Brain's inhibitory circuits generate multiple rhythms simultaneously, study shows

The brain's cortex hums with rhythms. These oscillations—the synchronized firing of thousands of neurons—are how the brain processes information, integrates sensory signals, and supports thought itself. But a puzzle has long nagged neuroscientists: why do recordings from the same patch of cortex often show multiple frequencies at once? A new computational study offers a mechanism: two distinct populations of inhibitory neurons, working in concert with excitatory cells, can generate multiple stable rhythms simultaneously in a single circuit.

The researchers built a mathematical model of a network containing three populations: excitatory neurons and two types of inhibitory interneurons known as PV cells and SOM cells. These populations are not wired identically. The SOM cells, for instance, inhibit both the excitatory neurons and the PV cells, but receive no inhibition in return. The PV cells, by contrast, inhibit only the excitatory neurons and other PV cells. This asymmetry in connectivity turns out to be crucial. When the researchers stimulated the excitatory population with varying levels of drive, the network exhibited a striking behavior: across a range of input strengths, two distinct oscillatory rhythms coexisted stably. The researchers called this state bi-rhythmicity. One rhythm involved primarily the excitatory and PV populations firing in a smaller, tighter pattern. The other engaged the SOM cells more fully, producing larger-amplitude oscillations. Both rhythms could persist at the same parameter values—the network could settle into either one depending on its initial state.

To understand how this multistability arose, the team constructed a reduced mathematical model that captured the essential dynamics without simulating every individual neuron. This mean-field approach—tracking only the average firing rates and synaptic strengths of each population—proved remarkably accurate. It reproduced the key behaviors seen in full spiking simulations and revealed the mathematical bifurcations underlying the transitions between different states. As excitatory drive increased, equilibrium points (representing silent or asynchronous activity) gave way to limit cycles (representing rhythmic firing). At certain critical points, stable and unstable oscillations collided and annihilated each other, or new oscillations were born. These bifurcations carved the parameter space into distinct regions, each with its own stable attractor or set of attractors.

The researchers then asked whether the network could be switched between its two rhythmic states by brief stimulation. It could. A 200-millisecond pulse to the SOM population, carefully timed and sized, suppressed the excitatory cells enough to push the network from the larger rhythm onto the smaller one. A pulse to the excitatory population itself could reverse the switch. Even more intriguingly, stimulating the SOM cells with the right amplitude could suppress the PV population selectively, allowing the excitatory cells to escape inhibition and jump to the larger rhythm—a counterintuitive result that hinged on the specific connectivity pattern. These findings suggest that the brain might use such switching mechanisms to flexibly shift between different processing modes.

The team then systematically varied the strength of inhibition from each population, mapping out how the network's behavior changed across two-dimensional parameter spaces. As SOM inhibition weakened, new oscillatory branches appeared and disappeared through bifurcations. Isolated islands of oscillations—isolas—emerged and merged with larger branches. Regions of bi-rhythmicity expanded and contracted. The same patterns held when varying PV inhibition, though the thresholds differed: SOM cells required stronger excitatory drive to engage because they receive inhibition from VIP neurons, a third inhibitory population the model treated as a tonic input. By varying this VIP-mediated inhibition, the researchers showed how it modulates SOM activity and, in turn, the presence and multiplicity of rhythms in the network.

One particularly striking finding emerged at very high levels of PV inhibition: the network could produce quasi-periodic behavior—a high-frequency oscillation whose amplitude was slowly modulated at a much lower frequency. Mathematically, this arose through a torus bifurcation, where a stable limit cycle lost stability and the dynamics began to fill a two-dimensional surface in state space. This quasi-periodic regime coexisted with large-amplitude rhythms, offering yet another form of multistability. The implications are significant. Local field potential recordings from cortex often show multiple peaks in the frequency spectrum. One explanation is that these peaks come from independent oscillatory populations. But the new model suggests an alternative: multiple frequency peaks could all emerge from a single circuit exhibiting quasi-periodic or multistable dynamics. The specific frequencies and their relative amplitudes would depend on which rhythm the network occupied and how the SOM and PV populations were engaged—parameters that could shift with attention, learning, or behavioral state. The findings thus provide a mechanistic foundation for understanding how a single cortical circuit can flexibly generate the rich temporal structure observed in brain recordings.