SUMMARY How do neurons develop, control, and maintain their electrical signaling properties in spite of ongoing protein turnover and perturbations to activity? From generic assumptions about the molecular biology underlying channel expression, we derive a simple model and show how it encodes an “activity set point” in single neurons. The model generates diverse self-regulating cell types and relates correlations in conductance expression observed in vivo to underlying channel expression rates. Synaptic as well as intrinsic conductances can be regulated to make a self-assembling central pattern generator network; thus, network-level homeostasis can emerge from cell-autonomous regulation rules. Finally, we demonstrate that the outcome of homeostatic regulation depends on the complement of ion channels expressed in cells: in some cases, loss of specific ion channels can be compensated; in others, the homeostatic mechanism itself causes pathological loss of function.

Perceptions, thoughts, and actions unfold over millisecond timescales, while learned behaviors can require many days to mature. While recent experimental advances enable large-scale and long-term neural recordings with high temporal fidelity, it remains a formidable challenge to extract unbiased and interpretable descriptions of how rapid single-trial circuit dynamics change slowly over many trials to mediate learning. We demonstrate a simple tensor component analysis (TCA) can meet this challenge by extracting three interconnected, low-dimensional descriptions of neural data: neuron factors, reflecting cell assemblies; temporal factors, reflecting rapid circuit dynamics mediating perceptions, thoughts, and actions within each trial; and trial factors, describing both long-term learning and trial-to-trial changes in cognitive state. We demonstrate the broad applicability of TCA by revealing insights into diverse datasets derived from artificial neural networks, large-scale calcium imaging of rodent prefrontal cortex during maze navigation, and multielectrode recordings of macaque motor cortex during brain machine interface learning.

Experimental observations reveal that the expression levels of different ion channels vary across neurons of a defined type, even when these neurons exhibit stereotyped electrical properties. However, there are robust correlations between different ion channel expression levels, although the mechanisms that determine these correlations are unknown. Using generic model neurons, we show that correlated conductance expression can emerge from simple homeostatic control mechanisms that couple expression rates of individual conductances to cellular readouts of activity. The correlations depend on the relative rates of expression of different conductances. Thus, variability is consistent with homeostatic regulation and the structure of this variability reveals quantitative relations between regulation dynamics of different conductances. Furthermore, we show that homeostatic regulation is remarkably insensitive to the details that couple the regulation of a given conductance to overall neuronal activity because of degeneracy in the function of multiple conductances and can be robust to "antihomeostatic" regulation of a subset of conductances expressed in a cell.neuronal excitability | robustness | computational models | control theory T he electrophysiological signature of every neuron is determined by the number and kind of voltage-dependent conductances in its membrane. Most neurons express many voltage-dependent conductances, some of which may have overlapping or degenerate physiological functions (1-6). Furthermore, neurons in the brains of long-lived animals must maintain reliable function over the animal's lifetime while all of their ion channels and receptors are replaced in the membrane over hours, days, or weeks. Consequently, ongoing turnover of ion channels of various types must occur without compromising the essential excitability properties of the neuron (5, 7-10).Both theoretical and experimental studies suggest that maintaining stable intrinsic excitability is accomplished via homeostatic, negative feedback processes that use intracellular Ca 2+ concentrations as a sensor of activity and then alter the synthesis, insertion, and degradation of membrane conductances to achieve a target activity level (11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27). Among the modeling studies are several different homeostatic tuning rules that differ in how sensor readout is coupled to the changes in conductance necessary to achieve a target activity (11,13,14,28). Regardless, these models can self-assemble from randomized initial conditions, and they will change their conductance densities in response to perturbation or synaptic drive. In one of these homeostatic self-tuning models (14), similar activity patterns can be associated with different sets of conductance densities.Thus, it is perhaps not surprising that experimental studies also find a considerable range in the conductance densities of voltagedependent channels and in the mRNA expression of their ion channel genes (29-36). The experimental st...

Identifying low-dimensional features that describe large-scale neural recordings is a major challenge in neuroscience. Repeated temporal patterns (sequences) are thought to be a salient feature of neural dynamics, but are not succinctly captured by traditional dimensionality reduction techniques. Here, we describe a software toolbox—called seqNMF—with new methods for extracting informative, non-redundant, sequences from high-dimensional neural data, testing the significance of these extracted patterns, and assessing the prevalence of sequential structure in data. We test these methods on simulated data under multiple noise conditions, and on several real neural and behavioral data sets. In hippocampal data, seqNMF identifies neural sequences that match those calculated manually by reference to behavioral events. In songbird data, seqNMF discovers neural sequences in untutored birds that lack stereotyped songs. Thus, by identifying temporal structure directly from neural data, seqNMF enables dissection of complex neural circuits without relying on temporal references from stimuli or behavioral outputs.

