Macrophage phenotype transitions in a stochastic gene-regulatory network model.

Polarization is the process by which a macrophage cell commits to a phenotype based on external signal stimulation. To know how this process is affected by random fluctuations and events within a cell is of utmost importance to better understand the underlying dynamics and predict possible phenotype transitions. For this purpose, we develop a stochastic modeling approach for the macrophage polarization process. We classify phenotype states using the Robust Perron Cluster Analysis and quantify transition pathways and probabilities by applying Transition Path Theory. Depending on the model parameters, we identify four bistable and one tristable phenotype configuration. We find that bistable transitions are fast but their states less robust. In contrast, phenotype transitions in the tristable situation have a comparatively long time duration, which reflects the robustness of the states. The results indicate parallels in the overall transition behavior of macrophage cells with other heterogeneous and plastic cell types, such as cancer cells. Our approach allows for a probabilistic interpretation of macrophage phenotype transitions and biological inference on phenotype robustness. In general, the methodology can easily be adapted to other systems where random state switches are known to occur.

Sexual attraction to visual sexual stimuli in association with steroid hormones across menstrual cycles and fertility treatment.

BACKGROUND: Steroid hormones (i.e., estradiol, progesterone, and testosterone) are considered to play a crucial role in the regulation of women's sexual desire and sexual attraction to sexual stimuli throughout the menstrual cycle. However, the literature is inconsistent, and methodologically sound studies on the relationship between steroid hormones and women's sexual attraction are rare. METHODS: This prospective longitudinal multisite study examined estradiol, progesterone, and testosterone serum levels in association with sexual attraction to visual sexual stimuli in naturally cycling women and in women undergoing fertility treatment (in vitro fertilization, IVF). Across ovarian stimulation of fertility treatment, estradiol reaches supraphysiological levels, while other ovarian hormones remain nearly stable. Ovarian stimulation hence offers a unique quasi-experimental model to study concentration-dependent effects of estradiol. Hormonal parameters and sexual attraction to visual sexual stimuli assessed with computerized visual analogue scales were collected at four time points per cycle, i.e., during the menstrual, preovulatory, mid-luteal, and premenstrual phases, across two consecutive menstrual cycles (n = 88 and n = 68 for the first and second cycle, respectively). Women undergoing fertility treatment (n = 44) were assessed twice, at the beginning and at the end of ovarian stimulation. Sexually explicit photographs served as visual sexual stimuli. RESULTS: In naturally cycling women, sexual attraction to visual sexual stimuli did not vary consistently across two consecutive menstrual cycles. While in the first menstrual cycle sexual attraction to male bodies, couples kissing, and at intercourse varied significantly with a peak in the preovulatory phase, (all p ≤ 0.001), there was no significant variability across the second cycle. Univariable and multivariable models evaluating repeated cross-sectional relationships and intraindividual change scores revealed no consistent associations between estradiol, progesterone, and testosterone and sexual attraction to visual sexual stimuli throughout both menstrual cycles. Also, no significant association with any hormone was found when the data from both menstrual cycles were combined. In women undergoing ovarian stimulation of IVF, sexual attraction to visual sexual stimuli did not vary over time and was not associated with estradiol levels despite intraindividual changes in estradiol levels from 122.0 to 11,746.0 pmol/l with a mean (SD) of 3553.9 (2472.4) pmol/l. CONCLUSIONS: These results imply that neither physiological levels of estradiol, progesterone, and testosterone in naturally cycling women nor supraphysiological levels of estradiol due to ovarian stimulation exert any relevant effect on women's sexual attraction to visual sexual stimuli.

The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations.

The menstrual cycle is characterized by various hormonal alterations and associations with mental and physical conditions have been postulated. Among endocrine factors, the androgen system has been a target of major interest in males and to a lesser extent in females and may influence emotion, cognition, behavior and somatic factors. Only few studies investigated alterations of these parameters throughout the menstrual cycle and there is a lack of studies exploring a link towards epigenetic and genetic regulation. This multisite longitudinal study examines behavioral parameters including affectivity, stress perception and various diary parameters of mental and physical well-being in conjunction with testosterone and LH plasma levels in 87 menstruating women. Additionally, Cysteine-Adenenine-Guanin (CAG) repeat length and methylation of the androgen receptor gene collected at four time points across two cycles comprising the menstrual, pre-ovulatory, mid-luteal and premenstrual phase were assesed. There was a significant increase of LH and testosterone plasma levels during the pre-ovulatory phase as well as a decrease of methylation of the androgen receptor at mid-luteal phase. Subjective ratings of physical condition and sexual interest peaked during the pre-ovulatory phase and the former correlated negatively with the androgen receptor gene methylation level. This longitudinal study shows alterations of the androgen system including epigenetic measurements throughout the menstrual cycle. While a link between peripheral testosterone and sexual activity and between increased physical condition and an upregulation of testosterone receptor protein expression can be assumed, the majority of parameters remained unchanged. These initial findings need validation by subsequent studies.

