*Front Endocrinol (Lausanne) ; 12: 613048, 2021.*

##### RESUMO

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.

*Horm Behav ; 130: 104951, 2021 Apr.*

##### RESUMO

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.

*J Theor Biol ; 509: 110511, 2021 01 21.*

##### RESUMO

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.

*Biofabrication ; 12(4): 045016, 2020 08 10.*

##### RESUMO

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.

*Biol Direct ; 15(1): 2, 2020 01 15.*

##### RESUMO

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).

##### Assuntos

Fenômenos Fisiológicos da Nutrição Animal , Bovinos/fisiologia , Ciclo Estral , Glucose/metabolismo , Animais , Indústria de Laticínios , Metabolismo Energético , Feminino , Modelos Biológicos*Front Psychol ; 10: 1296, 2019.*

##### RESUMO

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.

*J Math Biol ; 78(3): 579-606, 2019 02.*

##### RESUMO

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.

##### Assuntos

Bovinos/fisiologia , Modelos Biológicos , Folículo Ovariano/fisiologia , Animais , Feminino , Hormônio Foliculoestimulante/fisiologia , Humanos , Cinética , Conceitos Matemáticos , Ovulação/fisiologia*J Chem Theory Comput ; 14(7): 3579-3594, 2018 Jul 10.*

##### RESUMO

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.

##### Assuntos

Peptídeos beta-Amiloides/química , Fragmentos de Peptídeos/química , Algoritmos , Análise por Conglomerados , Eletricidade , Cinética , Cadeias de Markov , Simulação de Dinâmica Molecular*Macromol Biosci ; 17(12)2017 12.*

##### RESUMO

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.

##### Assuntos

Adesinas de Escherichia coli/metabolismo , Concanavalina A/metabolismo , Proteínas de Fímbrias/metabolismo , Glicoconjugados/química , Glicoconjugados/metabolismo , Aderência Bacteriana/efeitos dos fármacos , Calorimetria/métodos , Concanavalina A/química , Escherichia coli/efeitos dos fármacos , Glicoconjugados/farmacologia , Concentração de Íons de Hidrogênio , Cinética , Lectinas/metabolismo , Manose/química , Técnicas de Síntese em Fase Sólida , Relação Estrutura-Atividade , Termodinâmica*J Psychosom Res ; 99: 21-27, 2017 08.*

##### RESUMO

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.

##### Assuntos

Estradiol/metabolismo , Hormônio Foliculoestimulante/metabolismo , Hormônio Luteinizante/metabolismo , Ciclo Menstrual/fisiologia , Progesterona/metabolismo , Adolescente , Adulto , Feminino , Humanos , Estudos Longitudinais , Ciclo Menstrual/psicologia , Adulto Jovem*Front Behav Neurosci ; 11: 120, 2017.*

##### RESUMO

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.

*PLoS One ; 10(10): e0140954, 2015.*

##### RESUMO

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.

##### Assuntos

Corpo Lúteo/fisiologia , Ciclo Estral/fisiologia , Modelos Estatísticos , Folículo Ovariano/fisiologia , Análise de Sistemas , Animais , Bovinos , Dinoprostona/fisiologia , Feminino , Hormônio Foliculoestimulante/fisiologia , Hormônio Liberador de Gonadotropina/fisiologia , Hormônio Luteinizante/fisiologia , Prostaglandinas F/fisiologia*BMC Syst Biol ; 9: 67, 2015 Oct 08.*

##### RESUMO

BACKGROUND: The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level. RESULTS: We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time integration, the algorithm keeps track of the subset of states with significant probabilities (essential support). Secondly, the probability distribution that solves the equation is parametrised with a small number of coefficients using collocation on Gaussian radial basis functions. The system of basis functions is chosen in such a way that the solution is approximated only on the essential support instead of the whole state space. DISCUSSION: In order to demonstrate the effectiveness of the method, we consider four application examples: a) the self-regulating gene model, b) the 2-dimensional bistable toggle switch, c) a generalisation of the bistable switch to a 3-dimensional tristable problem, and d) a 3-dimensional cell differentiation model that, depending on parameter values, may operate in bistable or tristable modes. In all multidimensional examples the manifold containing the system states with significant probabilities undergoes drastic transformations over time. This fact makes the examples especially challenging for numerical methods. CONCLUSIONS: The proposed method is a new numerical approach permitting to approximately solve a wide range of problems that have been hard to tackle until now. A full representation of multi-dimensional distributions is recovered. The method is especially attractive when dealing with models that yield solutions of a complex structure, for instance, featuring multi-stability.

##### Assuntos

Algoritmos , Fenômenos Bioquímicos , Modelos Químicos , Diferenciação Celular , Retroalimentação Fisiológica , Regulação da Expressão Gênica , Cinética , Distribuição Normal , Processos Estocásticos*PLoS One ; 10(4): e0120607, 2015.*

##### RESUMO

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency- and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

##### Assuntos

Tuberculose/epidemiologia , Tuberculose/transmissão , Camarões/epidemiologia , Simulação por Computador , Humanos , Modelos Biológicos , Modelos Estatísticos , Mycobacterium tuberculosis/isolamento & purificação , Tuberculose/diagnóstico*J Chem Phys ; 139(19): 194110, 2013 Nov 21.*

##### RESUMO

A decomposition of a molecular conformational space into sets or functions (states) allows for a reduced description of the dynamical behavior in terms of transition probabilities between these states. Spectral clustering of the corresponding transition probability matrix can then reveal metastabilities. The more states are used for the decomposition, the smaller the risk to cover multiple conformations with one state, which would make these conformations indistinguishable. However, since the computational complexity of the clustering algorithm increases quadratically with the number of states, it is desirable to have as few states as possible. To balance these two contradictory goals, we present an algorithm for an adaptive decomposition of the position space starting from a very coarse decomposition. The algorithm is applied to small data classification problems where it was shown to be superior to commonly used algorithms, e.g., k-means. We also applied this algorithm to the conformation analysis of a tripeptide molecule where six-dimensional time series are successfully analyzed.

##### Assuntos

Simulação de Dinâmica Molecular , Oligopeptídeos/análise , Algoritmos , Conformação Proteica*J Theor Biol ; 321: 8-27, 2013 Mar 21.*

##### RESUMO

The paper presents a differential equation model for the feedback mechanisms between gonadotropin-releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. Compared to earlier human cycle models, there are three important differences: The model presented here (a) does not involve any delay equations, (b) is based on a deterministic modeling of the GnRH pulse pattern, and (c) contains less differential equations and less parameters. These differences allow for a faster simulation and parameter identification. The focus is on modeling GnRH-receptor binding, in particular, by inclusion of a pharmacokinetic/pharmacodynamic (PK/PD) model for a GnRH agonist, Nafarelin, and a GnRH antagonist, Cetrorelix, into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle of 12 healthy women. It correctly predicts hormonal changes following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.