Quantitative analyses of EGFR localization and trafficking dynamics in the follicular epithelium.

To bridge the gap between qualitative and quantitative analyses of the epidermal growth factor receptor (EGFR) in tissues, we generated an sfGFP-tagged EGF receptor (EGFR-sfGFP) in Drosophila The homozygous fly appears similar to wild type with EGFR expression and activation patterns that are consistent with previous reports in the ovary, early embryo, and imaginal discs. Using ELISA, we quantified an average of 1100, 6200 and 2500 receptors per follicle cell (FC) at stages 8/9, 10 and ≥11 of oogenesis, respectively. Interestingly, the spatial localization of the EGFR to the apical side of the FCs at early stages depended on the TGFα-like ligand Gurken. At later stages, EGFR localized to basolateral positions of the FCs. Finally, we followed the endosomal localization of EGFR in the FCs. The EGFR colocalized with the late endosome, but no significant colocalization of the receptor was found with the early endosome. The EGFR-sfGFP fly is an exciting new resource for studying cellular localization and regulation of EGFR in tissues.

Managing public transit during a pandemic: The trade-off between safety and mobility.

During a pandemic such as COVID-19, managing public transit effectively becomes a critical policy decision. On the one hand, efficient transportation plays a pivotal role in enabling the movement of essential workers and keeping the economy moving. On the other hand, public transit can be a vector for disease propagation due to travelers' proximity within shared and enclosed spaces. Without strategic preparedness, mass transit facilities are potential hotbeds for spreading infectious diseases. Thus, transportation agencies face a complex trade-off when developing context-specific operating strategies for public transit. This work provides a network-based analysis framework for understanding this trade-off, as well as tools for calculating targeted commute restrictions under different policy constraints, e.g., regarding public health considerations (limiting infection levels) and economic activity (limiting the reduction in travel). The resulting plans ensure that the traffic flow restrictions imposed on each route are adaptive to the time-varying epidemic dynamics. A case study based on the COVID-19 pandemic reveals that a well-planned subway system in New York City can sustain 88% of transit flow while reducing the risk of disease transmission by 50% relative to fully-loaded public transit systems. Transport policy-makers can exploit this optimization-based framework to address safety-and-mobility trade-offs and make proactive transit management plans during an epidemic outbreak.

A Two-Step Model of Human Entrainment: A Quantitative Study of Circadian Period and Phase of Entrainment.

One of the essential characteristics of an authentic circadian clock is that the free-running period sustains an approximately 24-hour cycle. When organisms are exposed to an external stimulus, the endogenous oscillators synchronize to the cycling environment signal in a process known as entrainment. These environmental cues perform an important role in resetting the phase and period of the circadian clock. A "generalized assumption" states that when an organism has a short period, it will experience a phase advance, while an organism with a long period experiences a phase delay. Despite widespread use, this positive relationship relating period to the phase of entrainment does not describe all known experimental data. We developed a two-step entrainment model to explain a broader range of results as well as provide more quantitative analysis. We prove existence and stability of periodic orbits and given analytical solutions of the range of entrainment, fit the phase trajectory over the entire entrainment process to data from a published study for 12 subjects in extended day cycles, i.e., longer than 24 h. Our simulations closely replicated the phase data and predicted correctly the phase of entrainment. We investigate the factors related to the rate of entrainment (ROE) and present the three-dimensional parameter spaces, illustrating the various behaviors of the phase of entrainment and ROE. Our findings can be applied to diagnostics and treatments for patients with sleep disorders caused by shift work or jet lag.

A pipeline for testing drug mechanism of action and combination therapies: From microarray data to simulations via Linear-In-Flux-Expressions: Testing four-drug combinations for tuberculosis treatment.

Computational methods are becoming commonly used in many areas of medical research. Recently, the modeling of biological mechanisms associated with disease pathophysiology have benefited from approaches such as Quantitative Systems Pharmacology (briefly QSP) and Physiologically Based Pharmacokinetics (briefly PBPK). These methodologies show the potential to enhance, if not substitute animal models. The main reasons for this success are the high accuracy and low cost. Solid mathematical foundations of such methods, such as compartmental systems and flux balance analysis, provide a good base on which to build computational tools. However, there are many choices to be made in model design, that will have a large impact on how these methods perform as we scale up the network or perturb the system to uncover the mechanisms of action of new compounds or therapy combinations. A computational pipeline is presented here that starts with available-omic data and utilizes advanced mathematical simulations to inform the modeling of a biochemical system. Specific attention is devoted to creating a modular workflow, including the mathematical rigorous tools to represent complex chemical reactions, and modeling drug action in terms of its impact on multiple pathways. An application to optimizing combination therapy for tuberculosis shows the potential of the approach.

A Unified Model for Entrainment by Circadian Clocks: Dynamic Circadian Integrated Response Characteristic (dCiRC).

