Efficient Estimation of the Human Circadian Phase via Kalman Filtering.

Circadian rhythms play a vital role in maintaining a person's well-being but remain difficult to quantify accurately. Numerous approaches exist to measure these rhythms, but they often suffer from performance issues on the individual level. This work implements a Steady-State Kalman Filter as a method for estimating the circadian phase shifts from biometric signals. Our framework can automatically fit the filter's parameters to biometric data obtained for each individual, and we were able to consistently estimate the phase shift within 1 hour of melatonin estimates on 100% of all subjects in this study. The estimation method opens up the possibility of real-time control and assessment of the circadian system, as well as chronotherapeutic intervention.Clinical relevance- This establishes a near real-time alternative to melatonin measurements for the estimation of circadian phase shifts, with potential applications in feedback circadian control and chronotherapeutics.

Optimization of light exposure and sleep schedule for circadian rhythm entrainment.

The circadian rhythm, called Process C, regulates a wide range of biological processes in humans including sleep, metabolism, body temperature, and hormone secretion. Light is the dominant synchronizer of the circadian rhythm-it has been used to regulate the circadian phase to cope with jet-lag, shift work, and sleep disorder. The homeostatic oscillation of the sleep drive is called Process S. Process C and Process S together determine the sleep-wake cycle in what is known as the two-process model. This paper addresses the regulation of both Process C and Process S by scheduling light exposure and sleep based on numerical simulations of circadian rhythm and sleep mathematical models. This is a significant step beyond the existing literature that only considers the entrainment of Process C. Regulation of the two-process model poses several unique features and challenges: 1. Process S is non-smooth, i.e., the homeostatic dynamics are different in the sleep and wake regimes; 2. Light only indirectly affects Process S through Process C; 3. Light does not affect Process C during sleep. We consider two scenarios: optimizing light intensity as the control input with spontaneous (i.e., unscheduled) sleep/wake times and jointly optimizing the light intensity and the sleep/wake times, which allows limited delayed sleep and early waking as part of the decision variables. We solve the time-optimal entrainment problem for the two-process model for both scenarios using an extension of the gradient descent algorithm to non-smooth systems. To illustrate the efficacy of our time-optimal entrainment strategies, we consider two common use cases: transmeridian travelers and shift workers. For transmeridian travelers, joint optimization of the two-process model avoids the unrealistic long wake duration when only Process C is considered. The entrainment time also decreases when both the light input and the sleep schedule are optimized compared to when only the light input is optimized. For shift workers, we show that the entrainment time is significantly shortened by optimizing the night shift working light.

Time optimal entrainment control for circadian rhythm.

The circadian rhythm functions as a master clock that regulates many physiological processes in humans including sleep, metabolism, hormone secretion, and neurobehavioral processes. Disruption of the circadian rhythm is known to have negative impacts on health. Light is the strongest circadian stimulus that can be used to regulate the circadian phase. In this paper, we consider the mathematical problem of time-optimal circadian (re)entrainment, i.e., computing the lighting schedule to drive a misaligned circadian phase to a reference circadian phase as quickly as possible. We represent the dynamics of the circadian rhythm using the Jewett-Forger-Kronauer (JFK) model, which is a third-order nonlinear differential equation. The time-optimal circadian entrainment problem has been previously solved in settings that involve either a reduced-order JFK model or open-loop optimal solutions. In this paper, we present (1) a general solution for the time-optimal control problem of fastest entrainment that can be applied to the full order JFK model (2) an evaluation of the impacts of model reduction on the solutions of the time-optimal control problem, and (3) optimal feedback control laws for fastest entrainment for the full order Kronauer model and evaluate their robustness under some modeling errors.

Transcriptional control of motility enables directional movement of Escherichia coli in a signal gradient.

Manipulation of cellular motility using a target signal can facilitate the development of biosensors or microbe-powered biorobots. Here, we engineered signal-dependent motility in Escherichia coli via the transcriptional control of a key motility gene. Without manipulating chemotaxis, signal-dependent switching of motility, either on or off, led to population-level directional movement of cells up or down a signal gradient. We developed a mathematical model that captures the behaviour of the cells, enables identification of key parameters controlling system behaviour, and facilitates predictive-design of motility-based pattern formation. We demonstrated that motility of the receiver strains could be controlled by a sender strain generating a signal gradient. The modular quorum sensing-dependent architecture for interfacing different senders with receivers enabled a broad range of systems-level behaviours. The directional control of motility, especially combined with the potential to incorporate tuneable sensors and more complex sensing-logic, may lead to tools for novel biosensing and targeted-delivery applications.

Controlling the outcome of the Toll-like receptor signaling pathways.

The Toll-Like Receptors (TLRs) are proteins involved in the immune system that increase cytokine levels when triggered. While cytokines coordinate the response to infection, they appear to be detrimental to the host when reaching too high levels. Several studies have shown that the deletion of specific TLRs was beneficial for the host, as cytokine levels were decreased consequently. It is not clear, however, how targeting other components of the TLR pathways can improve the responses to infections. We applied the concept of Minimal Cut Sets (MCS) to the ihsTLR v1.0 model of the TLR pathways to determine sets of reactions whose knockouts disrupt these pathways. We decomposed the TLR network into 34 modules and determined signatures for each MCS, i.e. the list of targeted modules. We uncovered 2,669 MCS organized in 68 signatures. Very few MCS targeted directly the TLRs, indicating that they may not be efficient targets for controlling these pathways. We mapped the species of the TLR network to genes in human and mouse, and determined more than 10,000 Essential Gene Sets (EGS). Each EGS provides genes whose deletion suppresses the network's outputs.