Model Suggests Steady Vision Depends on Holding Chaos in Check

The equations at the center of a new model of the visual cortex were not written with brains in mind. In a stripped-down computer simulation of the primary visual cortex, the first region of the cortex to handle what the eyes send it, two ordinary feedback loops were enough to turn chaotic activity into a steady rhythm, which suggests that stable vision may be something the brain works to maintain rather than a state it simply falls into. The capacity for chaos was never taken out of the model (it is baked into the math); the feedback just keeps it in check. That is a small reversal of an old question, and it is the one Mehdi Borjkhani at the International Centre for Translational Eye Research in Warsaw and his colleagues set out to probe.

Neurons in the cortex fire with an irregularity that would embarrass a metronome, the gaps between their spikes varying almost as much as if they were random, and yet the same image shown twice produces responses that are, once the noise is properly accounted for, strikingly consistent. You can read a road sign in the rain or pick out a face across a crowded room, and the picture doesn’t wobble.

Chaos, in the mathematician’s sense, is not the same thing as noise. “In this context, chaos does not mean ordinary noise or disorder. It is a deterministic form of dynamics in which a very small difference at the beginning can rapidly take the entire system in a different direction,” says Borjkhani. Full chaos would be a disaster for seeing, the same scene could send the cortex somewhere different every time. So how does a circuit live near that edge without toppling over it?

Seven Terms Borrowed From Predators and Prey

Rather than simulate millions of neurons, the team boiled the circuit down to three interacting populations: excitatory cells (the pyramidal neurons that make up roughly 80 percent of cortical neurons), fast inhibitory interneurons, and a slower modulatory drive standing in for input from the thalamus and the brain’s chemical signaling systems. Their scaffold was a Lotka-Volterra system, the family of equations first used to describe predators and prey rising and falling in turn, in a recently published version with just seven terms and two parameters that counts as the simplest known chaotic example of its kind. The authors are blunt that this is a mathematical scaffold and not a wiring diagram; a cubic term in the equations, they note, is not a literal three-spike interaction.

Left bare, the system is chaotic across roughly 87 percent of the parameter settings the team scanned. Then they added two things real cortex has in abundance: feedback, so that rising excitatory activity recruits inhibition, and homeostatic regulation, a slow self-correcting pull that keeps the modulatory drive near a baseline (plus an orientation-tuned visual input, for good measure). The strange attractor (the tangled, never-repeating path a chaotic system traces) collapsed into a repeating cycle, and the variance of the excitatory population fell from 0.325 to 0.024, a drop of 93 percent, with the stabilizing effect holding across most of the chaotic range and biting hardest where the bare system had been most chaotic.

“The most interesting point is that we did not have to remove the model’s capacity for chaotic activity. It was enough to introduce mechanisms that the real cortex uses every day: rapid inhibition and slower self-regulation.”

Edges, Spikes and a Stubborn Gap

A steadied model is only interesting if it still behaves like visual cortex, so the team ran it through three tests. Across thirty simulated trials started from slightly jittered conditions, switching on a visual input pinned the wandering trajectories to a shared path and sharply cut the trial-to-trial variance, echoing a drop in variability that recordings have picked up across the cortex whenever a stimulus appears. Next came orientation, the preference many visual neurons have for edges at a particular angle: 30 simulated neurons shown lines at 10 angles came out with an average selectivity index of 0.38 in the chaotic setting and 0.31 in the regular one, both inside the spread measured in macaque visual cortex. Odd, on the face of it. More irregular dynamics produced slightly sharper tuning, and the authors’ tentative explanation (that chaotic fluctuations average out over time while the stimulus-driven signal survives) is offered as a suggestion rather than a demonstration.

Finally, the team fed the population output into a classic Hodgkin-Huxley neuron, a model originally built from squid nerve and used here purely as a generic spike generator, and chaotic input made its firing far more irregular than a sine wave or a constant signal did, whose coefficients of variation were 0.05 and 0.005, landing inside the 0.1 to 0.3 range recorded from brain slices but well short of the 0.7 to 1.0 seen in living animals. Chaos, in other words, can supply some of the irregularity real neurons show, not all of it.

None of this involved a single recorded neuron. The 93 percent figure that leads the institute’s press release, framed there as a cut of up to that much in the variability of neural activity, is the variance of one model population at one operating point, and the model itself has no cortical layers, no spatial layout, no real timescales and only one kind of inhibitory cell.

The chaos also hinges on a peculiar term in the equations, one that flips net inhibition into net excitation once inhibitory activity climbs high enough; swap it for either of two gentler, bounded curves the team tried and the chaos vanished, and the authors call their reading of that term as biological disinhibition speculative. Other theorists, working with a different class of models, have described cases in which slow homeostatic regulation generates chaos rather than suppressing it, which is more or less the mirror image of this result.

What Would Knock the Cortex Off Balance

The model makes predictions, which is rather the point. Weaken the feedback that ties excitation to inhibition, the balance the whole circuit turns on, or slow the self-regulation, and variability should rise, something that could be checked by silencing fast inhibitory cells with light-controlled genetic tools. Another prediction runs against intuition: suppressing a particular class of disinhibitory interneurons should make cortical activity less complex, not more. The authors also float a connection to the irregular activity seen in epilepsy and schizophrenia, which the institute’s own release labels a hypothesis still to be tested in biological experiments.

Whether real cortex sits where this model puts it, near the edge and held back by its own wiring, is a question for electrodes rather than equations. If it does, the steadiness of an ordinary glance at the world would turn out to be the product of constant, invisible restraint.

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