Model-based exploration of hypokalemia in dairy cows.

Hypokalemia in dairy cows, which is characterized by too low serum potassium levels, is a severe mineral disorder that can be life threatening. In this paper, we explore different originating conditions of hypokalemia-reduced potassium intake, increased excretion, acid-base disturbances, and increased insulin-by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows. The simulations confirm observations described in literature. They illustrate, for example, that changes in dietary intake or excretion highly effect intracellular potassium levels, whereas extracellular levels vary only slightly. Simulations also show that the higher the potassium content in the diet, the more potassium is excreted with urine. Application of the mathematical model assists in experimental planning and therefore contributes to the 3R strategy: reduction, refinement and replacement of animal experiments.

Food preferences throughout the menstrual cycle - A computer-assisted neuro-endocrino-psychological investigation.

BACKGROUND: As eating behavior changes in relation to the menstrual cycle and weight changes with menopausal transition, ovarian hormones appear to be involved in regulating eating behavior. However, observations are contradictory and are difficult to compare, due to methodological problems related to nutritional epidemiology. To better understand the relationship between ovarian steroid hormones and eating behavior, our study evaluates women's responses to visual food cues at different points in the menstrual cycle with their specific serum estrogen/progesterone levels and women's responses in the case of strong estrogen changes in the context of fertility treatments. METHODS: We collected data from 129 women, 44 of whom received in vitro fertilization (IVF) at the Department of Reproductive Endocrinology, University Hospital Zurich. A total of 85 women with natural cycles were recruited at the University Hospital Zurich (n = 37) and at the Hannover Medical School (n = 48). Our observational study used 4 different measurement time points across the natural cycle and 2 measurement time points in women with supraphysiological estradiol levels during fertility treatments. Using a second cycle, we then tested our results for replication. At these predefined time points, women were shown pictures of 11 categories of food, with 4 items for each category and blood samples for measurement of hormone levels were taken. Food preferences registered at the time of the investigation were indicated on a visual analogue scale (0-100). RESULTS: We did not find any statistically significant association between women's serum hormone levels and the rating of visually presented food, either during the menstrual cycle or during fertility treatments after controlling for multiple testing (all p > 0.005). Ratings for fruits, vegetables, and carbohydrates showed a significant linear decline throughout the first menstrual cycle (p < 0.01), which did not replicate in the second cycle (p > 0.05). In contrast, the ratings for sweets showed a significant linear decline in both cycles (both p < 0.01), with a mean rating of 54.2 and 48.8 in the menstrual phase of the first and second cycle, respectively, to a mean rating of 47.7 and 43.4 in the premenstrual phase of the first and second cycle, respectively. During fertility treatments, no food rating showed a significant change (all p > 0.05). Mood such as negative and positive affects did not influence ratings for visual food cues neither throughout the menstrual cycles nor during fertility treatment. CONCLUSIONS: Serum levels of estradiol and progesterone do not correlate with food ratings in women, even when estradiol levels are above the physiological level of a natural menstrual cycle. Since, except for sweets, significant changes in food ratings in a first cycle did not replicate in a second menstrual cycle, significant findings from the literature based on animal or human studies focusing on a single-cycle have to be interpreted with caution.

Hormonal regulation of ovarian follicle growth in humans: Model-based exploration of cycle variability and parameter sensitivities.

We present a modelling and simulation framework for the dynamics of ovarian follicles and key hormones along the hypothalamic-pituitary-gonadal axis throughout consecutive human menstrual cycles. All simulation results (hormone concentrations and ovarian follicle sizes) are in biological units and can easily be compared to clinical data. The model takes into account variability in follicles' response to stimulating hormones, which introduces variability between cycles. The growth of ovarian follicles in waves is an emergent property in our model simulations and further supports the hypothesis that follicular waves are also present in humans. We use Approximate Bayesian Computation and cluster analysis to construct a population of virtual subjects and to study parameter distributions and sensitivities. The model can be used to compare and optimize treatment protocols for ovarian hyperstimulation, thus potentially forming the integral part of a clinical decision support system in reproductive endocrinology.

