Task-dependent changes in cross-level coupling between single neurons and oscillatory activity in multiscale networks

Abstract

Understanding the principles governing the dynamic coordination of functional brain networks remains an important unmet goal within neuroscience. How do distributed ensembles of neurons transiently coordinate their activity across a variety of spatial and temporal scales? While a complete mechanistic account of this process remains elusive, evidence suggests that neuronal oscillations may play a key role in this process, with different rhythms influencing both local computation and long-range communication. To investigate this question, we recorded multiple single unit and local field potential (LFP) activity from microelectrode arrays implanted bilaterally in macaque motor areas. Monkeys performed a delayed center-out reach task either manually using their natural arm (Manual Control, MC) or under direct neural control through a brain-machine interface (Brain Control, BC). In accord with prior work, we found that the spiking activity of individual neurons is coupled to multiple aspects of the ongoing motor beta rhythm (10-45 Hz) during both MC and BC, with neurons exhibiting a diversity of coupling preferences. However, here we show that for identified single neurons, this beta-to-rate mapping can change in a reversible and task-dependent way. For example, as beta power increases, a given neuron may increase spiking during MC but decrease spiking during BC, or exhibit a reversible shift in the preferred phase of firing. The within-task stability of coupling, combined with the reversible cross-task changes in coupling, suggest that task-dependent changes in the beta-to-rate mapping play a role in the transient functional reorganization of neural ensembles. We characterize the range of task-dependent changes in the mapping from beta amplitude, phase, and inter-hemispheric phase differences to the spike rates of an ensemble of simultaneously-recorded neurons, and discuss the potential implications that dynamic remapping from oscillatory activity to spike rate and timing may hold for models of computation and communication in distributed functional brain networks.

Figure 1. The Manual Control (MC) and Brain Control (BC) tasks.

A) Schematic of the MC task, where monkeys use their right arm to perform a delayed center-out reaching task to move an on-screen cursor from a center cue to one of 8 peripheral targets. B) Schematic of the BC task, where monkeys use changes in the firing rates of a subset of recorded cells in order to move a cursor from the center to one of 8 targets (irrespective of physical movement). C) Timing of different trial sub-stages in the MC and BC tasks. Trials start with the appearance of central cue. A hold period (MC: 500 ms; BC: 100 ms) begins once the cursor enters the central cue. Upcoming target appears onscreen once cursor enters center. Go cue (central cue color change) indicates that monkeys can move the cursor to the designated target (via hand movement in MC or firing rate changes in BC), with a range of movement times. Holding the cursor within the target (MC: 400 ms; BC: 50 ms) triggers juice reward (500 ms), followed by the start of the next trial.

Figure 2. Event-related changes in local field potential (LFP) activity.

A) Go-cue related ERP activity in right primary motor cortex (M1) during Brain Control (BC). The neurons driving the brain-machine interface are in right M1. B) Time-frequency plot showing frequency-specific changes in mean amplitude relative to the onset of the go cue (0 ms) in right M1 during BC, including amplitude changes in the theta (6 Hz), high beta (28 Hz), low gamma (36 Hz), and high gamma (>70 Hz) bands. Across all frequencies, color scale indicates increase (red) or decrease (blue) in amplitude relative to the mean of 1. Notice the strong drop in beta amplitude locked to the onset of the go cue. C) Smoothed single-trial traces of beta amplitude, sorted by movement duration (from go cue to cursor entering target). Vertical black line at −100 ms indicates when cursor entered the center cue, 0 ms is go cue onset. First curved black line indicates when cursor enters target, second indicates reward onset, and third indicates reward offset and beginning of the next trial. The sharp drop in beta amplitude during movement is followed by a beta amplitude increase during the reward delivery. D–F) As in A–C, during Manual Control (MC).

Figure 3. External and internal tuning curves.

Tuning curves characterize neural properties by conditioning spike rates on external factors such as movement direction or internal factors such as beta amplitude or phase. A–E show the external tuning properties for one neuron (sig045a), while F–J characterize the internal tuning properties for the same cell. A) Trial-related rate changes relative to baseline, collapsed across all targets. Go-cue onset is 0 ms. Four disjoint datasets are shown (BC1 & BC2, red; MC1 & MC2, blue). B) Target-specific rate changes (relative to baseline and trial-related activity) for the 8 BC targets. Solid lines show responses for BC1, dotted lines BC2. C) As in B, for MC. D) External tuning: joint display of trial- and target-related rate changes in BC1; color indicates spike rate. E) External tuning components (r_baseline, r_trial, and r_target) are learned from training data (BC1) and applied to novel test data (BC2) to predict instantaneous spike rate. F) Rate changes associated with different beta amplitudes. Beta amplitude normalized to a mean of 1. For this neuron, large beta amplitudes are associated with reduced firing and low amplitudes with increased spiking, but rate of change is task-dependent. G) As in F, conditioning spike rate on beta phase rather amplitude. H) Weight term governing the interaction between amplitude and phase (see Materials and Methods). I) Internal tuning: joint display of amplitude- and phase-related rate changes in BC1; color indicates spike rate. J) Internal tuning components (r_baseline, r_amp, r_phase, and w_amp) are learned from training data (BC1) and applied to novel test data (BC2) to predict instantaneous rate.

