Tuning of plasma cell lifespan by competition explains the longevity and heterogeneity of antibody persistence.

Plasma cells that emerge after infection or vaccination exhibit heterogeneous lifespans; most survive for days to months, whereas others persist for decades, providing antigen-specific long-term protection. We developed a mathematical framework to explore the dynamics of plasma cell removal and its regulation by survival factors. Analyses of antibody persistence following hepatitis A and B and HPV vaccination revealed specific patterns of longevity and heterogeneity within and between responses, implying that this process is fine-tuned near a critical "flat" state between two dynamic regimes. This critical state reflects the tuning of rates of the underlying regulatory network and is highly sensitive to variation in parameters, which amplifies lifespan differences between cells. We propose that fine-tuning is the generic outcome of competition over shared survival signals, with a competition-based mechanism providing a unifying explanation for a wide range of experimental observations, including the dynamics of plasma cell accumulation and the effects of survival factor deletion. Our theory is testable, and we provide specific predictions.

Major depressive disorder and bistability in an HPA-CNS toggle switch.

Major depressive disorder (MDD) is the most common psychiatric disorder. It has a complex and heterogeneous etiology. Most treatments take weeks to show effects and work well only for a fraction of the patients. Thus, new concepts are needed to understand MDD and its dynamics. One of the strong correlates of MDD is increased activity and dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis which produces the stress hormone cortisol. Existing mathematical models of the HPA axis describe its operation on the scale of hours, and thus are unable to explore the dynamic on the scale of weeks that characterizes many aspects of MDD. Here, we propose a mathematical model of MDD on the scale of weeks, a timescale provided by the growth of the HPA hormone glands under control of HPA hormones. We add to this the mutual inhibition of the HPA axis and the hippocampus and other regions of the central nervous system (CNS) that forms a toggle switch. The model shows bistability between euthymic and depressed states, with a slow timescale of weeks in its dynamics. It explains why prolonged but not acute stress can trigger a self-sustaining depressive episode that persists even after the stress is removed. The model explains the weeks timescale for drugs to take effect, as well as the dysregulation of the HPA axis in MDD, based on gland mass changes. This understanding of MDD dynamics may help to guide strategies for treatment.

Perspectives on adaptive dynamical systems.

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.

Damage dynamics and the role of chance in the timing of E. coli cell death.

Genetically identical cells in the same stressful condition die at different times. The origin of this stochasticity is unclear; it may arise from different initial conditions that affect the time of demise, or from a stochastic damage accumulation mechanism that erases the initial conditions and instead amplifies noise to generate different lifespans. To address this requires measuring damage dynamics in individual cells over the lifespan, but this has rarely been achieved. Here, we used a microfluidic device to measure membrane damage in 635 carbon-starved Escherichia coli cells at high temporal resolution. We find that initial conditions of damage, size or cell-cycle phase do not explain most of the lifespan variation. Instead, the data points to a stochastic mechanism in which noise is amplified by a rising production of damage that saturates its own removal. Surprisingly, the relative variation in damage drops with age: cells become more similar to each other in terms of relative damage, indicating increasing determinism with age. Thus, chance erases initial conditions and then gives way to increasingly deterministic dynamics that dominate the lifespan distribution.

Rules for body fat interventions based on an operating point mechanism.

Interventions to reduce fat are important for human health. However, they can have opposing effects such as exercise that decreases fat but increases food intake, or coherent effects such as leptin resistance which raises both. Furthermore, some interventions show an overshoot in food intake, such as recovery from a diet, whereas others do not. To explain these properties we present a graphical framework called the operating point model, based on leptin control of feeding behavior. Steady-state fat and food intake is given by the intersection of two experimental curves - steady-state fat at a given food intake and ad libitum food intake at a given fat level. Depending on which curve an intervention shifts, it has opposing or coherent effects with or without overshoot, in excellent agreement with rodent data. The model also explains the quadratic relation between leptin and fat in humans. These concepts may guide the understanding of fat regulation disorders.

Epigenetic inheritance of gene silencing is maintained by a self-tuning mechanism based on resource competition.