Modelling Oscillatory Patterns in the Bovine Estrous Cycle with Boolean Delay Equations.

Boolean delay equations (BDEs), with their relatively simple and intuitive mode of modelling, have been used in many research areas including, for example, climate dynamics and earthquake propagation. Their application to biological systems has been scarce and limited to the molecular level. Here, we derive and present two BDE models. One is directly derived from a previously published ordinary differential equation (ODE) model for the bovine estrous cycle, whereas the second model includes a modification of a particular biological mechanism. We not only compare the simulation results from the BDE models with the trajectories of the ODE model, but also validate the BDE models with two additional numerical experiments. One experiment induces a switch in the oscillatory pattern upon changes in the model parameters, and the other simulates the administration of a hormone that is known to shift the estrous cycle in time. The models presented here are the first BDE models for hormonal oscillators, and the first BDE models for drug administration. Even though automatic parameter estimation still remains challenging, our results support the role of BDEs as a framework for the systematic modelling of complex biological oscillators.

Mathematical Modeling and Simulation Provides Evidence for New Strategies of Ovarian Stimulation.

New approaches to ovarian stimulation protocols, such as luteal start, random start or double stimulation, allow for flexibility in ovarian stimulation at different phases of the menstrual cycle. It has been proposed that the success of these methods is based on the continuous growth of multiple cohorts ("waves") of follicles throughout the menstrual cycle which leads to the availability of ovarian follicles for ovarian controlled stimulation at several time points. Though several preliminary studies have been published, their scientific evidence has not been considered as being strong enough to integrate these results into routine clinical practice. This work aims at adding further scientific evidence about the efficiency of variable-start protocols and underpinning the theory of follicular waves by using mathematical modeling and numerical simulations. For this purpose, we have modified and coupled two previously published models, one describing the time course of hormones and one describing competitive follicular growth in a normal menstrual cycle. The coupled model is used to test ovarian stimulation protocols in silico. Simulation results show the occurrence of follicles in a wave-like manner during a normal menstrual cycle and qualitatively predict the outcome of ovarian stimulation initiated at different time points of the menstrual cycle.

Cognitive function in association with high estradiol levels resulting from fertility treatment.

The putative association between hormones and cognitive performance is controversial. While there is evidence that estradiol plays a neuroprotective role, hormone treatment has not been shown to improve cognitive performance. Current research is flawed by the evaluation of combined hormonal effects throughout the menstrual cycle or in the menopausal transition. The stimulation phase of a fertility treatment offers a unique model to study the effect of estradiol on cognitive function. This quasi-experimental observational study is based on data from 44 women receiving IVF in Zurich, Switzerland. We assessed visuospatial working memory, attention, cognitive bias, and hormone levels at the beginning and at the end of the stimulation phase of ovarian superstimulation as part of a fertility treatment. In addition to inter-individual differences, we examined intra-individual change over time (within-subject effects). The substantial increases in estradiol levels resulting from fertility treatment did not relate to any considerable change in cognitive functioning. As the tests applied represent a broad variety of cognitive functions on different levels of complexity and with various brain regions involved, we can conclude that estradiol does not show a significant short-term effect on cognitive function.

Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization.

In this paper, we present and analyze a mathematical model for polarization of a single macrophage which, despite its simplicity, exhibits complex dynamics in terms of multistability. In particular, we demonstrate that an asymmetry in the regulatory mechanisms and parameter values is important for observing multiple phenotypes. Bifurcation and sensitivity analyses show that external signaling cues are necessary for macrophage commitment and emergence to a phenotype, but that the intrinsic macrophage pathways are equally important. Based on our numerical results, we formulate hypotheses that could be further investigated by laboratory experiments to deepen our understanding of macrophage polarization.

Macroscale mesenchymal condensation to study cytokine-driven cellular and matrix-related changes during cartilage degradation.

Understanding the pathophysiological processes of cartilage degradation requires adequate model systems to develop therapeutic strategies towards osteoarthritis (OA). Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific disease aspects. This study aimed to combine in vitro and in silico modeling based on a tissue-engineering approach using mesenchymal condensation to mimic cytokine-induced cellular and matrix-related changes during cartilage degradation. Thus, scaffold-free cartilage-like constructs (SFCCs) were produced based on self-organization of mesenchymal stromal cells (mesenchymal condensation) and (i) characterized regarding their cellular and matrix composition or secondly (ii) treated with interleukin-1ß (IL-1ß) and tumor necrosis factor α (TNFα) for 3 weeks to simulate OA-related matrix degradation. In addition, an existing mathematical model based on partial differential equations was optimized and transferred to the underlying settings to simulate the distribution of IL-1ß, type II collagen degradation and cell number reduction. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and effects of new therapeutics.