Circadian rhythms are ubiquitous and are observed in all biological kingdoms. In nature, their primary characteristic or phenotype is the phase of entrainment. There are two main hypotheses related to how circadian clocks entrain, parametric and non-parametric models. The parametric model focuses on the gradual changes of the clock parameters in response to the changing ambient condition, whereas the non-parametric model focuses on the instantaneous change of the phase of the clock in response to the zeitgeber. There are ample empirical data supporting both models. However, only recently has a unifying model been proposed, the circadian integrated response characteristic (CiRC). In the current study, we developed a system of ordinary differential equations, dynamic CiRC (dCiRC), that describes parameters of circadian rhythms and predicts the phase of entrainment in zeitgeber cycles. dCiRC mathematically extracts the underlying information of velocity changes of the internal clock that reflects the parametric model and the phase shift trajectory that reflects the non-parametric model from phase data under entraining conditions. As a proof of concept, we measured clock parameters of 26 Neurospora crassa ecotypes in both cycling and constant conditions using dCiRC. Our data showed that the morning light shortens the period of the clock while the afternoon light lengthens it. We also found that individual ecotypes have different strategies of integrating light effects to accomplish the optimal phase of entrainment, a model feature that is consistent with our knowledge of how circadian clocks are organized and encoded. The unified model dCiRC will provide new insights into how circadian clocks function under different zeitgeber conditions. We suggest that this type of model may be useful in the advent of chronotherapies.

Effects of anisotropic interactions on the structure of animal groups.

This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the position of a limited number of close group mates. The proposed model is shown to produce clustered formations, as well as lines and V-like formations. The key factors which trigger the onset of different patterns are argued to be the relative strength of attraction and repulsion forces and, most important, the anisotropy in their application.

History and Future Perspectives on the Discipline of Quantitative Systems Pharmacology Modeling and Its Applications.

Mathematical biology and pharmacology models have a long and rich history in the fields of medicine and physiology, impacting our understanding of disease mechanisms and the development of novel therapeutics. With an increased focus on the pharmacology application of system models and the advances in data science spanning mechanistic and empirical approaches, there is a significant opportunity and promise to leverage these advancements to enhance the development and application of the systems pharmacology field. In this paper, we will review milestones in the evolution of mathematical biology and pharmacology models, highlight some of the gaps and challenges in developing and applying systems pharmacology models, and provide a vision for an integrated strategy that leverages advances in adjacent fields to overcome these challenges.

Habitat-Specific Clock Variation and Its Consequence on Reproductive Fitness.

The circadian clock controls daily activities at the cellular and organismic level, allowing an organism to anticipate incoming stresses and to use resources accordingly. The circadian clock has therefore been considered a fitness trait in multiple organisms. However, the mechanism of how circadian clock variation influences organismal reproductive fitness is still not well understood. Here we describe habitat-specific clock variation (HSCV) of asexual reproduction in Neurospora discreta, a species that is adapted to 2 different habitats, under or above tree bark. African (AF) N. discreta strains, whose habitat is above the tree bark in light-dark (LD) conditions, display a higher rhythmicity index compared with North American (NA) strains, whose habitat is under the tree bark in constant dark (DD). Although AF-type strains demonstrated an overall fitness advantage under LD and DD conditions, NA-type strains exhibit a habitat-specific fitness advantage in DD over the LD condition. In addition, we show that allelic variation of the clock-controlled gene, Ubiquinol cytochrome c oxidoreductase (NEUDI_158280), plays a role in HSCV by modulating cellular reactive oxygen species levels. Our results demonstrate a mechanism by which local adaptation involving circadian clock regulation influences reproductive fitness.

Determination of the optimal therapeutic protocols in cancer immunotherapy.

Cancer immunotherapy aims at eliciting an immune system response against the tumor. However, it is often characterized by toxic side-effects. Limiting the tumor growth and, concurrently, avoiding the toxicity of a drug, is the problem of protocol design. We formulate this question as an optimization problem and derive an algorithm for its solution. Unlike the standard optimal control approach, the algorithm simulates impulse-like drug administrations. It relies on an exact computation of the gradient of the cost function with respect to any protocol by means of the variational equations, that can be solved in parallel with the system. In comparison with previous versions of this method [F. Castiglione, B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy, Bull. Math. Biol. 68 (2006) 255-274; B. Piccoli, F. Castiglione, Optimal vaccine scheduling in cancer immunotherapy, Physica A. 370 (2) (2007) 672-680], we optimize both the timing and the dosage of each administration and introduce a penalty term to avoid clustering of subsequent injections, a requirement consistent with the clinical practice. In addition, we implement the optimization scheme to simulate the case of multi-therapies. The procedure works for any ODE system describing the pharmacokinetics and pharmacodynamics of an arbitrary number of therapeutic agents. In this work, it was tested for a well known model of the tumor-immune system interaction [D. Kirschner, J.C. Panetta, Modeling immunotherapy of tumor-immune interaction, J. Math. Biol. 37 (1998) 235-252]. Exploring three immunotherapeutic scenarios (CTL therapy, IL-2 therapy and combined therapy), we display the stability and efficacy of the optimization method, obtaining protocols that are successful compromises between various clinical requirements.

