of the precise patterns of vesicular release suggest that the likelihood that a vesicle of neurotransmitter will be released in response to a single action potential can be described as a random Poisson-like process. Vesicular release seems to be an apparently indeterminate process.

Careful study of other elements in the synapse seems to yield a set of similar, and highly stochastic, results. Postsynaptic membranes, for example, seem to possess only a tiny number of neurotransmitter receptors (cf. Takumi et al. 1999), and during synaptic transmission as few as one or two of a given type of receptor molecules may be activated (Nimchinski et al. 2004). Under these conditions, a single open ion channel may allow a countable number of calcium or sodium ions to enter the neuron, and there is evidence that the actions of a single receptor and the few ions that it channels into the cell may influence the postsynaptic membrane. Together, all of these data suggest that membrane voltage is the product of interactions at the atomic level, many of which are governed by quantum physics and thus are truly indeterminate events. Because of the tiny scale at which these processes operate, interactions between action potentials and transmitter release as well as interactions between transmitter molecules and postsynaptic receptors may be, and indeed seem likely to be, fundamentally indeterminate.

In 1944, Schrodinger argued that the fundamental indeterminacy of the physical universe would have no effect on living systems. He argued that were biological systems to become so small that the actions of single atoms or molecules could influence cells, the resulting organisms would surely perish from the evolutionary landscape. Studies of the mammalian synapse, however, seem to indicate that Schrodinger (1944) was simply wrong in this regard. Single synapses appear to be indeterminate devices; not apparently indeterminate, but fundamentally indeterminate. At base, physical indeterminacy seems to be a fundamental property of the brain. But how sure can we be that this fundamental indeterminacy at the level of the synapse has anything to do with indeterminacy at the level of a single cortical neuron, at the level of a cortical network, at the level of behavior, or at the level of a social theory of behavior?

The evidence that we have today suggests that membrane voltage can be influenced by quantum level events, like the random movement of individual calcium ions. So there is every reason to believe that membrane voltage can be viewed, at least under some circumstances, as a formally indeterminate process of the type that precludes Popperian falsifiability. How does this membrane voltage influence action potential generation? Recall that cells receive a mixture of excitation and inhibition from thousands of synapses and that the ratio of this mixture is variable. Imagine that the correlations between the activity of the individual synapses impinging on a given cell were variable. Under conditions in which the activity of many synapses is correlated and the membrane voltage is driven either way above or way below its threshold for action potential generation, the network of neurons itself would maintain a largely determinate characteristic even though the synapses themselves might appear stochastic. Alternatively, when the synaptic activity is uncorrelated and the forces of excitation and inhibition are balanced, small uncorrelated fluctuations in synaptic probabilities drive cells above or below threshold. Under these conditions, indeterminacy in the synapses propagates to the membrane voltage and thence to the pattern of action potential generation. Indeterminacy in the pattern of action potential generation, although variable, would reflect a fundamental indeterminacy in the nervous system.

At the level of behavior, apparent indeterminacy is reinforced by the environment and has been observed. Animals can produce behavior that appears to scientists to be indeterminate. How does this apparent indeterminacy arise? Given what we know about the behavior of synapses and action potentials, two possibilities present themselves. The fundamental indeterminacy observed at the cellular level could be prevented from influencing higher-level phenomena in the nervous system, rendering these higher-level phenomena determinate. These determinate processes could then instantiate pseudorandom computations that emulate the underlying cellular indeterminacy and yield apparently indeterminate behavior. Alternatively, we can propose the hypothesis that indeterminacy observed at the cellular level could propagate to behavior under some circumstances, yielding truly indeterminate behavior under some conditions and more determinate behaviors under others.