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1
Lomeli, Luis Martinez, Abdon Iniguez, Prasanthi Tata, Nilamani Jena, Zhong-Ying Liu, Richard Van Etten, Arthur D. Lander, Babak Shahbaba, John S. Lowengrub, and Vladimir N. Minin. "Optimal experimental design for mathematical models of haematopoiesis." Journal of The Royal Society Interface 18, no. 174 (January 2021): 20200729. http://dx.doi.org/10.1098/rsif.2020.0729.
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The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters.
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Pedersen, Morten Gram, Gianna M. Toffolo, and Claudio Cobelli. "Cellular modeling: insight into oral minimal models of insulin secretion." American Journal of Physiology-Endocrinology and Metabolism 298, no. 3 (March 2010): E597—E601. http://dx.doi.org/10.1152/ajpendo.00670.2009.
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The oral glucose tolerance test and meal tolerance test are common clinical tests of the glucose-insulin system. Several mathematical models have been suggested as means to extract information about β-cell function from data from oral tolerance tests. Any such model needs to be fairly simple but should at the same time be linked to the underlying biology of the insulin-secreting β-cells. The scope of the present work is to present a way to make such a connection using a recent model describing intracellular mechanisms. We show how the three main components of oral minimal secretion models, derivative control, proportional control, and delay, are related to subcellular events, thus providing mechanistic underpinning of the assumptions of the minimal models.
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DRASDO, DIRK. "COARSE GRAINING IN SIMULATED CELL POPULATIONS." Advances in Complex Systems 08, no. 02n03 (June 2005): 319–63. http://dx.doi.org/10.1142/s0219525905000440.
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The main mechanisms that control the organization of multicellular tissues are still largely open. A commonly used tool to study basic control mechanisms are in vitro experiments in which the growth conditions can be widely varied. However, even in vitro experiments are not free from unknown or uncontrolled influences. One reason why mathematical models become more and more a popular complementary tool to experiments is that they permit the study of hypotheses free from unknown or uncontrolled influences that occur in experiments. Many model types have been considered so far to model multicellular organization ranging from detailed individual-cell based models with explicit representations of the cell shape to cellular automata models with no representation of cell shape, and continuum models, which consider a local density averaged over many individual cells. However, how the different model description may be linked, and, how a description on a coarser level may be constructed based on the knowledge of the finer, microscopic level, is still largely unknown. Here, we consider the example of monolayer growth in vitro to illustrate how, in a multi-step process starting from a single-cell based off-lattice-model that subsumes the information on the sub-cellular scale by characteristic cell-biophysical and cell-kinetic properties, a cellular automaton may be constructed whose rules have been chosen based on the findings in the off-lattice model. Finally, we use the cellular automaton model as a starting point to construct a multivariate master equation from a compartment approach from which a continuum model can be derived by a systematic coarse-graining procedure. We find that the resulting continuum equation largely captures the growth behavior of the CA model. The development of our models is guided by experimental observations on growing monolayers.
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Adams, DS. "Mechanisms of cell shape change: the cytomechanics of cellular response to chemical environment and mechanical loading." Journal of Cell Biology 117, no. 1 (April 1, 1992): 83–93. http://dx.doi.org/10.1083/jcb.117.1.83.
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Processes such as cell locomotion and morphogenesis depend on both the generation of force by cytoskeletal elements and the response of the cell to the resulting mechanical loads. Many widely accepted theoretical models of processes involving cell shape change are based on untested hypotheses about the interaction of these two components of cell shape change. I have quantified the mechanical responses of cytoplasm to various chemical environments and mechanical loading regimes to understand better the mechanisms of cell shape change and to address the validity of these models. Measurements of cell mechanical properties were made with strands of cytoplasm submerged in media containing detergent to permeabilize the plasma membrane, thus allowing control over intracellular milieu. Experiments were performed with equipment that generated sinusoidally varying length changes of isolated strands of cytoplasm from Physarum polycephalum. Results indicate that stiffness, elasticity, and viscosity of cytoplasm all increase with increasing concentration of Ca2+, Mg2+, and ATP, and decrease with increasing magnitude and rate of deformation. These results specifically challenge assumptions underlying mathematical models of morphogenetic events such as epithelial folding and cell division, and further suggest that gelation may depend on both actin cross-linking and actin polymerization.
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Edwards, Aurélie. "Modeling transport in the kidney: investigating function and dysfunction." American Journal of Physiology-Renal Physiology 298, no. 3 (March 2010): F475—F484. http://dx.doi.org/10.1152/ajprenal.00501.2009.