Biological systems can maintain memories over long timescales, with examples including memories in the brain and immune system. It is unknown how functional properties of memory systems, such as memory persistence, can be established by biological circuits. To address this question, we focus on transgenerational epigenetic inheritance in Caenorhabditis elegans. In response to a trigger, worms silence a target gene for multiple generations, resisting strong dilution due to growth and reproduction. Silencing may also be maintained indefinitely upon selection according to silencing levels. We show that these properties imply the fine-tuning of biochemical rates in which the silencing system is positioned near the transition to bistability. We demonstrate that this behavior is consistent with a generic mechanism based on competition for synthesis resources, which leads to self-organization around a critical state with broad silencing timescales. The theory makes distinct predictions and offers insights into the design principles of long-term memory systems.

Dynamics of thyroid diseases and thyroid-axis gland masses.

Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid-stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life-years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto's thyroiditis and Graves' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.

The dopamine circuit as a reward-taxis navigation system.

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs 'reward-taxis' where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

Controls for Phylogeny and Robust Analysis in Pareto Task Inference.

Understanding the tradeoffs faced by organisms is a major goal of evolutionary biology. One of the main approaches for identifying these tradeoffs is Pareto task inference (ParTI). Two recent papers claim that results obtained in ParTI studies are spurious due to phylogenetic dependence (Mikami T, Iwasaki W. 2021. The flipping t-ratio test: phylogenetically informed assessment of the Pareto theory for phenotypic evolution. Methods Ecol Evol. 12(4):696-706) or hypothetical p-hacking and population-structure concerns (Sun M, Zhang J. 2021. Rampant false detection of adaptive phenotypic optimization by ParTI-based Pareto front inference. Mol Biol Evol. 38(4):1653-1664). Here, we show that these claims are baseless. We present a new method to control for phylogenetic dependence, called SibSwap, and show that published ParTI inference is robust to phylogenetic dependence. We show how researchers avoided p-hacking by testing for the robustness of preprocessing choices. We also provide new methods to control for population structure and detail the experimental tests of ParTI in systems ranging from ammonites to cancer gene expression. The methods presented here may help to improve future ParTI studies.

Temporal fluctuations in chemotaxis gain implement a simulated-tempering strategy for efficient navigation in complex environments.

Bacterial chemotaxis is a major testing ground for systems biology, including the role of fluctuations and individual variation. Individual bacteria vary in their tumbling frequency and adaptation time. Recently, large cell-cell variation was also discovered in chemotaxis gain, which determines the sensitivity of the tumbling rate to attractant gradients. Variation in gain is puzzling, because low gain impairs chemotactic velocity. Here, we provide a functional explanation for gain variation by establishing a formal analogy between chemotaxis and algorithms for sampling probability distributions. We show that temporal fluctuations in gain implement simulated tempering, which allows sampling of attractant distributions with many local peaks. Periods of high gain allow bacteria to detect and climb gradients quickly, and periods of low gain allow them to move to new peaks. Gain fluctuations thus allow bacteria to thrive in complex environments, and more generally they may play an important functional role for organism navigation.

An opponent process for alcohol addiction based on changes in endocrine gland mass.

Consuming addictive drugs is often initially pleasurable, but escalating drug intake eventually recruits physiological anti-reward systems called opponent processes that cause tolerance and withdrawal symptoms. Opponent processes are fundamental for the addiction process, but their physiological basis is not fully characterized. Here, we propose an opponent processes mechanism centered on the endocrine stress response, the hypothalamic-pituitary-adrenal (HPA) axis. We focus on alcohol addiction, where the HPA axis is activated and secretes ß-endorphin, causing euphoria and analgesia. Using a mathematical model, we show that slow changes in the functional mass of HPA glands act as an opponent process for ß-endorphin secretion. The model explains hormone dynamics in alcohol addiction and experiments on alcohol preference in rodents. The opponent process is based on fold-change detection (FCD) where ß-endorphin responses are relative rather than absolute; FCD confers vulnerability to addiction but has adaptive roles for learning. Our model suggests gland mass changes as potential targets for intervention in addiction.

Hormone seasonality in medical records suggests circannual endocrine circuits.

