Reimagining Synaptic Noise
The neuron is the fundamental unit of computation in the brain. In order to model the brain, we need to be able to accurately predict the behavior of neurons.
For the neuroscience newbies, here is how neurons fire. More advanced readers are free to skip this paragraph. A neuron fires when it is excited by an external stimulus. The stimulus causes its membrane potential, the difference between electrical charge inside and the outside of the neuron, to reach a threshold value. This event is called an action potential. When an action potential occurs, the neuron opens its sodium channel and allos Na+ ions to enter. This depolarizes the neuron, quickly brining it’s membrane potential to 0. At this point, the neuron is said to emit a spike because the event registers as a spike in the graph of the membrane potential. A neuron releases a neurotransmitter while firing. Different neurotransmitters transmit different types of messages, and the release of neurotransmitters excites surrounding neurons. Through this mechanism, a message is relayed across a network of neurons. In the case where the external stimulus is too weak, membrane potential does not reach its threshold and nothing perceivable happens; the stimulus is subthreshold.
At first glance, we should be able to model neurons accurately. If we know the current state of the neuron, we should be able to predict the neuron’s state in the next moment perfectly. If a neuron is excited, we can measure the level of incoming stimulus, and predict if it will fire or not. We can also accurately predict when a neuron will fire by treating it as an electrical circuit with capacitance, inductance and current. This works well in theory, but in practice our individual models break down as the entire system becomes more complicated. The reason for this is synaptic noise.
Synaptic noise is the result of various background processes in the brain, which cause neurons to exhibit output currents without any input current. Much of this noise is subthreshold, meaning it is too weak to cause the membrane potential to reach threshold. Synaptic noise is seen as a byproduct of complexity, and is often an annoyance when conducting neuroscience research.
Electrical Engineers also deal with noisy systems. Unwanted disturbances cause signals to become corrupted, and part of their job is to attenuate these disturbances, often through a feedback system.
Feedback systems work by feeding the output of the system back into the input. When used correctly feedback can make the system less sensitive to external changes, which in turn reduces signal distortion and noise.
When considering the behavior of systems, engineers often use a transfer function, which is the output-input ratio of the system. The transfer function of the feedback system above is G1+G*. Once a transfer function is found, engineers can tune systems by manipulating different parts to get the behavior they desire. For example, in the system above by using an attenuator with a higher , we can get a system that amplifies the input signal less. Sometimes transfer functions depend on the frequency of input which is useful for filtering noise. If the noise is of a higher frequency the system can be tuned to weaken higher frequencies and amplify lower ones.
In the brain, feedback is much more complicated. One of the best examples of feedback relates to sensory processing through the thalamus and the neocortex. The neocortex is responsible for perception and attention (among many other things) and the thalamus relays sensory information to the neocortex. However, the thalamus is not simply a messenger, about two-thirds of the thalamocortical neurons (neurons connected from the thalamus to the neocortex) are related to the activity of corticothalamic neurons (neurons connected from the neocortex to the thalamus). They form a feedback system. Research at the Unité de Neurosciences in France by Sébastian Béhuret sheds light on how this feedback system works in the presence of noise. The research suggests that subthreshold noise caused by communication in between the neocortex and the thalamus plays a functional role in selective attention. In particular, they found that the neocortex can modulate the background noise caused by corticothalamic connections. This has a detectable effect on the transfer function of thalamocortical neurons.
Without subthreshold noise, the transfer function has a sharp cutoff, which means there is a clear threshold the input has to cross in order to create an action potential. However, once noise is added, the transfer function becomes smoother and probabilistic. It can fire at lower inputs with low probability and fire at high inputs with higher probability. Without noise it fires deterministically after the input crosses a threshold. In fact, by increasing the standard deviation of the noise, the transfer function can be tuned. In certain situations, the neocortex may want more sensory information from the thalamus, and it can create a filter built on its specifications, similar to an engineer.
Noise is an interesting way to tune a circuit, but it seems like a roundabout way to get what we want. If the thalamocortical connections had less resistance, the neocortex could get more information from the thalamus. This seems like a more straightforward and elegant solution from a design perspective. However, when considering the resource constraints in the brain, the picture becomes much more clear.
Resistance attenuates electrical signals and slows them down. If the neocortex increases spike probability in the thalamocortical neurons, then it is safe to assume it wants a large amount of sensory information quickly. If the neocortex wants to gain this information without increasing spike probability, it would have to decrease resistance in thalamocortical neurons. This way, neurons that fire farther away from the neocortex would still have their spikes transmitted to the cortex. For this to occur, the diameter of the axon (middle part of the neuron) would need to thicken. Resistance decreases proportionally to d2, where d is the diameter of the axon. In order to decrease resistance, the volume of each individual neuron would have to increase quadratically. But there is not enough room in the brain for these larger neurons. This means less neurons would be used, and in turn there would be less information conveyed to the neocortex, which is the opposite of what we want. In order to circumvent this constraint, noise is used to modify the circuit.
Corticothalamic feedback endorses an interesting paradigm for system design. Instead of treating noise as something to get rid of, systems can be designed to incorporate noise to convey information. Using neuromorphic innovations like this can fundamentally change how engineers solve complex problems, enabling a new epoch of efficient and interesting design. It also transforms the way we look at neuron models. Synaptic noise can play an important role in neural computation and should be built into our understanding of neural systems.
References:
https://www.frontiersin.org/articles/10.3389/fncir.2015.00080/full