Neurons in cold-blooded animals remarkably maintain their function over a wide range of temperatures, even though the rates of many cellular processes increase twofold, threefold, or many-fold for each 10°C increase in temperature. Moreover, the kinetics of ion channels, maximal conductances, and Ca 2ϩ buffering each have independent temperature sensitivities, suggesting that the balance of biological parameters can be disturbed by even modest temperature changes. In stomatogastric ganglia of the crab Cancer borealis, the duty cycle of the bursting pacemaker kernel is highly robust between 7 and 23°C (Rinberg et al., 2013). We examined how this might be achieved in a detailed conductance-based model in which exponential temperature sensitivities were given by Q 10 parameters. We assessed the temperature robustness of this model across 125,000 random sets of Q 10 parameters. To examine how robustness might be achieved across a variable population of animals, we repeated this analysis across six sets of maximal conductance parameters that produced similar activity at 11°C. Many permissible combinations of maximal conductance and Q 10 parameters were found over broad regions of parameter space and relatively few correlations among Q 10 s were observed across successful parameter sets. A significant portion of Q 10 sets worked for at least 3 of the 6 maximal conductance sets (ϳ11.1%). Nonetheless, no Q 10 set produced robust function across all six maximal conductance sets, suggesting that maximal conductance parameters critically contribute to temperature robustness. Overall, these results provide insight into principles of temperature robustness in neuronal oscillators.

Though the temporal precision of neural computation has been studied intensively, a data-driven determination of this precision remains a fundamental challenge. Reproducible spike patterns may be obscured on single trials by uncontrolled temporal variability in behavior and cognition, and may not be time locked to measurable signatures in behavior or local field potentials (LFP). To overcome these challenges, we describe a general-purpose time warping framework that reveals precise spike-time patterns in an unsupervised manner, even when these patterns are decoupled from behavior or are temporally stretched across single trials. We demonstrate this method across diverse systems: cued reaching in nonhuman primates, motor sequence production in rats, and olfaction in mice. This approach flexibly uncovers diverse dynamical firing patterns, including pulsatile responses to behavioral events, LFP-aligned oscillatory spiking, and even unanticipated patterns, like 7 Hz oscillations in rat motor cortex that are not time-locked to measured behaviors or LFP.

1Though the temporal precision of neural computation has been studied intensively, a data-driven determination 2 of this precision remains a fundamental challenge. Reproducible spike time patterns may be obscured on single 3 trials by uncontrolled temporal variability in behavior and cognition, or may not even be time locked to measurable 4 signatures in either behavior or local field potentials (LFP). To overcome these challenges, we describe a general-5 purpose time warping framework that reveals precise spike-time patterns in an unsupervised manner, even when 6 spiking is decoupled from behavior or is temporally stretched across single trials. We demonstrate this method 7 across diverse systems: cued reaching in nonhuman primates, motor sequence production in rats, and olfaction in 8 mice. This approach flexibly uncovers diverse dynamical firing patterns, including pulsatile responses to behavioral 9 events, LFP-aligned oscillatory spiking, and even unanticipated patterns, like 7 Hz oscillations in rat motor cortex 10 that are not time-locked to measured behaviors or LFP. 11 14 Amarasingham et al. 2015; Brette 2015; Denève and Machens 2016), engendering intense debates in systems 15neuroscience over the last several decades. Empirically determining the degree of temporal precision from data is 16 challenging because multi-neuronal spike trains may contain highly structured temporal patterns that are completely 17 1 masked by temporal variations in behavioral and cognitive variables not under direct experimental control. For 18 example, precise spike patterns may not be temporally locked to naïvely chosen sensory or behavioral events. 19 Indeed, the fidelity of olfactory coding may be underestimated by factors of two to four when spike times are aligned 20 to stimulus delivery instead of inhalation onset (Shusterman et al. 2011; Cury and Uchida 2010; Shusterman et al. 21 2018). 22 Thus, experimental estimates of spike time precision hinge on the choice of an alignment point, which defines the 23 origin of the time axis on each trial. This choice can often be challenging and subjective. Even in relatively simple 24 behavioral tasks, animals can experience a sequence of stimuli, actions, and rewards, each of which occur with 25 varying latencies on different trials. Such tasks thus provide multiple choices for aligning multineuronal spike trains 26 to measurable events marking an origin of time. Moreover, in addition to choosing an origin of time, we must also 27 choose its units. Should spike times be measured in absolute clock time relative to some measured event, or in 28 units of fractional time between two events? Should the units of time change between successive pairs of events? 29 Could any one of these choices unmask spike-timing precision that is otherwise invisible? 30 Past studies have addressed these challenges in a number of ways: grouping trials together with similar durations 31 before averaging spike counts (Murakami et al. 2014; Starkweather et al. 2017; Wang et al. 2018), manually 32...

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