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Mathematical models of water and solute transport in the kidney have significantly expanded our understanding of renal function in both health and disease. This review describes recent theoretical developments and emphasizes the relevance of model findings to major unresolved questions and controversies. These include the fundamental processes by which urine is concentrated in the inner medulla, the ultrastructural basis of proteinuria, irregular flow oscillation patterns in spontaneously hypertensive rats, and the mechanisms underlying the hypotensive effects of thiazides. Macroscopic models of water, NaCl, and urea transport in populations of nephrons have served to test, confirm, or refute a number of hypotheses related to the urine concentrating mechanism. Other macroscopic models focus on the mechanisms, role, and irregularities of renal hemodynamic control and on the regulation of renal oxygenation. At the mesoscale, models of glomerular filtration have yielded significant insight into the ultrastructural basis underlying a number of disorders. At the cellular scale, models of epithelial solute transport and pericyte Ca2+ signaling are being used to elucidate transport pathways and the effects of hormones and drugs. Areas where further theoretical progress is conditional on experimental advances are also identified.
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Goryachev, Andrew B., and Marcin Leda. "Compete or Coexist? Why the Same Mechanisms of Symmetry Breaking Can Yield Distinct Outcomes." Cells 9, no. 9 (September 1, 2020): 2011. http://dx.doi.org/10.3390/cells9092011.
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Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of dense protein clusters. Thus, a cluster of active GTPase Cdc42 marks the site of nascent bud in the baker’s yeast. An important biological question is which mechanisms control the number of pattern maxima (spots) and, thus, the number of nascent cellular structures. Distinct flavors of theoretical models seem to suggest different predictions. While the classical Turing scenario leads to an array of stably coexisting multiple structures, mass-conserved models predict formation of a single spot that emerges via the greedy competition between the pattern maxima for the common molecular resources. Both the outcome and the kinetics of this competition are of significant biological importance but remained poorly explored. Recent theoretical analyses largely addressed these questions, but their results have not yet been fully appreciated by the broad biological community. Keeping mathematical apparatus and jargon to the minimum, we review the main conclusions of these analyses with their biological implications in mind. Focusing on the specific example of pattern formation by small GTPases, we speculate on the features of the patterning mechanisms that bypass competition and favor formation of multiple coexisting structures and contrast them with those of the mechanisms that harness competition to form unique cellular structures.
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Tallarida, R. J. "Receptor discrimination and control of agonist-antagonist binding." American Journal of Physiology-Endocrinology and Metabolism 269, no. 2 (August 1, 1995): E379—E391. http://dx.doi.org/10.1152/ajpendo.1995.269.2.e379.
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The law of mass action is the common model for the interaction of agonist and antagonist compounds with cellular receptors. Parameters of the interaction, obtained from functional and radioligand-binding studies, allow discrimination and subtyping of receptors and aid in understanding specific mechanisms. This article reviews the theory and associated mathematical models and graphical transformations of data that underlie the determination of receptor parameters. The main theory assumes that agonist and antagonist compounds bind to cells that have a fixed number of receptors and provides the framework for obtaining drug-receptor parameters from data and their graphical transformations. Conditions that produce a change in receptor number, a newer concept in pharmacology, can have an important effect on the parameter values derived in the usual way. This review concludes with a discussion of the quantitative study of receptor-mediated feedback control of endogenous ligands, a very new topic with potentially important implications for understanding antagonist effectiveness, loss of control, and chaos in regulated mass action binding.
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Dawn Parente, Jacquelyn, Knut Möller, Sabine Hensler, Claudia Kühlbach, Margareta M. Mueller, Paola Belloni, and J. Geoffrey Chase. "Technical Support of Wound Healing Processes: Project Status." Current Directions in Biomedical Engineering 5, no. 1 (September 1, 2019): 521–23. http://dx.doi.org/10.1515/cdbme-2019-0131.
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AbstractThe optimized wound healing (OWID) project provides technical support of wound healing processes. Advanced biophysical treatment therapies using light (photobiomodulation), negative pressure wound therapy (NPWT), and electrical stimulation show biological effects. Specifically, a biphasic dose-response curve is observed where lower doses activate cells, while above a threshold, higher doses are inhibitory. However, no standard protocols and no multi-modal treatment studies determine specific therapy needs. The OWID project aims to develop a multi-modal treatment device and modelbased therapy for individualized wound healing. This work presents the OWID project status. Currently, a photobiomodulation prototype delivers red, green, and blue light ‘medicine’ at prescribed therapeutic ‘doses’. The calculation of incident light necessarily considers transmission properties of the intervening cell culture plate. Negative pressure wound therapy (NPWT) and electrical impedance tomography (EIT) hardware are being adapted for use in vitro. Development of mathematical models of wound healing and therapy control are supported by treatment experiment outcome measures conducted in a wounded 3D tissue model. Parameter sensitivity analysis conducted on an existing mathematical model of reepithelialization results in changing parameter values influencing cellular movement rates. Thus, the model is robust to fit model parameters to observed reepithelialization rates under treatment conditions impacting cellular activation, inhibition, and untreated controls. Developed image analysis techniques have not captured changes in wound area after photobiomodulation treatment experiments. Alternatively, EIT will be tested for wound area analysis. Additionally, live dyes will be introduced to non-invasively visualize the reepithelialization front on a smaller, cellular scale. Finally, an overall therapeutic feedback control model uses model reference adaptive control to incorporate the intrinsic biological reepithelialization mechanism, treatment loops, and treatment controller modulation at a wound state. Currently, the OWID project conducts photobiomodulation treatment experiments in vitro and has developed mathematical models. Future work includes the incorporation of multi-modal wound healing treatment experiments.