Figure 4. Beta amplitude-to-rate mapping.

A) A diversity of amplitude-to-rate mappings hold across neurons during a given task; shown are 12 example neurons during BC. Dots indicate measured spike rates, lines show best-fit sigmoids. Increased beta amplitude associated with decreased rate in some neurons while others exhibit increased firing; vertical lines indicate cross-over points associated with change in firing-rate rank order within ensemble. B–G) Amplitude-to-rate mapping can change as function of task; six example neurons shown. H) Within-task CLC parameter stability assessed by computing amplitude-to-rate mapping for disjoint BC datasets; positive (negative) rate changes indicate that spike probability and amplitude are positively (negatively) correlated. I) As in H, for MC. J–K) Direct comparison of BC/MC datasets provides evidence for cross-task remapping; the amplitude-to-rate mapping for one task may not hold for different task. Similarity of J and K indicates reliable task-dependent remapping.

Figure 5. Beta phase-to-rate mapping.

A–H) Eight example neurons that exhibit task-dependent remapping of beta phase-to-rate relationship; fits for all neurons shown in grey. Vertical lines indicate phase of maximal spiking for BC (red) and MC (blue). Preferred phase varies across neurons within a task, but all BC phases occur earlier than preferred MC phases. I) Preferred phase for BC vs. MC for all 53 neurons in right M1, exhibiting task-dependent shift to later phase for MC. J) Preferred beta phases map to times of peak spike probability relative to the ongoing beta rhythm; shown are peak times for all neurons in right M1, sorted relative to beta trough during BC (red). MC (blue) does not preserve the BC ensemble timing order. K) As in I, for neurons in left M1. L) As in J, for left M1.

Figure 6. Modulation of phase-to-rate mapping by beta amplitude.

Beta phase has a stronger impact on spike rate when beta amplitude is large, but gain modulation is not uniform across neurons. A–D show the phase-to-rate mappings for 9 example neurons, where instantaneous phases and spike times were pre-sorted into one of four bins based on beta amplitude (see Materials and Methods). Phase-to-rate modulation depth (difference between maximum and baseline rates) is largest for bin with largest amplitudes (c.f. scale of y-axis of A–D), but some modulation depth increases faster for some neurons than others; sig045a (black) has highest rate in smallest amplitude bin but ranks third in the largest amplitude bin, while sig043c (cyan) moves from rank 4 to 2. Differential changes can shift the beta phase where two neurons exchange spike rate rank order, even if the preferred phases do not change (note shift in phase of crossover of sig043c (cyan) with sig029a (blue), indicated by vertical lines. E) Phase-to-rate modulation depth as a function of mean beta amplitude. F) Amplitude modulation of phase-to-rate mapping can be expressed as a product of two terms, one of which is a quadratic weight factor (see Materials and Methods).

Figure 7. Target-specific modulation of phase-to-rate modulation depth.

Sorting trials based on the intended BC target prior to computing the phase-to-rate mapping reveals differences in baseline firing (due to direction tuning) as well as changes in the phase-to-rate modulation depth. A–L show 6 example neurons where the phase-to-rate modulation depth is positively correlated with the target-specific shift in baseline spike rate. Colors indicate phase-to-rate mappings computed from trials moving toward different targets. Shown are phase-to-rate mappings with target-specific baseline shifts included (A–D, I, J) or removed (E–H, K, L). For example, sig045b (A, E) fires the most for Target 8 (black) and the least for Target 4 (green), and also exhibits the largest phase-to-rate modulation depth for Target 8 and the least for Target 4 – that is, target-specific spike rates and phase-to-rate modulation depth are positively correlated (c.f. sig038a in B, F). In contrast, the phase-to-rate modulation depth is largely independent of target direction for sig043b and sig020a, despite the large target-specific shift in baseline spike rates. Finally, sig073b and sig043c provide examples of negative correlation between target-specific shifts in baseline spike rates and target-specific changes in phase-to-rate modulation depth. Correlations for these 6 examples are shown in M.

Figure 8. Frequency dependence of amplitude- and phase-to-rate mappings.

A) Amplitude-to-rate mapping for one neuron (sig045a), computed for a range of center frequencies (1–100 Hz). Vertical axis gives filter center frequency, horizontal axis gives amplitude at that center frequency (normalized to a mean of 1 for all frequencies); color gives spike rate change relative to baseline. This neuron exhibits different responses for different frequencies; positive correlation of rate with theta and high gamma bands, but negative correlation with beta and low gamma. B) Same data as A, showing only four frequency bands at 6, 27, 34, and 90 Hz. Dots indicate measured rates, lines are best fit sigmoids. C) As in A, for the phase-to-rate mapping. Strongest response for this neuron is seen at 34 Hz for this neuron. D) As in B, for the phase-to-rate mapping. E) Range of rate change for sig045a as function of center frequency. Peaks of the amplitude- and phase-to-rate ranges are offset, with the amplitude-to-rate mapping strongest ∼27 Hz while the phase-to-rate mapping is strongest ∼34 Hz. F) As in A, for a finer frequency resolution from 20–40 Hz. G–J) As in F, for neurons sig062a, sig081b, sig031a, and sig029a. K) As in C, from 20 to 40 Hz for neuron sig045a. L–O) As in K, for neurons sig062a, sig081b, sig031a, and sig029a.

