Efficient "communication through coherence" requires oscillations structured to minimize interference between signals

Abstract

The 'communication through coherence' (CTC) hypothesis proposes that selective communication among neural networks is achieved by coherence between firing rate oscillation in a sending region and gain modulation in a receiving region. Although this hypothesis has stimulated extensive work, it remains unclear whether the mechanism can in principle allow reliable and selective information transfer. Here we use a simple mathematical model to investigate how accurately coherent gain modulation can filter a population-coded target signal from task-irrelevant distracting inputs. We show that selective communication can indeed be achieved, although the structure of oscillatory activity in the target and distracting networks must satisfy certain previously unrecognized constraints. Firstly, the target input must be differentiated from distractors by the amplitude, phase or frequency of its oscillatory modulation. When distracting inputs oscillate incoherently in the same frequency band as the target, communication accuracy is severely degraded because of varying overlap between the firing rate oscillations of distracting inputs and the gain modulation in the receiving region. Secondly, the oscillatory modulation of the target input must be strong in order to achieve a high signal-to-noise ratio relative to stochastic spiking of individual neurons. Thus, whilst providing a quantitative demonstration of the power of coherent oscillatory gain modulation to flexibly control information flow, our results identify constraints imposed by the need to avoid interference between signals, and reveal a likely organizing principle for the structure of neural oscillations in the brain.

Figure 1. Selective communication by coherent gain modulation.

Independent orientation stimuli are represented in separate input networks as population codes with bell-shaped firing rate tuning curves. These input networks converge to provide a combined input to the receiving network. To selectively route the information encoded in one input network (the ‘target’ input) to the output of the receiving network, a top-down control signal imposes an oscillatory modulation on the target network firing rate and a coherent oscillatory gain modulation in the receiving network. The output of the receiving network is integrated over time to produce a spatial pattern of activity, which is decoded to produce an estimate of the target stimulus.

Figure 2. Oscillation structure determines communication accuracy.

(A–D) Example firing rate modulation of the target (red) and distracting inputs (gray) over the 100 ms integration time. Gain modulation (blue) produced by the optimized receiving network. (E) Firing rate as a function of oscillation phase for synchronization strengths from 0.1–0.9. (F) Fisher information as a function of the synchronization strength of the target input for stimulus estimates decoded from receiving network output integrated over 100 ms. Distractor condition indicated by color as shown in key. (G) Comparison of Fisher information for asynchronous and incoherently oscillating distracting inputs as functions of firing rate of input networks. (H) Separation of target and distractors in frequency. Fisher information as function of oscillation frequency of distractor networks for narrowband (purple) and broadband (orange) sinusoidal oscillations and narrowband Von Mises oscillations (blue). Frequency of target input modulation (50 Hz) is indicated by black arrow. (I) Amplitude spectrum of oscillatory modulations for narrowband Von Mises modulation and narrow and broadband sinusoidal oscillations (F₀ is oscillation center frequency).

Figure 3. Comparison of optimized and biologically plausible gain modulations.

(A) Blue trace is the gain modulation generated by the optimized receiving network; brown trace is a gain modulation that oscillates around zero with the same waveform as the firing rate modulation of the target. (B) Frequency response of the filter that transforms the firing rate modulation of the target input into the optimized gain modulation. (C) Comparison of Fisher information for receiving networks using optimized and alternative gain modulations.

Figure 4. Integration time, modulation frequency and communication accuracy.

(A–D) Fisher information as a function of integration time. Target modulation frequency is indicated by line color (see key). For incoherent distractors (A) and phase separation (D) conditions, distractor frequency was the same as target frequency. For frequency separation condition (C), distractor frequency is indicated by line style (see key). The duration of one period of the target input modulation is indicated by the vertical dashed lines, color coded by target modulation frequency.

Figure 5. Bottom-up coherence.

(A) Diagram illustrating receiving network in which gain modulation is a filtered version of the summed combined spike input. (B–E) Comparison of Fisher information of decoded stimulus estimates for original ‘top-down’ model (solid lines) and ‘bottom-up’ model (dashed lines).

Figure 6. Filtering with arbitrary gain modulations.

(A–D) Example input firing rate modulations, gain modulations generated by optimized linear filter (blue trace), and gain modulations found to optimize decoding accuracy for specific examples of target firing rate modulation (green traces). (E) Effect of synchronization strength on decoding accuracy for asynchronous distractors (blue), distractors oscillating incoherently in the same frequency band as the target (red) and distractors oscillating coherently with the target but equally space in phase (yellow). (F) Effect of distractor frequency on decoding accuracy. (G) Comparison of decoding accuracy for different distractor conditions indicated by color as above for synchronization strength of 0.5 and average neuronal firing rate of 5 Hz.