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Sánchez-Jiménez, F., R. Montañez, F. Correa-Fiz, P. Chaves, C. Rodríguez-Caso, J. L. Urdiales, J. F. Aldana, and M. A. Medina. "The usefulness of post-genomics tools for characterization of the amine cross-talk in mammalian cells." Biochemical Society Transactions 35, no. 2 (March 20, 2007): 381–85. http://dx.doi.org/10.1042/bst0350381.
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Evidence is growing in favour of a relationship between cancer and chronic inflammation, and particularly of the role of a polyamine and histamine metabolic interplay involved in these physiopathological problems, which are indeed highly complex biological systems. Decodification of the complex inter- and intra-cellular signalling mechanisms that control these effects is not an easy task, which must be helped by systems biology technologies, including new tools for location and integration of database-stored information and predictive mathematical models, as well as functional genomics and other experimental molecular approaches necessary for hypothesis validation. We review the state of the art and present our latest efforts in this area, focused on the amine metabolism field.
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Almeida, S., M. Chaves, and F. Delaunay. "Control of synchronization ratios in clock/cell cycle coupling by growth factors and glucocorticoids." Royal Society Open Science 7, no. 2 (February 2020): 192054. http://dx.doi.org/10.1098/rsos.192054.
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The cell cycle and the circadian clock are essential cyclic cellular processes often synchronous in healthy cells. In this work, we use previously developed mathematical models of the mammalian cell cycle and circadian cellular clock in order to investigate their dynamical interactions. Firstly, we study unidirectional cell cycle → clock coupling by proposing a mechanism of mitosis promoting factor (MPF)-controlled REV-ERB α degradation. Secondly, we analyse a bidirectional coupling configuration, where we add the CLOCK : BMAL1-mediated MPF repression via the WEE1 kinase to the first system. Our simulations reproduce ratios of clock to cell cycle period in agreement with experimental observations and give predictions of the system’s synchronization state response to a variety of control parameters. Specifically, growth factors accelerate the coupled oscillators and dexamethasone (Dex) drives the system from a 1 : 1 to a 3 : 2 synchronization state. Furthermore, simulations of a Dex pulse reveal that certain time regions of pulse application drive the system from 1 : 1 to 3 : 2 synchronization while others have no effect, revealing the existence of a responsive and an irresponsive system’s phase, a result we contextualize with observations on the segregation of Dex-treated cells into two populations.
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Afschrift, Maarten, Friedl De Groote, and Ilse Jonkers. "Similar sensorimotor transformations control balance during standing and walking." PLOS Computational Biology 17, no. 6 (June 25, 2021): e1008369. http://dx.doi.org/10.1371/journal.pcbi.1008369.
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Standing and walking balance control in humans relies on the transformation of sensory information to motor commands that drive muscles. Here, we evaluated whether sensorimotor transformations underlying walking balance control can be described by task-level center of mass kinematics feedback similar to standing balance control. We found that delayed linear feedback of center of mass position and velocity, but not delayed linear feedback from ankle angles and angular velocities, can explain reactive ankle muscle activity and joint moments in response to perturbations of walking across protocols (discrete and continuous platform translations and discrete pelvis pushes). Feedback gains were modulated during the gait cycle and decreased with walking speed. Our results thus suggest that similar task-level variables, i.e. center of mass position and velocity, are controlled across standing and walking but that feedback gains are modulated during gait to accommodate changes in body configuration during the gait cycle and in stability with walking speed. These findings have important implications for modelling the neuromechanics of human balance control and for biomimetic control of wearable robotic devices. The feedback mechanisms we identified can be used to extend the current neuromechanical models that lack balance control mechanisms for the ankle joint. When using these models in the control of wearable robotic devices, we believe that this will facilitate shared control of balance between the user and the robotic device.
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Dias Louro, Marco António, Mónica Bettencourt-Dias, and Jorge Carneiro. "A first-takes-all model of centriole copy number control based on cartwheel elongation." PLOS Computational Biology 17, no. 5 (May 10, 2021): e1008359. http://dx.doi.org/10.1371/journal.pcbi.1008359.
