Math shows how brain stays stable amid internal noise and a widely
varying world

Date:
August 10, 2020
Source:
Picower Institute at MIT
Summary:
A new theoretical framework shows that many properties of
neural connections help biological circuits produce consistent
computations.



FULL STORY ========================================================================== Whether you are playing Go in a park amid chirping birds, a gentle breeze
and kids playing catch nearby or you are playing in a den with a ticking
clock on a bookcase and a purring cat on the sofa, if the game situation
is identical and clear, your next move likely would be, too, regardless of those different conditions. You'll still play the same next move despite
a wide range of internal feelings or even if a few neurons here and there
are just being a little erratic. How does the brain overcome unpredictable
and varying disturbances to produce reliable and stable computations? A
new study by MIT neuroscientists provides a mathematical model showing how
such stability inherently arises from several known biological mechanisms.


==========================================================================
More fundamental than the willful exertion of cognitive control over
attention, the model the team developed describes an inclination toward
robust stability that is built in to neural circuits by virtue of the connections, or "synapses" that neurons make with each other. The
equations they derived and published in PLOS Computational Biology
show that networks of neurons involved in the same computation will
repeatedly converge toward the same patterns of electrical activity, or
"firing rates," even if they are sometimes arbitrarily perturbed by the
natural noisiness of individual neurons or arbitrary sensory stimuli
the world can produce.

"How does the brain make sense of this highly dynamic, non-linear
nature of neural activity?" said co-senior author Earl Miller, Picower Professor of Neuroscience in The Picower Institute for Learning and
Memory and the Department of Brain and Cognitive Sciences (BCS) at
MIT. "The brain is noisy, there are different starting conditions --
how does the brain achieve a stable representation of information in
the face of all these factors that can knock it around?" To find out,
Miller's lab, which studies how neural networks represent information,
joined forces with BCS colleague and mechanical engineering Professor Jean-Jacques Slotine, who leads the Nonlinear Systems Laboratory at
MIT. Slotine brought the mathematical method of "contraction analysis,"
a concept developed in control theory, to the problem along with tools
his lab developed to apply the method. Contracting networks exhibit the property of trajectories that start from disparate points ultimately
converging into one trajectory, like tributaries in a watershed. They
do so even when the inputs vary with time. They are robust to noise and disturbance, and they allow for many other contracting networks to be
combined together without a loss of overall stability -- much like brain typically integrates information from many specialized regions.

"In a system like the brain where you have [hundreds of billions]
of connections the questions of what will preserve stability and what
kinds of constraints that imposes on the system's architecture become
very important," Slotine said.

Math reflects natural mechanisms Leo Kozachkov, a graduate student
in both Miller's and Slotine's labs, led the study by applying
contraction analysis to the problem of the stability of computations
in the brain. What he found is that the variables and terms in the
resulting equations that enforce stability directly mirror properties and processes of synapses: inhibitory circuit connections can get stronger, excitatory circuit connections can get weaker, both kinds of connections
are typically tightly balanced relative to each other, and neurons make
far fewer connections than they could (each neuron, on average, could
make roughly 10 million more connections than it does).



========================================================================== "These are all things that neuroscientists have found, but they haven't
linked them to this stability property," Kozachkov said. "In a sense,
we're synthesizing some disparate findings in the field to explain
this common phenomenon." The new study, which also involved Miller lab
postdoc Mikael Lundqvist, was hardly the first to grapple with stability
in the brain, but the authors argue it has produced a more advanced
model by accounting for the dynamics of synapses and by allowing for
wide variations in starting conditions. It also offers mathematical
proofs of stability, Kozachkov added.

Though focused on the factors that ensure stability, the authors noted,
their model does not go so far as to doom the brain to inflexibility
or determinism.

The brain's ability to change -- to learn and remember -- is just as fundamental to its function as its ability to consistently reason and
formulate stable behaviors.

"We're not asking how the brain changes," Miller said. "We're asking how
the brain keeps from changing too much." Still, the team plans to keep iterating on the model, for instance by encompassing a richer accounting
for how neurons produce individual spikes of electrical activity, not
just rates of that activity.

They are also working to compare the model's predictions with data from experiments in which animals repeatedly performed tasks in which they
needed to perform the same neural computations, despite experiencing
inevitable internal neural noise and at least small sensory input
differences.

Finally, the team is considering how the models may inform understanding
of different disease states of the brain. Aberrations in the delicate
balance of excitatory and inhibitory neural activity in the brain
is considered crucial in epilepsy, Kozachkov notes. A symptom of
Parkinson's disease, as well, entails a neurally-rooted loss of motor stability. Miller adds that some patients with autism spectrum disorders struggle to stably repeat actions (e.g. brushing teeth) when external conditions vary (e.g. brushing in a different room).

The National Institute of Mental Health, the Office of Naval Research, the National Science Foundation and the JPB Foundation supported the research

========================================================================== Story Source: Materials provided by Picower_Institute_at_MIT. Note:
Content may be edited for style and length.


========================================================================== Journal Reference:
1. Leo Kozachkov, Mikael Lundqvist, Jean-Jacques Slotine, Earl
K. Miller.

Achieving stable dynamics in neural circuits. PLOS Computational
Biology, 2020; 16 (8): e1007659 DOI: 10.1371/journal.pcbi.1007659 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/08/200810103253.htm

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