Experimental and Mathematical Analyses Relating Circadian Period and Phase of Entrainment in Neurospora crassa.

Circadian rhythms are observed in most organisms on earth and are known to play a major role in successful adaptation to the 24-h cycling environment. Circadian phenotypes are characterized by a free-running period that is observed in constant conditions and an entrained phase that is observed in cyclic conditions. Thus, the relationship between the free-running period and phase of entrainment is of interest. A popular simple rule has been that the entrained phase is the expression of the period in a cycling environment (i.e., that a short period causes an advanced phase and a long period causes a delayed phase). However, there are experimental data that are not explained by this simple relationship, and no systematic study has been done to explore all possible period-phase relationships. Here, we show the existence of stable period-phase relationships that are exceptions to this rule. First, we analyzed period-phase relationships using populations with different degrees of genome complexity. Second, we generated isogenic F1 populations by crossing 14 classical period mutants to the same female and analyzed 2 populations with a short period/delayed phase and a long period/advanced phase. Third, we generated a mathematical model to account for such variable relationships between period and phase. Our analyses support the view that the circadian period of an organism is not the only predictor of the entrained phase.

Linear-In-Flux-Expressions Methodology: Toward a Robust Mathematical Framework for Quantitative Systems Pharmacology Simulators.

Quantitative Systems Pharmacology (QSP) modeling is increasingly used as a quantitative tool for advancing mechanistic hypotheses on the mechanism of action of a drug, and its pharmacological effect in relevant disease phenotypes, to enable linking the right drug to the right patient. Application of QSP models relies on creation of virtual populations for simulating scenarios of interest. Creation of virtual populations requires 2 important steps, namely, identification of a subset of model parameters that can be associated with a phenotype of disease and development of a sampling strategy from identified distributions of these parameters. We improve on existing sampling methodologies by providing a means of representing the structural relationship across model parameters and describing propagation of variability in the model. This gives a robust, systematic method for creating a virtual population. We have developed the Linear-In-Flux-Expressions (LIFE) method to simulate variability in patient pharmacokinetics and pharmacodynamics using relationships between parameters at baseline to create a virtual population. We demonstrate the importance of this methodology on a model of cholesterol metabolism. The LIFE methodology brings us a step closer toward improved QSP simulators through enhanced capture of the observed variability in drug and disease clinical data.

Control of reaction-diffusion equations on time-evolving manifolds.

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

Mean-field sparse optimal control.

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dynamics of the probability distribution of the followers. In the classical mean-field theory, one studies the behaviour of a large number of small individuals freely interacting with each other, by simplifying the effect of all the other individuals on any given individual by a single averaged effect. In this paper, we address instead the situation where the leaders are actually influenced also by an external policy maker, and we propagate its effect for the number N of followers going to infinity. The technical derivation of the sparse mean-field optimal control is realized by the simultaneous development of the mean-field limit of the equations governing the followers dynamics together with the Γ-limit of the finite dimensional sparse optimal control problems.

Evaluation of HIV-1 and CD4+ T cell dynamic parameters in patients treated with genotypic resistance testing-guided HAART.

The extent of immune restoration in HIV-1 patients on antiretroviral therapy is an important marker of disease progression. In this work, we investigate the dynamics of immune reconstitution and address the question of whether the early response to antiretroviral treatments allows to predict the late immune restoration. We select a cohort of twelve patients on GRT-HAART who achieve virological suppression, but show variable recovery of immune competence. HIV-RNA and CD4+ T cell assessments are used for estimation of the dynamic parameters of an established mathematical model of the viral-immune system interactions. We find that failure in immune reconstitution is associated with an abnormal increase of the death rate of uninfected CD4+ T cells. In contrast, their production rate is up to three times higher than in healthy seronegative individuals. This finding is in line with the view of chronic activation as a major cause of immune depletion. According to non parametric statistics, CD4+ T cell responders and non responders do not show significantly different dynamic parameters. Such result suggests that the employed model does not allow to predict the long term immune reconstitution.

Optimal control in a model of dendritic cell transfection cancer immunotherapy.

We construct a population dynamics model of the competition among immune system cells and generic tumor cells. Then, we apply the theory of optimal control to find the optimal schedule of injection of autologous dendritic cells used as immunotherapeutic agent. The optimization method works for a general ODE system and can be applied to find the optimal schedule in a variety of medical treatments that have been described by a mathematical model.