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How cells control the numbers of its subcellular components is a fundamental question in biology. Given that biosynthetic processes are fundamentally stochastic it is utterly puzzling that some structures display no copy number variation within a cell population. Centriole biogenesis, with each centriole being duplicated once and only once per cell cycle, stands out due to its remarkable fidelity. This is a highly controlled process, which depends on low-abundance rate-limiting factors. How can exactly one centriole copy be produced given the variation in the concentration of these key factors? Hitherto, tentative explanations of this control evoked lateral inhibition- or phase separation-like mechanisms emerging from the dynamics of these rate-limiting factors but how strict centriole number is regulated remains unsolved. Here, a novel solution to centriole copy number control is proposed based on the assembly of a centriolar scaffold, the cartwheel. We assume that cartwheel building blocks accumulate around the mother centriole at supercritical concentrations, sufficient to assemble one or more cartwheels. Our key postulate is that once the first cartwheel is formed it continues to elongate by stacking the intermediate building blocks that would otherwise form supernumerary cartwheels. Using stochastic models and simulations, we show that this mechanism may ensure formation of one and only one cartwheel robustly over a wide range of parameter values. By comparison to alternative models, we conclude that the distinctive signatures of this novel mechanism are an increasing assembly time with cartwheel numbers and the translation of stochasticity in building block concentrations into variation in cartwheel numbers or length.
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Stopard, Isaac J., Thomas S. Churcher, and Ben Lambert. "Estimating the extrinsic incubation period of malaria using a mechanistic model of sporogony." PLOS Computational Biology 17, no. 2 (February 16, 2021): e1008658. http://dx.doi.org/10.1371/journal.pcbi.1008658.
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During sporogony, malaria-causing parasites infect a mosquito, reproduce and migrate to the mosquito salivary glands where they can be transmitted the next time blood feeding occurs. The time required for sporogony, known as the extrinsic incubation period (EIP), is an important determinant of malaria transmission intensity. The EIP is typically estimated as the time for a given percentile, x, of infected mosquitoes to develop salivary gland sporozoites (the infectious parasite life stage), which is denoted by EIPx. Many mechanisms, however, affect the observed sporozoite prevalence including the human-to-mosquito transmission probability and possibly differences in mosquito mortality according to infection status. To account for these various mechanisms, we present a mechanistic mathematical model, which explicitly models key processes at the parasite, mosquito and observational scales. Fitting this model to experimental data, we find greater variation in the EIP than previously thought: we estimated the range between EIP10 and EIP90 (at 27°C) as 4.5 days compared to 0.9 days using existing statistical methods. This pattern holds over the range of study temperatures included in the dataset. Increasing temperature from 21°C to 34°C decreased the EIP50 from 16.1 to 8.8 days. Our work highlights the importance of mechanistic modelling of sporogony to (1) improve estimates of malaria transmission under different environmental conditions or disease control programs and (2) evaluate novel interventions that target the mosquito life stages of the parasite.
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Rombouts, Jan, and Lendert Gelens. "Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions." PLOS Computational Biology 17, no. 1 (January 7, 2021): e1008231. http://dx.doi.org/10.1371/journal.pcbi.1008231.
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Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent.
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Pedersen, Morten Gram, Alessia Tagliavini, and Jean-Claude Henquin. "Calcium signaling and secretory granule pool dynamics underlie biphasic insulin secretion and its amplification by glucose: experiments and modeling." American Journal of Physiology-Endocrinology and Metabolism 316, no. 3 (March 1, 2019): E475—E486. http://dx.doi.org/10.1152/ajpendo.00380.2018.
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Glucose-stimulated insulin secretion from pancreatic β-cells is controlled by a triggering pathway that culminates in calcium influx and regulated exocytosis of secretory granules, and by a less understood amplifying pathway that augments calcium-induced exocytosis. In response to an abrupt increase in glucose concentration, insulin secretion exhibits a first peak followed by a lower sustained second phase. This biphasic secretion pattern is disturbed in diabetes. It has been attributed to depletion and subsequent refilling of a readily releasable pool of granules or to the phasic cytosolic calcium dynamics induced by glucose. Here, we apply mathematical modeling to experimental data from mouse islets to investigate how calcium and granule pool dynamics interact to control dynamic insulin secretion. Experimental calcium traces are used as inputs in three increasingly complex models of pool dynamics, which are fitted to insulin secretory patterns obtained using a set of protocols of glucose and tolbutamide stimulation. New calcium and secretion data for so-called staircase protocols, in which the glucose concentration is progressively increased, are presented. These data can be reproduced without assuming any heterogeneity in the model, in contrast to previous modeling, because of nontrivial calcium dynamics. We find that amplification by glucose can be explained by increased mobilization and priming of granules. Overall, our results indicate that calcium dynamics contribute substantially to shaping insulin secretion kinetics, which implies that better insight into the events creating phasic calcium changes in human β-cells is needed to understand the cellular mechanisms that disturb biphasic insulin secretion in diabetes.