Hormones control the major biological functions of stress response, growth, metabolism, and reproduction. In animals, these hormones show pronounced seasonality, with different set-points for different seasons. In humans, the seasonality of these hormones remains unclear, due to a lack of datasets large enough to discern common patterns and cover all hormones. Here, we analyze an Israeli health record on 46 million person-years, including millions of hormone blood tests. We find clear seasonal patterns: The effector hormones peak in winter-spring, whereas most of their upstream regulating pituitary hormones peak only months later, in summer. This delay of months is unexpected because known delays in the hormone circuits last hours. We explain the precise delays and amplitudes by proposing and testing a mechanism for the circannual clock: The gland masses grow with a timescale of months due to trophic effects of the hormones, generating a feedback circuit with a natural frequency of about a year that can entrain to the seasons. Thus, humans may show coordinated seasonal set-points with a winter-spring peak in the growth, stress, metabolism, and reproduction axes.

Senescent cells and the incidence of age-related diseases.

Age-related diseases such as cancer, cardiovascular disease, kidney failure, and osteoarthritis have universal features: Their incidence rises exponentially with age with a slope of 6-8% per year and decreases at very old ages. There is no conceptual model which explains these features in so many diverse diseases in terms of a single shared biological factor. Here, we develop such a model, and test it using a nationwide medical record dataset on the incidence of nearly 1000 diseases over 50 million life-years, which we provide as a resource. The model explains incidence using the accumulation of senescent cells, damaged cells that cause inflammation and reduce regeneration, whose level rise stochastically with age. The exponential rise and late drop in incidence are captured by two parameters for each disease: the susceptible fraction of the population and the threshold concentration of senescent cells that causes disease onset. We propose a physiological mechanism for the threshold concentration for several disease classes, including an etiology for diseases of unknown origin such as idiopathic pulmonary fibrosis and osteoarthritis. The model can be used to design optimal treatments that remove senescent cells, suggeting that treatment starting at old age can sharply reduce the incidence of all age-related diseases, and thus increase the healthspan.

Senescent cell accumulation mechanisms inferred from parabiosis.

Senescent cells are growth-arrested cells that cause inflammation and play a causal role in aging. They accumulate with age, and preventing this accumulation delays age-related diseases. However, the mechanism for senescent cell accumulation is not fully understood. Accumulation can result from increasing production or decreasing removal of senescent cells with age, or both. To distinguish between these possibilities, we analyze data from parabiosis, the surgical conjoining of two mice so that they share circulation. Parabiosis between a young and old mouse, called heterochronic parabiosis, reduces senescent cell levels in the old mouse, while raising senescent cell levels in the young mouse. We show that parabiosis data can reject mechanisms for senescent cell accumulation in which only production rises with age or only removal decreases with age; both must vary with age. Since removal drops with age, senescent cell half-life rises with age. This matches a recent model for senescent cell accumulation developed from independent data on senescent cell dynamics, called the SR model, in which production rises linearly with age and senescent cells inhibit their own removal. The SR model further explains the timescales and mechanism of rejuvenation in parabiosis, based on transfer of spare removal capacity from the young mouse to the old. The present quantitative understanding can help design optimal treatments that remove senescent cells, by matching the time between treatments to the time it takes senescent cells to re-accumulate.

A new model for the HPA axis explains dysregulation of stress hormones on the timescale of weeks.

Stress activates a complex network of hormones known as the hypothalamic-pituitary-adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Senescent cell turnover slows with age providing an explanation for the Gompertz law.

A causal factor in mammalian aging is the accumulation of senescent cells (SnCs). SnCs cause chronic inflammation, and removing SnCs decelerates aging in mice. Despite their importance, turnover rates of SnCs are unknown, and their connection to aging dynamics is unclear. Here we use longitudinal SnC measurements and induction experiments to show that SnCs turn over rapidly in young mice, with a half-life of days, but slow their own removal rate to a half-life of weeks in old mice. This leads to a critical-slowing-down that generates persistent SnC fluctuations. We further demonstrate that a mathematical model, in which death occurs when fluctuating SnCs cross a threshold, quantitatively recapitulates the Gompertz law of mortality in mice and humans. The model can go beyond SnCs to explain the effects of lifespan-modulating interventions in Drosophila and C. elegans, including scaling of survival-curves and rapid effects of dietary shifts on mortality.