Model-based exploration of the impact of glucose metabolism on the estrous cycle dynamics in dairy cows.

BACKGROUND: Nutrition plays a crucial role in regulating reproductive hormones and follicular development in cattle. This is visible particularly during the time of negative energy balance at the onset of milk production after calving. Here, elongated periods of anovulation have been observed, resulting from alterations in luteinizing hormone concentrations, likely caused by lower glucose and insulin concentrations in the blood. The mechanisms that result in a reduced fertility are not completely understood, although a close relationship to the glucose-insulin metabolism is widely supported. RESULTS: Following this idea, we developed a mathematical model of the hormonal network combining reproductive hormones and hormones that are coupled to the glucose compartments within the body of the cow. The model is built on ordinary differential equations and relies on previously introduced models on the bovine estrous cycle and the glucose-insulin dynamics. Necessary modifications and coupling mechanisms are thoroughly discussed. Depending on the composition and the amount of feed, in particular the glucose content in the dry matter, the model quantifies reproductive hormones and follicular development over time. Simulation results for different nutritional regimes in lactating and non-lactating dairy cows are examined and compared with experimental studies. The simulations describe realistically the effects of nutritional glucose supply on the ovulatory cycle of dairy cattle. CONCLUSIONS: The mathematical model enables the user to explore the relationship between nutrition and reproduction by running simulations and performing parameter studies. Regarding its applicability, this work is an early attempt towards developing in silico feeding strategies and may eventually help to refine and reduce animal experiments. REVIEWERS: This article was reviewed by John McNamara and Tin Pang (nominated by Martin Lercher).

Associations Between Natural Physiological and Supraphysiological Estradiol Levels and Stress Perception.

Stress is a risk factor for impaired general, mental, and reproductive health. The role of physiological and supraphysiological estradiol concentrations in stress perception and stress processing is less well understood. We, therefore, conducted a prospective observational study to investigate the association between estradiol, stress perception, and stress-related cognitive performance within serial measurements either during the natural menstrual cycle or during fertility treatment, where estradiol levels are strongly above the physiological level of a natural cycle, and consequently, represent a good model to study dose-dependent effects of estradiol. Data from 44 women receiving in vitro fertilization (IVF) at the Department of Reproductive Endocrinology in Zurich, Switzerland was compared to data from 88 women with measurements during their natural menstrual cycle. The German version of the Perceived Stress Questionnaire (PSQ) and the Cognitive Bias Test (CBT), in which cognitive performance is tested under time stress were used to evaluate subjective and functional aspects of stress. Estradiol levels were investigated at four different time points during the menstrual cycle and at two different time points during a fertility treatment. Cycle phases were associated with PSQ worry and cognitive bias in normally cycling women, but different phases of fertility treatment were not associated with subjectively perceived stress and stress-related cognitive bias. PSQ lack of joy and PSQ demands related to CBT in women receiving fertility treatment but not in women with a normal menstrual cycle. Only strong changes of the estradiol level during fertility treatment were weakly associated with CBT, but not with subjectively experienced stress. Our research emphasizes the multidimensional character of stress and the necessity to adjust stress research to the complex nature of stress perception and processing. Infertility is associated with an increased psychological burden in patients. However, not all phases of the process to overcome infertility do significantly increase patient stress levels. Also, research on the psychological burden of infertility should consider that stress may vary during the different phases of fertility treatment. Clinical trial registration: ClinicalTrials.gov # NCT02098668.

Follicular competition in cows: the selection of dominant follicles as a synergistic effect.

The reproductive cycle of mono-ovulatory species such as cows or humans is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the [Formula: see text]-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed.

Generalized Markov State Modeling Method for Nonequilibrium Biomolecular Dynamics: Exemplified on Amyloid ß Conformational Dynamics Driven by an Oscillating Electric Field.

Markov state models (MSMs) have received an unabated increase in popularity in recent years, as they are very well suited for the identification and analysis of metastable states and related kinetics. However, the state-of-the-art Markov state modeling methods and tools enforce the fulfillment of a detailed balance condition, restricting their applicability to equilibrium MSMs. To date, they are unsuitable to deal with general dominant data structures including cyclic processes, which are essentially associated with nonequilibrium systems. To overcome this limitation, we developed a generalization of the common robust Perron Cluster Cluster Analysis (PCCA+) method, termed generalized PCCA (G-PCCA). This method handles equilibrium and nonequilibrium simulation data, utilizing Schur vectors instead of eigenvectors. G-PCCA is not limited to the detection of metastable states but enables the identification of dominant structures in a general sense, unraveling cyclic processes. This is exemplified by application of G-PCCA on nonequilibrium molecular dynamics data of the Amyloid ß (1-40) peptide, periodically driven by an oscillating electric field.

Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH.

A series of precision glycomacromolecules is prepared following previously established solid phase synthesis allowing for controlled variations of interligand spacing and the overall number of carbohydrate ligands. In addition, now also different linkers are installed between the carbohydrate ligand and the macromolecular scaffold. The lectin binding behavior of these glycomacromolecules is then evaluated in isothermal titration calorimetry (ITC) and kinITC experiments using the lectin Concanavalin A (Con A) in its dimeric and tetrameric form. The results indicate that both sterical and statistical effects impact lectin binding of precision glycomacromolecules. Moreover, ITC results show that highest affinity toward Con A can be achieved with an ethyl phenyl linker, which parallels earlier findings with the bacterial lectin FimH. In this way, a first set of glycomacromolecule structures is selected for testing in a bacterial adhesion-inhibition study. Here, the findings point to a one-sugar binding mode mainly affected by sterical restraints of the nonbinding parts of the respective glycomacromolecule.

Negative affect is unrelated to fluctuations in hormone levels across the menstrual cycle: Evidence from a multisite observational study across two successive cycles.

BACKGROUND: Female sex hormones may play a crucial role in the occurrence of cycle-related mood disorders. However, the literature is inconsistent and methodologically stringent observational studies on the relationship between sex hormones and negative affect are lacking. METHODS: In this longitudinal multisite study from Hannover, Germany, and Zurich, Switzerland, we examined oestrogen, progesterone, luteinizing hormone (LH), follicle-stimulating hormone (FSH), and testosterone serum levels in association with negative affect as measured with the Positive and Negative Affect Schedule (PANAS). Negative affect and hormone assays were collected at four consecutive time points comprising menstrual, pre-ovulatory, mid-luteal and premenstrual phase across two cycles (n=87 and n=67 for the first and second cycles). The Beck Depression Inventory (BDI) was assessed once prior to the first cycle and included as a secondary measure. RESULTS: Mean negative affect scores did not significantly fluctuate across both cycles and there was in particular no symptom increase premenstrually. No sex hormone consistently related to repeated measures of negative affect across two consecutive cycles. The BDI sum-score assessed at baseline was not related to hormone levels across the first cycle. CONCLUSIONS: This is the first multisite longitudinal study on the association between negative affect and sex hormone levels encompassing two consecutive menstrual cycles. Negative affect did not fluctuate across the cycle and there was no direct and uniform association between sex hormones and self-reported negative affect. These findings suggest that moderators such as personality traits and epigenetics should be considered in future research.

Lack of Associations between Female Hormone Levels and Visuospatial Working Memory, Divided Attention and Cognitive Bias across Two Consecutive Menstrual Cycles.

Background: Interpretation of observational studies on associations between prefrontal cognitive functioning and hormone levels across the female menstrual cycle is complicated due to small sample sizes and poor replicability. Methods: This observational multisite study comprised data of n = 88 menstruating women from Hannover, Germany, and Zurich, Switzerland, assessed during a first cycle and n = 68 re-assessed during a second cycle to rule out practice effects and false-positive chance findings. We assessed visuospatial working memory, attention, cognitive bias and hormone levels at four consecutive time-points across both cycles. In addition to inter-individual differences we examined intra-individual change over time (i.e., within-subject effects). Results: Estrogen, progesterone and testosterone did not relate to inter-individual differences in cognitive functioning. There was a significant negative association between intra-individual change in progesterone and change in working memory from pre-ovulatory to mid-luteal phase during the first cycle, but that association did not replicate in the second cycle. Intra-individual change in testosterone related negatively to change in cognitive bias from menstrual to pre-ovulatory as well as from pre-ovulatory to mid-luteal phase in the first cycle, but these associations did not replicate in the second cycle. Conclusions: There is no consistent association between women's hormone levels, in particular estrogen and progesterone, and attention, working memory and cognitive bias. That is, anecdotal findings observed during the first cycle did not replicate in the second cycle, suggesting that these are false-positives attributable to random variation and systematic biases such as practice effects. Due to methodological limitations, positive findings in the published literature must be interpreted with reservation.

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation.

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.