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Nagamori, Akira, Christopher M. Laine, Gerald E. Loeb, and Francisco J. Valero-Cuevas. "Force variability is mostly not motor noise: Theoretical implications for motor control." PLOS Computational Biology 17, no. 3 (March 8, 2021): e1008707. http://dx.doi.org/10.1371/journal.pcbi.1008707.
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Variability in muscle force is a hallmark of healthy and pathological human behavior. Predominant theories of sensorimotor control assume ‘motor noise’ leads to force variability and its ‘signal dependence’ (variability in muscle force whose amplitude increases with intensity of neural drive). Here, we demonstrate that the two proposed mechanisms for motor noise (i.e. the stochastic nature of motor unit discharge and unfused tetanic contraction) cannot account for the majority of force variability nor for its signal dependence. We do so by considering three previously underappreciated but physiologically important features of a population of motor units: 1) fusion of motor unit twitches, 2) coupling among motoneuron discharge rate, cross-bridge dynamics, and muscle mechanics, and 3) a series-elastic element to account for the aponeurosis and tendon. These results argue strongly against the idea that force variability and the resulting kinematic variability are generated primarily by ‘motor noise.’ Rather, they underscore the importance of variability arising from properties of control strategies embodied through distributed sensorimotor systems. As such, our study provides a critical path toward developing theories and models of sensorimotor control that provide a physiologically valid and clinically useful understanding of healthy and pathologic force variability.
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Yacoubi, S. El. "A mathematical method for control problems on cellular automata models." International Journal of Systems Science 39, no. 5 (May 2008): 529–38. http://dx.doi.org/10.1080/00207720701847232.
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Nakao, M., A. Karashima, and N. Katayama. "Mathematical models of regulatory mechanisms of sleep-wake rhythms." Cellular and Molecular Life Sciences 64, no. 10 (March 15, 2007): 1236–43. http://dx.doi.org/10.1007/s00018-007-6534-z.
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Sego, T. J., James A. Glazier, and Andres Tovar. "Unification of aggregate growth models by emergence from cellular and intracellular mechanisms." Royal Society Open Science 7, no. 8 (August 2020): 192148. http://dx.doi.org/10.1098/rsos.192148.
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Multicellular aggregate growth is regulated by nutrient availability and removal of metabolites, but the specifics of growth dynamics are dependent on cell type and environment. Classical models of growth are based on differential equations. While in some cases these classical models match experimental observations, they can only predict growth of a limited number of cell types and so can only be selectively applied. Currently, no classical model provides a general mathematical representation of growth for any cell type and environment. This discrepancy limits their range of applications, which a general modelling framework can enhance. In this work, a hybrid cellular Potts model is used to explain the discrepancy between classical models as emergent behaviours from the same mathematical system. Intracellular processes are described using probability distributions of local chemical conditions for proliferation and death and simulated. By fitting simulation results to a generalization of the classical models, their emergence is demonstrated. Parameter variations elucidate how aggregate growth may behave like one classical growth model or another. Three classical growth model fits were tested, and emergence of the Gompertz equation was demonstrated. Effects of shape changes are demonstrated, which are significant for final aggregate size and growth rate, and occur stochastically.
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Schall, Jeffrey D., Thomas J. Palmeri, and Gordon D. Logan. "Models of inhibitory control." Philosophical Transactions of the Royal Society B: Biological Sciences 372, no. 1718 (February 27, 2017): 20160193. http://dx.doi.org/10.1098/rstb.2016.0193.
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We survey models of response inhibition having different degrees of mathematical, computational and neurobiological specificity and generality. The independent race model accounts for performance of the stop-signal or countermanding task in terms of a race between GO and STOP processes with stochastic finishing times. This model affords insights into neurophysiological mechanisms that are reviewed by other authors in this volume. The formal link between the abstract GO and STOP processes and instantiating neural processes is articulated through interactive race models consisting of stochastic accumulator GO and STOP units. This class of model provides quantitative accounts of countermanding performance and replicates the dynamics of neural activity producing that performance. The interactive race can be instantiated in a network of biophysically plausible spiking excitatory and inhibitory units. Other models seek to account for interactions between units in frontal cortex, basal ganglia and superior colliculus. The strengths, weaknesses and relationships of the different models will be considered. We will conclude with a brief survey of alternative modelling approaches and a summary of problems to be addressed including accounting for differences across effectors, species, individuals, task conditions and clinical deficits. This article is part of the themed issue ‘Movement suppression: brain mechanisms for stopping and stillness’.
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Rodriguez-Brenes, Ignacio A., and Dominik Wodarz. "Preventing clonal evolutionary processes in cancer: Insights from mathematical models." Proceedings of the National Academy of Sciences 112, no. 29 (July 21, 2015): 8843–50. http://dx.doi.org/10.1073/pnas.1501730112.