Dynamic Proteomics of Herpes Simplex Virus Infection.

The cellular response to viral infection is usually studied at the level of cell populations. Currently, it remains an open question whether and to what extent cell-to-cell variability impacts the course of infection. Here we address this by dynamic proteomics-imaging and tracking 400 yellow fluorescent protein (YFP)-tagged host proteins in individual cells infected by herpes simplex virus 1. By quantifying time-lapse fluorescence imaging, we analyze how cell-to-cell variability impacts gene expression from the viral genome. We identify two proteins, RFX7 and geminin, whose levels at the time of infection correlate with successful initiation of gene expression. These proteins are cell cycle markers, and we find that the position in the cell cycle at the time of infection (along with the cell motility and local cell density) can reasonably predict in which individual cells gene expression from the viral genome will commence. We find that the onset of cell division dramatically impacts the progress of infection, with 70% of dividing cells showing no additional gene expression after mitosis. Last, we identify four host proteins that are specifically modulated in infected cells, of which only one has been previously recognized. SUMO2 and RPAP3 levels are rapidly reduced, while SLTM and YTHDC1 are redistributed to form nuclear foci. These modulations are dependent on the expression of ICP0, as shown by infection with two mutant viruses that lack ICP0. Taken together, our results provide experimental validation for the long-held notion that the success of infection is dependent on the state of the host cell at the time of infection.IMPORTANCE High-throughput assays have revolutionized many fields in biology, both by allowing a more global understanding of biological processes and by deciphering rare events in subpopulations. Here we use such an assay, dynamic proteomics, to study viral infection at the single-cell level. We follow tens of thousands of individual cells infected by herpes simplex virus using fluorescence live imaging. Our results link the state of a cell at the time of virus infection with its probability to successfully initiate gene expression from the viral genome. Further, we identified three cellular proteins that were previously unknown to respond to viral infection. We conclude that dynamic proteomics provides a powerful tool to study single-cell differences during viral infection.

Biphasic response as a mechanism against mutant takeover in tissue homeostasis circuits.

Tissues use feedback circuits in which cells send signals to each other to control their growth and survival. We show that such feedback circuits are inherently unstable to mutants that misread the signal level: Mutants have a growth advantage to take over the tissue, and cannot be eliminated by known cell-intrinsic mechanisms. To resolve this, we propose that tissues have biphasic responses in and the signal is toxic at both high and low levels, such as glucotoxicity of beta cells, excitotoxicity in neurons, and toxicity of growth factors to T cells. This gives most of these mutants a frequency-dependent selective disadvantage, which leads to their elimination. However, the biphasic mechanisms create a new unstable fixed point in the feedback circuit beyond which runaway processes can occur, leading to risk of diseases such as diabetes and neurodegenerative disease. Hence, glucotoxicity, which is a dangerous cause of diabetes, may have a protective anti-mutant effect. Biphasic responses in tissues may provide an evolutionary stable strategy that avoids invasion by commonly occurring mutants, but at the same time cause vulnerability to disease.

Dynamical compensation in physiological circuits.

Biological systems can maintain constant steady-state output despite variation in biochemical parameters, a property known as exact adaptation. Exact adaptation is achieved using integral feedback, an engineering strategy that ensures that the output of a system robustly tracks its desired value. However, it is unclear how physiological circuits also keep their output dynamics precise-including the amplitude and response time to a changing input. Such robustness is crucial for endocrine and neuronal homeostatic circuits because they need to provide a precise dynamic response in the face of wide variation in the physiological parameters of their target tissues; how such circuits compensate their dynamics for unavoidable natural fluctuations in parameters is unknown. Here, we present a design principle that provides the desired robustness, which we call dynamical compensation (DC). We present a class of circuits that show DC by means of a nonlinear feedback loop in which the regulated variable controls the functional mass of the controlling endocrine or neuronal tissue. This mechanism applies to the control of blood glucose by insulin and explains several experimental observations on insulin resistance. We provide evidence that this mechanism may also explain compensation and organ size control in other physiological circuits.