Röblitz, Susanna
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The androgen system across the menstrual cycle: Hormonal, (epi-)genetic and psychometric alterations
(2022)
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.
The Robust Perron Cluster Analysis (PCCA+) has become a popular spectral clustering algorithm for coarse-graining transition matrices of nearly decomposable Markov chains with transition states. Originally developed for reversible Markov chains, the algorithm only worked for transition matrices with real eigenvalues. In this paper, we therefore extend the theoretical framework of PCCA+ to Markov chains with a complex eigen-decomposition. We show that by replacing a complex conjugate pair of eigenvectors by their real and imaginary components, a real representation of the same subspace is obtained, which is suitable for the cluster analysis. We show that our approach leads to the same results as the generalized PCCA+ (GPCCA), which replaces the complex eigen-decomposition by a conceptually more difficult real Schur decomposition. We apply the method on non-reversible Markov chains, including circular chains, and demonstrate its efficiency compared to GPCCA. The experiments are performed in the Matlab programming language and codes are provided.
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.
In addition to the conventional Isothermal Titration Calorimetry (ITC), kinetic ITC (kinITC) not only gains thermodynamic information, but also kinetic data from a biochemical binding process. Moreover, kinITC gives insights into reactions consisting of two separate kinetic steps, such as protein folding or sequential binding processes. The ITC method alone cannot deliver kinetic parameters, especially not for multivalent bindings. This paper describes how to solve the problem using kinITC and an invariant subspace projection. The algorithm is tested for multivalent systems with different valencies.
We present a mechanistic pharmacokinetic-pharmacodynamic model to simulate the effect of dexamethasone on the glucose metabolism in dairy cows.
The coupling of the pharmacokinetic model to the pharmacodynamic model
is based on mechanisms underlying homeostasis regulation by dexamethasone.
In particular, the coupling takes into account the predominant role of dexamethasone in stimulating glucagon secretion, glycogenolysis and lipolysis and in
impairing the sensitivity of cells to insulin. Simulating the effect of a single
dose of dexamethasone on the physiological behaviour of the system shows that
the adopted mechanisms are able to induce a temporary hyperglycemia and
hyperinsulinemia, which captures the observed data in non-lactating cows. In
lactating cows, the model simulations show that a single dose of dexamethasone
reduces the lipolytic effect, owing to the reduction of glucose uptake by the
mammary gland.
Our project aimed at building an in silico model based on our recently developed in vitro osteoarthritis (OA) model seeking for refinement of the model to enhance validity and translatability towards the more sophisticated simulation of OA. In detail, the previously 3D in vitro model is based on 3D chondrogenic constructs generated solely from human bone marrow derived mesenchymal stromal cells (hMSCs). Besides studying the normal state of the model over 3 weeks, the in vitro model was treated with interleukin-1β (IL-1β) and tumor necrosis factor alpha (TNFα) to mimic an OA-like environment.
Understanding the pathophysiological processes of osteoarthritis (OA) require adequate model systems. Although different in vitro or in vivo models have been described, further comprehensive approaches are needed to study specific parts of the disease. This study aimed to combine in vitro and in silico modeling to describe cellular and matrix-related changes during the early phase of OA. We developed an in vitro OA model based on scaffold-free cartilage-like constructs (SFCCs), which was mathematically modeled using a partial differential equation (PDE) system to resemble the processes during the onset of OA. SFCCs were produced from mesenchymal stromal cells and analyzed weekly by histology and qPCR to characterize the cellular and matrix-related composition. To simulate the early phase of OA, SFCCs were treated with interleukin-1β (IL-1β), tumor necrosis factor α (TNFα) and examined after 3 weeks or cultivated another 3 weeks without inflammatory cytokines to validate the regeneration potential. Mathematical modeling was performed in parallel to the in vitro experiments. SFCCs expressed cartilage-specific markers, and after stimulation an increased expression of inflammatory markers, matrix degrading enzymes, a loss of collagen II (Col-2) and a reduced cell density was observed which could be partially reversed by retraction of stimulation. Based on the PDEs, the distribution processes within the SFCCs, including those of IL-1β, Col-2 degradation and cell number reduction was simulated. By combining in vitro and in silico methods, we aimed to develop a valid, efficient alternative approach to examine and predict disease progression and new therapeutic strategies.
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 luteiniz-
ing hormone concentrations, likely caused by lower glucose and insulin concen-
trations 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. Following this idea, 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 was developed.
