TY - JOUR AB - Cellular heterogeneity is known to have important effects on signal processing and cellular decision making. To understand these processes, multiple classes of mathematical models have been introduced. The hierarchical population model builds a novel class which allows for the mechanistic description of heterogeneity and explicitly takes into account subpopulation structures. However, this model requires a parametric distribution assumption for the cell population and, so far, only the normal distribution has been employed. Here, we incorporate alternative distribution assumptions into the model, assess their robustness against outliers and evaluate their influence on the performance of model calibration in a simulation study and a real-world application example. We found that alternative distributions provide reliable parameter estimates even in the presence of outliers, and can in fact increase the convergence of model calibration. (C) 2019 Elsevier Ltd. All rights reserved. AU - Loos, C. AU - Hasenauer, J. C1 - 57776 C2 - 47976 CY - 24-28 Oval Rd, London Nw1 7dx, England TI - Robust calibration of hierarchical population models for heterogeneous cell populations. JO - J. Theor. Biol. VL - 488 PB - Academic Press Ltd- Elsevier Science Ltd PY - 2020 SN - 0022-5193 ER - TY - JOUR AB - During pancreas development, Neurog3 positive endocrine progenitors are specified by Delta/Notch (D/N) mediated lateral inhibition in the growing ducts. During neurogenesis, genes that determine the transition from the proneural state to neuronal or glial lineages are oscillating before their expression is sustained. Although the basic gene regulatory network is very similar, cycling gene expression in pancreatic development was not investigated yet, and previous simulations of lateral inhibition in pancreas development excluded by design the possibility of oscillations. To explore this possibility, we developed a dynamic model of a growing duct that results in an oscillatory phase before the determination of endocrine progenitors by lateral inhibition. The basic network (D/N + Hes1 + Neurog3) shows scattered, stable Neurog3 expression after displaying transient expression. Furthermore, we included the Hes1 negative feedback as previously discussed in neurogenesis and show the consequences for Neurog3 expression in pancreatic duct development. Interestingly, a weakened HES1 action on the Hes1 promoter allows the coexistence of stable patterning and oscillations. In conclusion, cycling gene expression and lateral inhibition are not mutually exclusive. In this way, we argue for a unified mode of D/N mediated lateral inhibition in neurogenic and pancreatic progenitor specification. AU - Tiedemann, H.B. AU - Schneltzer, E. AU - Beckers, J. AU - Przemeck, G.K.H. AU - Hrabě de Angelis, M. C1 - 51419 C2 - 43187 CY - London SP - 32-44 TI - Modeling coexistence of oscillation and Delta/Notch-mediated lateral inhibition in pancreas development and neurogenesis. JO - J. Theor. Biol. VL - 430 PB - Academic Press Ltd- Elsevier Science Ltd PY - 2017 SN - 0022-5193 ER - TY - JOUR AB - Bacterial communication is enabled through the collective release and sensing of signalling molecules in a process called quorum sensing. Cooperative processes can easily be destabilized by the appearance of cheaters, who contribute little or nothing at all to the production of common goods. This especially applies for planktonic cultures. In this study, we analyse the dynamics of bacterial quorum sensing and its evolutionary stability under two levels of cooperation, namely signal and enzyme production. The model accounts for mutation rates and switches between planktonic and biofilm state of growth. We present a mathematical approach to model these dynamics using age-dependent colony models. We explore the conditions under which cooperation is stable and find that spatial structuring can lead to long-term scenarios such as coexistence or bistability, depending on the non-linear combination of different parameters like death rates and production costs. AU - Mund, A.* AU - Kuttler, C.