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Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.
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Edwards, Andrew G., and William E. Louch. "Species-Dependent Mechanisms of Cardiac Arrhythmia: A Cellular Focus." Clinical Medicine Insights: Cardiology 11 (January 1, 2017): 117954681668606. http://dx.doi.org/10.1177/1179546816686061.
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Although ventricular arrhythmia remains a leading cause of morbidity and mortality, available antiarrhythmic drugs have limited efficacy. Disappointing progress in the development of novel, clinically relevant antiarrhythmic agents may partly be attributed to discrepancies between humans and animal models used in preclinical testing. However, such differences are at present difficult to predict, requiring improved understanding of arrhythmia mechanisms across species. To this end, we presently review interspecies similarities and differences in fundamental cardiomyocyte electrophysiology and current understanding of the mechanisms underlying the generation of afterdepolarizations and reentry. We specifically highlight patent shortcomings in small rodents to reproduce cellular and tissue-level arrhythmia substrate believed to be critical in human ventricle. Despite greater ease of translation from larger animal models, discrepancies remain and interpretation can be complicated by incomplete knowledge of human ventricular physiology due to low availability of explanted tissue. We therefore point to the benefits of mathematical modeling as a translational bridge to understanding and treating human arrhythmia.
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NAUROSCHAT, J., and U. AN DER HEIDEN. "NONLINEAR MATHEMATICAL MODELS OF HORMONAL SYSTEMS." Journal of Biological Systems 03, no. 03 (September 1995): 719–30. http://dx.doi.org/10.1142/s0218339095000666.
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The paper considers various approaches to mathematical modelling of endocrine systems. The functional and operational complexity of hormonal activities turns out to be the result of the cooperation of three factors: global feedback structures on the level of glands, subtle feedback and regulatory mechanisms on the level of single cells and molecules (including messengers, receptors and functional proteins like G-proteins) and finally, coupling to other organs (predominantly to the brain, e.g. via hypothalamus). To date, it is practically impossible to construct a mathematical model comprising together all these aspects. The paper aims at providing some major building bricks to such an endeavor. In the first part we summarize some of our recent models on the gobal structure of hormonal systems, in the form of nonlinear differential equations containing delay terms; oscillatory input from the brain is taken into account. Solutions of the equations display nearly all kinds of dynamical behaviour as stable limit cycles, phase locking, quasi-periodic and chaotic motions. Special emphasis is put on developing a mathematical model for the fine-tuned sequence of hormone-induced transmembrane signalling, where agonist couples to some cellular effector via transfer-proteins — this principle is widely spread among the hormone-targeted cells and crucially involved in regulating cells' behaviour towards external stimuli, e.g. their ability to desensitize as a reaction to sustained hormonal input.
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Takahashi, Daisuke, Yang Xiao, and Fei Hu. "A Survey of Insulin-Dependent Diabetes—Part II: Control Methods." International Journal of Telemedicine and Applications 2008 (2008): 1–14. http://dx.doi.org/10.1155/2008/739385.
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We survey blood glucose control schemes for insulin-dependent diabetes therapies and systems. These schemes largely rely on mathematical models of the insulin-glucose relations, and these models are typically derived in an empirical or fundamental way. In an empirical way, the experimental insulin inputs and resulting blood-glucose outputs are used to generate a mathematical model, which includes a couple of equations approximating a very complex system. On the other hand, the insulin-glucose relation is also explained from the well-known facts of other biological mechanisms. Since these mechanisms are more or less related with each other, a mathematical model of the insulin-glucose system can be derived from these surrounding relations. This kind of method of the mathematical model derivation is called a fundamental method. Along with several mathematical models, researchers develop autonomous systems whether they involve medical devices or not to compensate metabolic disorders and these autonomous systems employ their own control methods. Basically, in insulin-dependent diabetes therapies, control methods are classified into three categories: open-loop, closed-loop, and partially closed-loop controls. The main difference among these methods is how much the systems are open to the outside people.
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Sree Hari Rao, V., and P. Raja Sekhara Rao. "Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment." Chaos, Solitons & Fractals 28, no. 5 (June 2006): 1222–51. http://dx.doi.org/10.1016/j.chaos.2005.07.015.
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MELNIK, RODERICK V. N., XILIN WEI, and GABRIEL MORENO–HAGELSIEB. "NONLINEAR DYNAMICS OF CELL CYCLES WITH STOCHASTIC MATHEMATICAL MODELS." Journal of Biological Systems 17, no. 03 (September 2009): 425–60. http://dx.doi.org/10.1142/s0218339009002879.
