Optimal stimulus shapes for neuronal excitation

The work is made available under the Creative Commons CC0 public domain dedication. The definitive version was published in PLoS Computational Biology 7 (2011): e1002089, doi:10.1371/journal.pcbi.1002089.An important problem in neuronal computation is to discern how features of stimuli control the timing of action potentials. One aspect of this problem is to determine how an action potential, or spike, can be elicited with the least energy cost, e.g., a minimal amount of applied current. Here we show in the Hodgkin & Huxley model of the action potential and in experiments on squid giant axons that: 1) spike generation in a neuron can be highly discriminatory for stimulus shape and 2) the optimal stimulus shape is dependent upon inputs to the neuron. We show how polarity and time course of post-synaptic currents determine which of these optimal stimulus shapes best excites the neuron. These results are obtained mathematically using the calculus of variations and experimentally using a stochastic search methodology. Our findings reveal a surprising complexity of computation at the single cell level that may be relevant for understanding optimization of signaling in neurons and neuronal networks.This work was supported by the Intramural Research Program of the National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892 and NIH grant R01 HL718884 to DP. DBF is an AFOSR Young Investigator (FA 9550-08-01-0076)

A mechanism for robust circadian timekeeping via stoichiometric balance

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102189/1/msb201262.reviewer_comments.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/102189/2/msb201262.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/102189/3/msb201262-sup-0001.pd

Evolution of the repression mechanisms in circadian clocks

Background: Circadian (daily) timekeeping is essential to the survival of many organisms. An integral part of all circadian timekeeping systems is negative feedback between an activator and repressor. However, the role of this feedback varies widely between lower and higher organisms. Results: Here, we study repression mechanisms in the cyanobacterial and eukaryotic clocks through mathematical modeling and systems analysis. We find a common mathematical model that describes the mechanism by which organisms generate rhythms; however, transcription’s role in this has diverged. In cyanobacteria, protein sequestration and phosphorylation generate and regulate rhythms while transcription regulation keeps proteins in proper stoichiometric balance. Based on recent experimental work, we propose a repressor phospholock mechanism that models the negative feedback through transcription in clocks of higher organisms. Interestingly, this model, when coupled with activator phosphorylation, allows for oscillations over a wide range of protein stoichiometries, thereby reconciling the negative feedback mechanism in Neurospora with that in mammals and cyanobacteria. Conclusions: Taken together, these results paint a picture of how circadian timekeeping may have evolved

A Level Set Kalman Filter Approach to Estimate the Circadian Phase and its Uncertainty from Wearable Data

Daily (~24hr) rhythms of behavior and physiology such as sleep and hormone secretion are coordinated by an endogenous timer, the circadian clock. The accurate estimation of the clock state (i.e., the circadian phase) outside of the laboratory has enormous potential for precision medicine. Several methods that predict the phase from measurements collected with wearables (e.g., Apple Watch) have been recently developed. However, computation of the uncertainty in the estimation remains an open problem. The uncertainty analysis is necessary because the estimation accuracy can largely change even by a small perturbation of daily routine. Here, we present a method to account for the uncertainty and estimate the circadian phase using a new extension of Kalman filtering named the level set Kalman filter. Using the newly proposed method, we study the relationship between phase uncertainty and process noise from various sources. This allows the identification of the magnitude of the noise in the circadian system, which is impossible with previous methods. Moreover, our study reveals how much the uncertainty of the phase estimate of the central clock that is inaccessibly located in the brain can be reduced when measurements of the peripheral clock phase are given from wearables. We also show that our method has a performance improvement over the previous methods. Finally, we apply our method to real-world data to further identify its usefulness. These results set the stage for systematically understanding the circadian dynamics in the real world

Taking the lag out of jet lag through model-based schedule design

Travel across multiple time zones results in desynchronization of environmental time cues and the sleep–wake schedule from their normal phase relationships with the endogenous circadian system. Circadian misalignment can result in poor neurobehavioral performance, decreased sleep efficiency, and inappropriately timed physiological signals including gastrointestinal activity and hormone release. Frequent and repeated transmeridian travel is associated with long-term cognitive deficits, and rodents experimentally exposed to repeated schedule shifts have increased death rates. One approach to reduce the short-term circadian, sleep–wake, and performance problems is to use mathematical models of the circadian pacemaker to design countermeasures that rapidly shift the circadian pacemaker to align with the new schedule. In this paper, the use of mathematical models to design sleep–wake and countermeasure schedules for improved performance is demonstrated. We present an approach to designing interventions that combines an algorithm for optimal placement of countermeasures with a novel mode of schedule representation. With these methods, rapid circadian resynchrony and the resulting improvement in neurobehavioral performance can be quickly achieved even after moderate to large shifts in the sleep–wake schedule. The key schedule design inputs are endogenous circadian period length, desired sleep–wake schedule, length of intervention, background light level, and countermeasure strength. The new schedule representation facilitates schedule design, simulation studies, and experiment design and significantly decreases the amount of time to design an appropriate intervention. The method presented in this paper has direct implications for designing jet lag, shift-work, and non-24-hour schedules, including scheduling for extreme environments, such as in space, undersea, or in polar regions

Emergence of Noise-Induced Oscillations in the Central Circadian Pacemaker

Computational modeling and experimentation explain how intercellular coupling and intracellular noise can generate oscillations in a mammalian neuronal network even in the absence of cell-autonomous oscillators

Guidelines for Genome-Scale Analysis of Biological Rhythms

Genome biology approaches have made enormous contributions to our understanding of biological rhythms, particularly in identifying outputs of the clock, including RNAs, proteins, and metabolites, whose abundance oscillates throughout the day. These methods hold significant promise for future discovery, particularly when combined with computational modeling. However, genome-scale experiments are costly and laborious, yielding “big data” that are conceptually and statistically difficult to analyze. There is no obvious consensus regarding design or analysis. Here we discuss the relevant technical considerations to generate reproducible, statistically sound, and broadly useful genome-scale data. Rather than suggest a set of rigid rules, we aim to codify principles by which investigators, reviewers, and readers of the primary literature can evaluate the suitability of different experimental designs for measuring different aspects of biological rhythms. We introduce CircaInSilico, a web-based application for generating synthetic genome biology data to benchmark statistical methods for studying biological rhythms. Finally, we discuss several unmet analytical needs, including applications to clinical medicine, and suggest productive avenues to address them