* AU - Pérez-Velázquez, J. AU - Hense, B.A. C1 - 47733 C2 - 39493 CY - London SP - 104-115 TI - An age-dependent model to analyse the evolutionary stability of bacterial quorum sensing. JO - J. Theor. Biol. VL - 405 PB - Academic Press Ltd- Elsevier Science Ltd PY - 2016 SN - 0022-5193 ER - TY - JOUR AB - Efficient adaptation strategies to changing environmental conditions are essential for bacteria to survive and grow. Fundamental restructuring of their metabolism is usually mediated by corresponding gene regulation. Here, often several different environmental stimuli have to be integrated into a reasonable, energy-efficient response. Fast fluctuations and overshooting have to be filtered out. The gene regulatory network for the anaerobic adaptation of the pathogenic bacterium Pseudomonas aeruginosa is organized as a feed-forward loop (FFL), which is a three-gene network motif composed of two transcription factors (Anr for oxygen, NarxL for nitrate) and one target (Nar for nitrate reductase). The upstream transcription factor (Anr) induces the downstream transcription factor (NarXL). Both regulators act together positively by inducing the target (Nar) via a direct and indirect regulation path (coherent type-1 FFL). Since full promoter activity is only achieved when both transcription factors are present the target operon is expressed with a delay. Thus, in response to environmental stimuli (oxygen, nitrate), signals are mediated and processed in a way that short pulses are filtered out. In this study we analyze a special kind of FFL called FFLk by means of a family of ordinary differential equation models. The secondary FFL regulator (NarXL) is expressed constitutively but further induced in the presence of the upstream stimuli. This FFL modification has substantial influence on the response time and cost-benefit ratio mediated by environmental fluctuations. In order to find conditions where this regulatory network motif might be beneficial, we analyzed various models and environments. We describe the observed evolutional advantage of FFLk and its role in environmental adaptation and pathogenicity. AU - Roselius, L.* AU - Langemann, D.* AU - Müller, J. AU - Hense, B.A. AU - Filges, S.* AU - Jahn, D.* AU - Münch, R.* C1 - 32077 C2 - 34951 CY - London SP - 290-299 TI - Modeling and analysis of a gene-regulatory feed-forward loop with basal expression of the second regulator. JO - J. Theor. Biol. VL - 363 PB - Academic Press Ltd- Elsevier Science Ltd PY - 2014 SN - 0022-5193 ER - TY - JOUR AB - We investigate the evolution of bet-hedging in a population that experiences a stochastically switching environment by means of adaptive dynamics. The aim is to extend known results to the situation at hand, and to deepen the understanding of the range of validity of these results. We find three different types of evolutionarily stable strategies (ESSs) depending on the frequency at which the environment changes: for a rapid change, a monomorphic phenotype adapted to the mean environment; for an intermediate range, a bimorphic bet-hedging phenotype; for slowly changing environments, a monomorphic phenotype adapted to the current environment. While the last result is only obtained by means of heuristic arguments and simulations, the first two results are based on the analysis of Lyapunov exponents for stochastically switching systems. AU - Müller, J. AU - Hense, B.A. AU - Fuchs, T.M.* AU - Utz, M.* AU - Pötzsche, C.* C1 - 27459 C2 - 32680 SP - 144-157 TI - Bet-hedging in stochastically switching environments. JO - J. Theor. Biol. VL - 336 PB - Academic Press - Elsevier PY - 2013 SN - 0022-5193 ER - TY - JOUR AB - Cell proliferation and differentiation is described by a multi-type branching process, a probability model that defines the inheritance of cell type. Cell type is defined by (i) a repression index related to the time required for S-phase entry and (ii) phenotype as determined by cell markers and division history. The inheritance of cell type is expressed as the expected number and type of progeny cells produced by a mother cell given her type. Expressions for the expected number and type of cells produced by a multi-cellular (bulk culture) system are derived from the general model by making the simplifying assumption that cell generation times are independent. The multi-type Smith-Martin model (MSM) makes the further assumption that cell generation times are lag-exponentially distributed with phenotype transitions occurring just before entry into S-phase. The inheritance-modified MSM (IMSM) model includes the influence of generation time memory so that mother and daughter generation times are correlated. The expansion of human cord blood CD34(+) cells by haematopoietic growth factors was division tracked in bulk culture using carboxyfluorescein diacetate, succinimidyl ester (CFDA-SE). The MSM model was fitted to division tracking data to identify cell cycle length, and the rates of CD34 antigen down-regulation and apoptosis. The IMSM model was estimated for mouse granulocyte-macrophage progenitors using live cell imaging data. Multi-type branching models describe cell differentiation dynamics at both single- and multi-cell scales, providing a new paradigm for systematic analysis of stem and progenitor cell development. AU - Nordon, R.E.