Combined mechanisms of neural firing rate homeostasis

Gating of homeostatic regulation of intrinsic excitability produces cryptic long-term storage of prior perturbations

Neurons and neuronal circuits must maintain their function throughout the life of the organism despite changing environments. Previous theoretical and experimental work suggests that neurons monitor their activity using intracellular calcium concentrations to regulate their intrinsic excitability. Models with multiple sensors can distinguish among different patterns of activity, but previous work using models with multiple sensors produced instabilities that lead the models' conductances to oscillate and then to grow without bound and diverge. We now introduce a nonlinear degradation term that explicitly prevents the maximal conductances to grow beyond a bound. We combine the sensors' signals into a master feedback signal that can be used to modulate the timescale of conductance evolution. Effectively, this means that the negative feedback can be gated on and off according to how far the neuron is from its target. The modified model recovers from multiple perturbations. Interestingly, depolarizing the models to the same membrane potential with current injection or with simulated high extracellular K+ produces different changes in conductances, arguing that caution must be used in interpreting manipulations that serve as a proxy for increased neuronal activity. Finally, these models accrue traces of prior perturbations that are not visible in their control activity after perturbation but that shape their responses to subsequent perturbations. These cryptic or hidden changes may provide insight into disorders such as posttraumatic stress disorder that only become visible in response to specific perturbations.

Altered Odor-Evoked Electrophysiological Responses in the Anterior Piriform Cortex of Conscious APP/PS1 Mice

Background: Olfactory decline is an indicator of early-stage Alzheimer’s disease (AD). Although the anterior piriform cortex (aPC) is an important brain area involved in processing olfactory input, little is known about how its neuronal activity is affected in early-stage AD. Objective: To elucidate whether odor-induced electrophysiological responses are altered in the aPC of 3-5-month-old APP/PS1 mice. Methods: Using head-fixed multi-channel recording techniques in APP/PS1 AD mouse model to uncover potential aberrance of the aPC neuronal firing and local field potential (LFP) in response to vanillin. Results: We show that the firing rate of aPC neurons evoked by vanillin is significantly reduced in conscious APP/PS1 mice. LFP analysis demonstrates reduced low- and high-gamma (γ low, γ high) oscillations during both the baseline and odor stimulation periods in APP/PS1 mice. Moreover, according to spike-field coherence (SFC) analysis, APP/PS1 mice show decreased coherence between odor-evoked spikes and γ low rhythms, while the coherence with γ high rhythms and the ΔSFC of the oscillations is unaffected. Furthermore, APP/PS1 mice show reduced phase-locking strength in the baseline period, such that there is no difference between baseline and odor-stimulation conditions. This contrasts markedly with wild type mice, where phase-locking strength decreases on stimulation. Conclusion: The abnormalities in both the neuronal and oscillatory activities of the aPC may serve as electrophysiological indicators of underlying olfactory decline in early AD.

New insights from small rhythmic circuits

Small rhythmic circuits, such as those found in invertebrates, have provided fundamental insights into how circuit dynamics depend on individual neuronal and synaptic properties. Degenerate circuits are those with different network parameters and similar behavior. New work on degenerate circuits and their modulation illustrates some of the rules that help maintain stable and robust circuit function despite environmental perturbations. Advances in neuropeptide isolation and identification provide enhanced understanding of the neuromodulation of circuits for behavior. The advent of molecular studies of mRNA expression provides new insight into animal-to-animal variability and the homeostatic regulation of excitability in neurons and networks.

Self-healing codes: How stable neural populations can track continually reconfiguring neural representations

The brain is capable of adapting while maintaining stable long-term memories and learned skills. Recent experiments show that neural responses are highly plastic in some circuits, while other circuits maintain consistent responses over time, raising the question of how these circuits interact coherently. We show how simple, biologically motivated Hebbian and homeostatic mechanisms in single neurons can allow circuits with fixed responses to continuously track a plastic, changing representation without reference to an external learning signal.

As an adaptive system, the brain must retain a faithful representation of the world while continuously integrating new information. Recent experiments have measured population activity in cortical and hippocampal circuits over many days and found that patterns of neural activity associated with fixed behavioral variables and percepts change dramatically over time. Such “representational drift” raises the question of how malleable population codes can interact coherently with stable long-term representations that are found in other circuits and with relatively rigid topographic mappings of peripheral sensory and motor signals. We explore how known plasticity mechanisms can allow single neurons to reliably read out an evolving population code without external error feedback. We find that interactions between Hebbian learning and single-cell homeostasis can exploit redundancy in a distributed population code to compensate for gradual changes in tuning. Recurrent feedback of partially stabilized readouts could allow a pool of readout cells to further correct inconsistencies introduced by representational drift. This shows how relatively simple, known mechanisms can stabilize neural tuning in the short term and provides a plausible explanation for how plastic neural codes remain integrated with consolidated, long-term representations.

Biophysical models of intrinsic homeostasis: Firing rates and beyond

In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of cell-intrinsic properties, biophysical models of neurons permit one to identify relevant physiological substrates that can serve as regulators of neuronal excitability and to test how feedback loops can stabilize crucial variables such as long-term calcium levels and firing rates. Mathematical theory has also revealed a rich set of complementary computational properties arising from distinct cellular dynamics and even shaping processing at the network level. Here, we provide an overview over recently explored homeostatic mechanisms derived from biophysical models and hypothesize how multiple dynamical characteristics of cells, including their intrinsic neuronal excitability classes, can be stably controlled.

Control theory in biology and medicine : Introduction to the special issue

From September-December 2017, the Mathematical Biosciences Institute at Ohio State University hosted a series of workshops on control theory in biology and medicine, including workshops on control and modulation of neuronal and motor systems, control of cellular and molecular systems, control of disease / personalized medicine across heterogeneous populations, and sensorimotor control of animals and robots. This special issue presents tutorials and research articles by several of the participants in the MBI workshops.