Figure 9. Phase-difference-to-rate mapping.

A) Joint probability density function of instantaneous phases of left and right primary motor cortex (M1). B) Same data as A, after change of variables to isolate the phase difference between left and right M1. Inter-hemispheric phase differences are statistically independent from local M1 phase. C) Example neuron sensitive to beta phase difference between left and right M1. During BC, lowest rate occurs near the most probable phase difference (peak of distribution in D), but the neuron increases spiking when the inter-hemispheric phase difference shifts to less probable values. Dots indicate measured rate, red line is best-fit von Mises type function (see Materials and Methods). D) Distribution of inter-hemispheric phase differences (left M1 phase minus right M1 phase) during BC; empirical histogram estimate (black) and best-fit von Mises distribution (red). E) Same neuron as C, during MC. Despite only a small shift in the phase-difference distribution, the phase-difference-to-rate mapping has flipped for this cell. F) As in D, for MC.

Figure 10. Impact of task-dependent changes predictability of spiking.

A) Schematic of 8×8 microelectrode array implanted in left primary motor cortex (M1). Interelectrode separation is 500 microns on average. Color indicates groups with different numbers of electrodes, including 4 (blue), 16 (blue and green), 36 (blue, green, black), and 64 (blue, green, black, and red). B) Including more channels in a multivariate model improves prediction performance – the spike rate range increases as one considers groups of 4 (blue), 16 (green), 36 (black), or 64 (red) channels. Improvement of prediction performance suggests that distal electrodes contribute information independent of information from proximal electrodes. The predicted rate (x-axis) is shown in normalized units in order to emphasize the increase in range of the measured rate. C–H) Examples of 6 neurons where within-task predictability (red; train on BC data, test on novel BC data) is higher than cross-task predictability (blue; train on BC data, test on novel MC data). Dots indicate measured rates, lines give best linear fit. Within-task predictions are accurate for neurons across both BC and MC, implying that low cross-task predictive performance is due to task-dependent remapping rather than a lack of cross-level coupling in one of the tasks.

Figure 11. Neuro-computational consequences of amplitude- and phase-to-rate mappings.

For a given neuron, the amplitude- and phase-to-rate mappings are produced by the combined synaptic input to that cell. But since information about the population rhythm is broadly accessible, neurons may use this information to dynamically organize relative activity within a functional ensemble. This activity includes winner-take-all interactions arising from recurrent local connectivity and relative spike timing among ordered sets of cells. A) Two excitatory cells (E₁ and E₂, red) that connect to a common inhibitory cell (I, blue) – and which in turn provides inhibitory synaptic connections to E₁ and E₂ to form re-entrant or recurrent excitatory-inhibitory loops – can act as a simple winner-take-all (WTA) module. That is, given different levels of input to E₁ and E₂, then either E₁ or E₂ (but not both) will produce tonic spike output. B–C) If two cells with different amplitude-to-rate mappings provide input to such a WTA module, then the WTA module will provide different output at low and high beta amplitudes. For example, given the purple (sig045a) and gold (sig062a) amplitude to rate mappings shown in Figure S10, then WTA cell E₁ generates spike output only at low amplitudes while E₂ spikes at high amplitudes; E₁ and E₂ switch roles at the beta amplitude where the amplitude-to-rate sigmoids intersect. Critically, task-dependent remapping implies that this intersection point can shift to different values for each pair of input neurons. D) One second example trace of filtered LFP activity during BC showing beta amplitude (black) and phase (grey) variation over time. E) Amplitude-to-rate mappings for seven example neurons: sig015a (blue), sig029a (green), sig029b (red), sig031a (cyan), sig045a (purple), sig062a (gold), and sig081b (black). Baseline rate has been removed to emphasize rate changes associated with amplitude variation. F) Changes in spike rates (relative to baseline) over one second induced by the amplitude-to-rate mappings (color as in E). Colors are as in Figure 4A. Note the two alternating periods of rank-ordered regimes. G) Close up of 180 ms of beta activity, showing amplitude (grey) and phase (black) variation. H) Rate changes induced by the amplitude-weighted phase-to-rate mapping for sig081a (black) and sig062a (gold). I) Periods of high beta amplitude are associated with a bias towards a relative spike timing order, while periods of low beta amplitude are not. Task-dependent remapping of preferred phases can switch this order. Task-dependent changes in the relative spike timing order of an ensemble – via the independent phase-to-rate remapping of each cell – provides a potential mechanism linking the global or top-down input changes associated with task switching to local features such as cell assembly activation or synfire chain propagation (thus influencing local cortical computation) as well as spike-timing dependent plasticity (thus influencing learning).