* AU - Ko, K.H.* AU - Odell, R.* AU - Schroeder, T. C1 - 6650 C2 - 29040 CY - Amsterdam SP - 7-18 TI - Multi-type branching models to describe cell differentiation programs. JO - J. Theor. Biol. VL - 277 IS - 1 PB - Elsevier PY - 2011 SN - 0022-5193 ER - TY - JOUR AB - We generalize random Boolean networks by softening the hard binary discretization into multiple discrete states. These multistate networks are generic models of gene regulatory networks, where each gene is known to assume a finite number of functionally different expression levels. We analytically determine the critical connectivity that separates the biologically unfavorable frozen and chaotic regimes. This connectivity is inversely proportional to a parameter which measures the heterogeneity of the update rules. Interestingly, the latter does not necessarily increase with the mean number of discrete states per node. Still, allowing for multiple states decreases the critical connectivity as compared to random Boolean networks, and thus leads to biologically unrealistic situations. Therefore, we study two approaches to increase the critical connectivity. First, we demonstrate that each network can be kept in its frozen regime by sufficiently biasing the update rules. Second, we restrict the randomly chosen update rules to a subclass of biologically more meaningful functions. These functions are characterized based on a thermodynamic model of gene regulation. We analytically show that their usage indeed increases the critical connectivity. From a general point of view, our thermodynamic considerations link discrete and continuous models of gene regulatory networks. AU - Wittmann, D.M. AU - Marr, C. AU - Theis, F.J. C1 - 2780 C2 - 27867 SP - 436-448 TI - Biologically meaningful update rules increase the critical connectivity of generalized Kauffman networks. JO - J. Theor. Biol. VL - 266 IS - 3 PB - Elsevier PY - 2010 SN - 0022-5193 ER - TY - JOUR AB - Many bacteria developed a possibility to recognise aspects of their environment or to communicate with each other by chemical signals. An important strategy is the so-called quorum sensing (QS), a regulatory mechanism for the gene expression, where the bacteria measure their own cell density by means of this signalling pathway. One of the best-studied species using QS is the marine luminescent bacterium Vibrio fischeri which is considered here as a model organism. The two main regulatory pathways (lux and ain) are combined to a regulation system, the dynamics is modelled by an ODE system. This system is analysed thoroughly, considering stationary states, dynamical behaviour and the possible biological meaning of it. The influence of different parameter values on the behaviour is examined, the same basic system is able to reflect the peculiarities of different bacteria strains (respectively, their mutants). AU - Kuttler, C. AU - Hense, B.A. C1 - 625 C2 - 25503 SP - 167-180 TI - Interplay of two quorum sensing regulation systems of Vibrio fischeri. JO - J. Theor. Biol. VL - 251 IS - 1 PB - Elsevier PY - 2008 SN - 0022-5193 ER - TY - JOUR AB - To model dynamic expression patterns in somitogenesis we developed a Java-application for simulating gene regulatory networks in many cells in parallel and visualising the results using the Java3D API, thus simulating the collective behaviour of many thousand cells. According to the ‘clock-and-wave-front’ model mesodermal segmentation of vertebrate embryos is regulated by a ‘segmentation clock’, which oscillates with a period of about 2 h in mice, and a ‘wave front’ moving back with the growing caudal end of the presomitic mesoderm. The clock is realised through cycling expression of genes such as Hes1 and Hes7, whose gene products repress the transcription of their encoding genes in a negative feedback loop. By coupling the decay of the Hes1 mRNA to a gradient with the same features and mechanism of formation as the mesodermal Fgf8 gradient we can simulate typical features of the dynamic expression pattern of Hes1 in the presomitic mesoderm. Furthermore, our program is able to synchronise Hes1 oscillations in thousands of cells through simulated Delta–Notch signalling interactions. AU - Tiedemann, H.B. AU - Schneltzer, E. AU - Zeiser, S. AU - Rubio-Aliaga, I. AU - Wurst, W. AU - Beckers, J. AU - Przemeck, G.K.H. AU - Hrabě de Angelis, M. C1 - 5197 C2 - 24533 SP - 120-129 TI - Cell-based simulation of dynamic expression patterns in the presomitic mesoderm. JO - J. Theor. Biol. VL - 248 IS - 1 PB - Elsevier PY - 2007 SN - 0022-5193 ER -