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Cell cycles are fundamental components of all living organisms and their systematic studies extend our knowledge about the interconnection between regulatory, metabolic, and signaling networks, and therefore open new opportunities for our ultimate efficient control of cellular processes for disease treatments, as well as for a wide variety of biomedical and biotechnological applications. In the study of cell cycles, nonlinear phenomena play a paramount role, in particular in those cases where the cellular dynamics is in the focus of attention. Quantification of this dynamics is a challenging task due to a wide range of parameters that require estimations and the presence of many stochastic effects. Based on the originally deterministic model, in this paper we develop a hierarchy of models that allow us to describe the nonlinear dynamics accounting for special events of cell cycles. First, we develop a model that takes into account fluctuations of relative concentrations of proteins during special events of cell cycles. Such fluctuations are induced by varying rates of relative concentrations of proteins and/or by relative concentrations of proteins themselves. As such fluctuations may be responsible for qualitative changes in the cell, we develop a new model that accounts for the effect of cellular dynamics on the cell cycle. Finally, we analyze numerically nonlinear effects in the cell cycle by constructing phase portraits based on the newly developed model and carry out a parametric sensitivity analysis in order to identify parameters for an efficient cell cycle control. The results of computational experiments demonstrate that the metabolic events in gene regulatory networks can qualitatively influence the dynamics of the cell cycle.
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Bruce, David M. "Mathematical modelling of the cellular mechanics of plants." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no. 1437 (July 30, 2003): 1437–44. http://dx.doi.org/10.1098/rstb.2003.1337.
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The complex mechanical behaviour of plant tissues reflects the complexity of their structure and material properties. Modelling has been widely used in studies of how cell walls, single cells and tissue respond to loading, both externally applied loading and loads on the cell wall resulting from changes in the pressure within fluid–filled cells. This paper reviews what approaches have been taken to modelling and simulation of cell wall, cell and tissue mechanics, and to what extent models have been successful in predicting mechanical behaviour. Advances in understanding of cell wall ultrastructure and the control of cell growth present opportunities for modelling to clarify how growth–related mechanical properties arise from wall polymeric structure and biochemistry.
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Curcio, Luciano, Laura D'Orsi, and Andrea De Gaetano. "Seven Mathematical Models of Hemorrhagic Shock." Computational and Mathematical Methods in Medicine 2021 (June 3, 2021): 1–34. http://dx.doi.org/10.1155/2021/6640638.
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Although mathematical modelling of pressure-flow dynamics in the cardiocirculatory system has a lengthy history, readily finding the appropriate model for the experimental situation at hand is often a challenge in and of itself. An ideal model would be relatively easy to use and reliable, besides being ethically acceptable. Furthermore, it would address the pathogenic features of the cardiovascular disease that one seeks to investigate. No universally valid model has been identified, even though a host of models have been developed. The object of this review is to describe several of the most relevant mathematical models of the cardiovascular system: the physiological features of circulatory dynamics are explained, and their mathematical formulations are compared. The focus is on the whole-body scale mathematical models that portray the subject’s responses to hypovolemic shock. The models contained in this review differ from one another, both in the mathematical methodology adopted and in the physiological or pathological aspects described. Each model, in fact, mimics different aspects of cardiocirculatory physiology and pathophysiology to varying degrees: some of these models are geared to better understand the mechanisms of vascular hemodynamics, whereas others focus more on disease states so as to develop therapeutic standards of care or to test novel approaches. We will elucidate key issues involved in the modeling of cardiovascular system and its control by reviewing seven of these models developed to address these specific purposes.
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Oyarzún, Diego A., and Madalena Chaves. "Design of a bistable switch to control cellular uptake." Journal of The Royal Society Interface 12, no. 113 (December 2015): 20150618. http://dx.doi.org/10.1098/rsif.2015.0618.
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Bistable switches are widely used in synthetic biology to trigger cellular functions in response to environmental signals. All bistable switches developed so far, however, control the expression of target genes without access to other layers of the cellular machinery. Here, we propose a bistable switch to control the rate at which cells take up a metabolite from the environment. An uptake switch provides a new interface to command metabolic activity from the extracellular space and has great potential as a building block in more complex circuits that coordinate pathway activity across cell cultures, allocate metabolic tasks among different strains or require cell-to-cell communication with metabolic signals. Inspired by uptake systems found in nature, we propose to couple metabolite import and utilization with a genetic circuit under feedback regulation. Using mathematical models and analysis, we determined the circuit architectures that produce bistability and obtained their design space for bistability in terms of experimentally tuneable parameters. We found an activation–repression architecture to be the most robust switch because it displays bistability for the largest range of design parameters and requires little fine-tuning of the promoters' response curves. Our analytic results are based on on–off approximations of promoter activity and are in excellent qualitative agreement with simulations of more realistic models. With further analysis and simulation, we established conditions to maximize the parameter design space and to produce bimodal phenotypes via hysteresis and cell-to-cell variability. Our results highlight how mathematical analysis can drive the discovery of new circuits for synthetic biology, as the proposed circuit has all the hallmarks of a toggle switch and stands as a promising design to control metabolic phenotypes across cell cultures.