The model is built on ordinary differential equations and relies on previously
introduced models on the bovine estrous cycle and the glucose-insulin dynam-
ics. Necessary modifications and coupling mechanisms are thoroughly discussed.
Depending on the composition and the amount of food, in particular the glu-
cose 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. Regarding its applicability, this work is an early
attempt towards developing in silico feeding strategies and may eventually help
refining and reducing animal experiments.
Hypokalemia, characterized by too low serum potassium levels, is a severe mineral disorder which can be life threatening. It is increasingly diagnosed in veterinarian healthcare and a topic of ongoing research. In this paper, we explore the different originating conditions of hypokalemia: reduced potassium intake, increased excretion, acid-base disturbances, or increased insulin, by using a dynamic mathematical model for potassium balance in non-lactating and lactating cows.
Simulations are compared with literature. The results give insights into the network dynamics and point to scenarios on which experimental effort should be focused. Application of mathematical models can assist in experimental planning as well as the reduction, refinement and replacement of animal experiments.
Lactating dairy cows require a particular composition of nutritional ingredients depending on their production status.
The optimal supply of energy and minerals in diet, one of them potassium, is indispensable for the prevention of disbalances like hypokalemia or hypoglycaemia.
Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and closely interacts with glucose and electrolyte metabolism, in which postpartum veterinary treatments frequently intervene.
We present a mechanistic, dynamic model for potassium balance together with a glucose insulin model in non-lactating and lactating dairy cows based on ordinary differential equations.
Parameter values were obtained from data of a clinical trial as well as from literature. To verify the mechanistic functioning of the model, we validate the model by comparing simulation outcomes with clinical study findings. Furthermore we perform numerical experiments and compare them with expected behaviour according to mechanistic knowledge. The results give insight into the dynamic behaviour of the network and open the way for further open questions and hypothesis to be tested.
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 ω-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.
Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models.
In Silico Clinical Trials (ISCT), i.e., clinical experimental campaigns carried out by means of computer simulations, hold the promise to decrease time and cost for the safety and efficacy assessment of pharmacological treatments, reduce the need for animal and human testing, and enable precision medicine.
In this paper we present a case study aiming at quantifying, by means of a multi-arm ISCT supervised by intelligent search, the potential impact of precision medicine approaches on a real pharmacological treatment, namely the downregulation phase of a complex clinical protocol for assisted reproduction.
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 β (1−40) peptide, periodically driven by an oscillating electric field.
Mathematical models for bioregulatory networks can be based on different formalisms, depending on the quality of available data and the research question to be answered. Discrete boolean models can be constructed based on qualitative data, which are frequently available. On the other hand, continuous models in terms of ordinary differential equations (ODEs) can incorporate time-series data and give more detailed insight into the dynamics of the underlying system. A few years ago, a method based on multivariate polynomial interpolation and Hill functions has been developed for an automatic conversion of boolean models to systems of ordinary differential equations. This method is frequently used by modellers in systems biology today, but there are only a few results available about the conservation of mathematical structures and properties across the formalisms. Here, we consider subsets of the phase space where some components stay fixed, called trap spaces, and demonstrate how boolean trap spaces can be linked to invariant sets in the continuous state space. This knowledge is of practical relevance since finding trap spaces in the boolean setting, which is relatively easy, allows for the construction of reduced ODE models.
A seminar and interactive workshop on “In silico Methods –
Computational Alternatives to Animal Testing” was held in
Berlin, Germany, organized by Annemarie Lang, Frank Butt-
gereit and Andrea Volkamer at the Charité-Universitätsmedizin
Berlin, on August 17-18, 2017. During the half-day seminar, the
variety and applications of in silico methods as alternatives to
animal testing were presented with room for scientific discus-
sions with experts from academia, industry and the German fed-
eral ministry (Fig. 1). Talks on computational systems biology
were followed by detailed information on predictive toxicology
in order to display the diversity of in silico methods and the
potential to embrace them in current approaches (Hartung and
Hoffmann, 2009; Luechtefeld and Hartung, 2017). The follow-
ing interactive one-day Design Thinking Workshop was aimed
at experts, interested researchers and PhD-students interested in
the use of in silico as alternative methods to promote the 3Rs
(Fig. 2). Forty participants took part in the seminar while the
workshop was restricted to sixteen participants.