Endocrine gland size is proportional to its target tissue size.

Endocrine glands secrete hormones into the circulation to target distant tissues and regulate their functions. The qualitative relationship between hormone-secreting organs and their target tissues is well established, but a quantitative approach is currently limited. Quantification is important, as it could allow us to study the endocrine system using engineering concepts of optimality and tradeoffs. In this study, we collected literature data on 24 human hormones secreted from dedicated endocrine cells. We find that the number of endocrine cells secreting a hormone is proportional to the number of its target cells. A single endocrine cell serves approximately 2,000 target cells, a relationship that spans 6 orders of magnitude of cell numbers. This suggests an economic principle of cells working near their maximal capacity, and glands that are no bigger than they need to be.

Longitudinal hair cortisol in bipolar disorder and a mechanism based on HPA dynamics.

Bipolar disorder (BD) is marked by fluctuating mood states over months to years, often with elevated cortisol levels. Elevated cortisol can also trigger mood episodes. Here, we combine longitudinal hair cortisol and mood measurements with mathematical modeling to provide a potential mechanistic link between cortisol and mood timescales in BD. Using 12 cm hair samples, representing a year of growth, we found enhanced year-scale cortisol fluctuations whose amplitude averaged 4-fold higher in BD (n = 26) participants than controls (n = 59). The proximal 2 cm of hair correlated with recent mood scores. Depression (n = 266) and mania (n = 273) scores from a longitudinal study of BD showed similar frequency spectra. These results suggest a mechanism for BD in which high emotional reactivity excites the slow timescales in the hypothalamic-pituitary-adrenal (HPA) axis to generate elevated months-scale cortisol fluctuations, triggering cortisol-induced mood episodes.

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.

Excitable dynamics of flares and relapses in autoimmune diseases.

Many autoimmune disorders exhibit flares in which symptoms erupt and then decline, as exemplified by multiple sclerosis (MS) in its relapsing-remitting form. Existing mathematical models of autoimmune flares often assume regular oscillations, failing to capture the stochastic and non-periodic nature of flare-ups. We suggest that autoimmune flares are driven by excitable dynamics triggered by stochastic events auch as stress, infection and other factors. Our minimal model, involving autoreactive and regulatory T-cells, demonstrates this concept. Autoimmune response initiates antigen-induced expansion through positive feedback, while regulatory cells counter the autoreactive cells through negative feedback. The model explains the decrease in MS relapses during pregnancy and the subsequent surge postpartum, based on lymphocyte dynamics. Additionally, it identifies potential therapeutic targets, predicting significant reduction in relapse rate from mild adjustments of regulatory T cell activity or production. These findings indicate that excitable dynamics may underlie flare-ups across various autoimmune disorders, potentially informing treatment strategies.

The tumor microenvironment shows a hierarchy of cell-cell interactions dominated by fibroblasts.

The tumor microenvironment (TME) is comprised of non-malignant cells that interact with each other and with cancer cells, critically impacting cancer biology. The TME is complex, and understanding it requires simplifying approaches. Here we provide an experimental-mathematical approach to decompose the TME into small circuits of interacting cell types. We find, using female breast cancer single-cell-RNA-sequencing data, a hierarchical network of interactions, with cancer-associated fibroblasts (CAFs) at the top secreting factors primarily to tumor-associated macrophages (TAMs). This network is composed of repeating circuit motifs. We isolate the strongest two-cell circuit motif by culturing fibroblasts and macrophages in-vitro, and analyze their dynamics and transcriptomes. This isolated circuit recapitulates the hierarchy of in-vivo interactions, and enables testing the effect of ligand-receptor interactions on cell dynamics and function, as we demonstrate by identifying a mediator of CAF-TAM interactions - RARRES2, and its receptor CMKLR1. Thus, the complexity of the TME may be simplified by identifying small circuits, facilitating the development of strategies to modulate the TME.

Autoimmune thyroid diseases as a cost of physiological autoimmune surveillance.

Graves' disease (GD) and Hashimoto's thyroiditis (HT) are common autoimmune diseases of the thyroid gland, causing hyperthyroidism and hypothyroidism, respectively. Despite their opposing clinical manifestation, they have several enigmatic links. Here, we propose that GD and HT have the same fundamental origin: both diseases are the cost of a beneficial physiological process called autoimmune surveillance of hypersecreting mutants. Autoreactive T cells selectively eliminate mutant cells that hypersecrete the hormones and threaten to become toxic nodules. These T cells can trigger a humoral response in susceptible individuals, leading to the production of antibodies against thyroid antigens. This shared origin can explain similarities in incidence and risk factors between HT and GD, despite their opposite clinical phenotypes.

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.

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.

Timescales of Human Hair Cortisol Dynamics.

Cortisol is a major human stress hormone, secreted within minutes of acute stress. Cortisol also has slower patterns of variation: a strong circadian rhythm and a seasonal rhythm. However, longitudinal cortisol dynamics in healthy individuals over timescales of months has rarely been studied. Here, we measured longitudinal cortisol in 55 healthy participants using 12 cm of hair, which provides a retrospective measurement over one year. Individuals showed (non-seasonal) fluctuations averaging about 22% around their baseline. Fourier analysis reveals dominant slow frequencies with periods of months to a year. These frequencies can be explained by a mathematical model of the hormonal cascade that controls cortisol, the HPA axis, when including the slow timescales of tissue turnover of the glands. Measuring these dynamics is important for understanding disorders in which cortisol secretion is impaired over months, such as mood disorders, and to test models of cortisol feedback control.

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.