TY - JOUR A1 - Hartung, Niklas A1 - Benary, Uwe A1 - Wolf, Jana A1 - Kofahl, Bente T1 - Paracrine and autocrine regulation of gene expression by Wnt-inhibitor Dickkopf in wild-type and mutant hepatocytes JF - BMC systems biology N2 - Background: Cells are able to communicate and coordinate their function within tissues via secreted factors. Aberrant secretion by cancer cells can modulate this intercellular communication, in particular in highly organised tissues such as the liver. Hepatocytes, the major cell type of the liver, secrete Dickkopf (Dkk), which inhibits Wnt/beta-catenin signalling in an autocrine and paracrine manner. Consequently, Dkk modulates the expression of Wnt/beta-catenin target genes. We present a mathematical model that describes the autocrine and paracrine regulation of hepatic gene expression by Dkk under wild-type conditions as well as in the presence of mutant cells. Results: Our spatial model describes the competition of Dkk and Wnt at receptor level, intra-cellular Wnt/beta-catenin signalling, and the regulation of target gene expression for 21 individual hepatocytes. Autocrine and paracrine regulation is mediated through a feedback mechanism via Dkk and Dkk diffusion along the porto-central axis. Along this axis an APC concentration gradient is modelled as experimentally detected in liver. Simulations of mutant cells demonstrate that already a single mutant cell increases overall Dkk concentration. The influence of the mutant cell on gene expression of surrounding wild-type hepatocytes is limited in magnitude and restricted to hepatocytes in close proximity. To explore the underlying molecular mechanisms, we perform a comprehensive analysis of the model parameters such as diffusion coefficient, mutation strength and feedback strength. Conclusions: Our simulations show that Dkk concentration is elevated in the presence of a mutant cell. However, the impact of these elevated Dkk levels on wild-type hepatocytes is confined in space and magnitude. The combination of inter-and intracellular processes, such as Dkk feedback, diffusion and Wnt/beta-catenin signal transduction, allow wild-type hepatocytes to largely maintain their gene expression. KW - Wnt/beta-catenin signalling pathway KW - Dickkopf diffusion and feedback regulation KW - APC concentration gradient KW - Mathematical model KW - Paracrine and autocrine regulation KW - Reaction-diffusion system Y1 - 2017 U6 - https://doi.org/10.1186/s12918-017-0470-9 SN - 1752-0509 VL - 11 PB - BioMed Central CY - London ER - TY - JOUR A1 - Sinn, Petra A1 - Engbert, Ralf T1 - Small saccades versus microsaccades: Experimental distinction and model-based unification JF - Vision research : an international journal for functional aspects of vision. N2 - Natural vision is characterized by alternating sequences of rapid gaze shifts (saccades) and fixations. During fixations, microsaccades and slower drift movements occur spontaneously, so that the eye is never motionless. Theoretical models of fixational eye movements predict that microsaccades are dynamically coupled to slower drift movements generated immediately before microsaccades, which might be used as a criterion to distinguish microsaccades from small voluntary saccades. Here we investigate a sequential scanning task, where participants generate goal-directed saccades and microsaccades with overlapping amplitude distributions. We show that properties of microsaccades are correlated with precursory drift motion, while amplitudes of goal-directed saccades do not dependent on previous drift epochs. We develop and test a mathematical model that integrates goal-directed and fixational eye movements, including microsaccades. Using model simulations, we reproduce the experimental finding of correlations within fixational eye movement components (i.e., between physiological drift and microsaccades) but not between goal-directed saccades and fixational drift motion. These results lend support to a functional difference between microsaccades and goal-directed saccades, while, at the same time, both types of behavior may be part of an oculomotor continuum that is quantitatively described by our mathematical model. (C) 2015 Elsevier Ltd. All rights reserved. KW - Eye movements KW - Visual fixation KW - Microsaccades KW - Mathematical model Y1 - 2016 U6 - https://doi.org/10.1016/j.visres.2015.05.012 SN - 0042-6989 SN - 1878-5646 VL - 118 SP - 132 EP - 143 PB - Elsevier CY - Oxford ER - TY - JOUR A1 - Kruegel, Andre A1 - Engbert, Ralf T1 - A model of saccadic landing positions in reading under the influence of sensory noise JF - Visual cognition KW - Bayesian estimation KW - Word boundaries KW - Saccade planning KW - Mathematical model KW - Eye movements during reading Y1 - 2014 U6 - https://doi.org/10.1080/13506285.2014.894166 SN - 1350-6285 SN - 1464-0716 VL - 22 IS - 3-4 SP - 334 EP - 353 PB - Routledge, Taylor & Francis Group CY - Abingdon ER - TY - JOUR A1 - Ebenhoeh, Oliver A1 - Houwaart, Torsten A1 - Lokstein, Heiko A1 - Schlede, Stephanie A1 - Tirok, Katrin T1 - A minimal mathematical model of nonphotochemical quenching of chlorophyll fluorescence JF - Biosystems : journal of biological and information processing sciences N2 - Under natural conditions, plants are exposed to rapidly changing light intensities. To acclimate to such fluctuations, plants have evolved adaptive mechanisms that optimally exploit available light energy and simultaneously minimise damage of the photosynthetic apparatus through excess light. An important mechanism is the dissipation of excess excitation energy as heat which can be measured as nonphotochemical quenching of chlorophyll fluorescence (NPQ). In this paper, we present a highly simplified mathematical model that captures essential experimentally observed features of the short term adaptive quenching dynamics. We investigate the stationary and dynamic behaviour of the model and systematically analyse the dependence of characteristic system properties on key parameters such as rate constants and pool sizes. Comparing simulations with experimental data allows to derive conclusions about the validity of the simplifying assumptions and we further propose hypotheses regarding the role of the xanthophyll cycle in NPQ. We envisage that the presented theoretical description of the light reactions in conjunction with short term adaptive processes serves as a basis for the development of more detailed mechanistic models by which the molecular mechanisms of NPQ can be theoretically studied. KW - Photosynthesis KW - Light reactions KW - Nonphotochemical quenching of chlorophyll fluorescence KW - Chlorophyll fluorescence KW - Mathematical model Y1 - 2011 U6 - https://doi.org/10.1016/j.biosystems.2010.10.011 SN - 0303-2647 VL - 103 IS - 2 SP - 196 EP - 204 PB - Elsevier CY - Oxford ER -