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Kimmel, M., and D. E. Axelrod. "Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity." Genetics 125, no. 3 (July 1, 1990): 633–44. http://dx.doi.org/10.1093/genetics/125.3.633.
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Abstract An increased number of copies of specific genes may offer an advantage to cells when they grow in restrictive conditions such as in the presence of toxic drugs, or in a tumor. Three mathematical models of gene amplification and deamplification are proposed to describe the kinetics of unstable phenotypes of cells with amplified genes. The models differ in details but all assume probabilistic mechanisms of increase and decrease in gene copy number per cell (gene amplification/deamplification). Analysis of the models indicates that a stable distribution of numbers of copies of genes per cell, observed experimentally, exists only if the probability of deamplification exceeds the probability of amplification. The models are fitted to published data on the loss of methotrexate resistance in cultured cell lines, due to the loss of amplified dihydrofolate reductase gene. For two mouse cell lines unstably resistant to methotrexate the probabilities of amplification and deamplification of the dihydrofolate reductase gene on double minute chromosomes are estimated to be approximately 2% and 10%, respectively. These probabilities are much higher than widely presumed. The models explain the gradual disappearance of the resistant phenotype when selective pressure is withdrawn, by postulating that the rate of deamplification exceeds the rate of amplification. Thus it is not necessary to invoke a growth advantage of nonresistant cells which has been the standard explanation. For another analogous process, the loss of double minute chromosomes containing the myc oncogene from SEWA tumor cells, the growth advantage model does seem to be superior to the amplification and deamplification model. In a more theoretical section of the paper, it is demonstrated that gene amplification/deamplification can result in reduction to homozygosity, such as is observed in some tumors. Other applications are discussed.
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Asano, Daiki, Masaki Hokazono, Shogo Hirano, Akane Morita, and Tsutomu Nakahara. "Cellular Mechanisms of Angiogenesis in Neonatal Rat Models of Retinal Neurodegeneration." International Journal of Molecular Sciences 20, no. 19 (September 25, 2019): 4759. http://dx.doi.org/10.3390/ijms20194759.
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Νeuronal and glial cells play an important role in the development of vasculature in the retina. In this study, we investigated whether re-vascularization occurs in retinal neurodegenerative injury models. To induce retinal injury, N-methyl-D-aspartic acid (NMDA, 200 nmol) or kainic acid (KA, 20 nmol) was injected into the vitreous chamber of the eye on postnatal day (P)7. Morphological changes in retinal neurons and vasculature were assessed on P14, P21, and P35. Prevention of vascular growth and regression of some capillaries were observed on P14 in retinas of NMDA- and KA-treated eyes. However, vascular growth and re-vascularization started on P21, and the retinal vascular network was established by P35 in retinas with neurodegenerative injuries. The re-vascularization was suppressed by a two-day treatment with KRN633, an inhibitor of VEGF receptor tyrosine kinase, on P21 and P22. Astrocytes and Müller cells expressed vascular endothelial growth factor (VEGF), and the distribution pattern of VEGF was almost the same between the control and the NMDA-induced retinal neurodegenerative injury model, except for the difference in the thickness of the inner retinal layer. During re-vascularization, angiogenic sprouts from pre-existing blood vessels were present along the network of fibronectins formed by astrocytes. These results suggest that glial cells contribute to angiogenesis in neonatal rat models of retinal neurodegeneration.
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Лихошвай, В. А., and V. A. Likhoshvai. "Phenotypic Variability of Bacterial Cell Cycle: Mathematical Model." Mathematical Biology and Bioinformatics 11, no. 1 (May 20, 2016): 91–113. http://dx.doi.org/10.17537/2016.11.91.
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The results of the study of mechanisms of different cell phenotypes occurrence in a genetically homogenous population using the bacterial cell cycle model are presented. It was shown that phenotypic variability represents an internal, immanent property of bacteria. The basis of this phenomenon is universal non-linear properties of the conjugated transcription-translation system, that controls all cellular processes. Phenotypic variability occurs in a simple, deterministic, self-reproducing system under the uniform transmission of the structural components to the daughter cells during division and in the absence of any special control mechanisms of molecular-genetic processes and enzymatic reactions.
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Vanin, Viktor, Mykola Kruhol, and Oleksandr Lasurenko. "MATHEMATICAL MODELLING OF ONE-GROUP GAS-HYDRAULIC CIRCUIT OF THERMAL POWER PLANT STEAM BOILER AUXILIARIES." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1 (March 5, 2021): 3–14. http://dx.doi.org/10.20998/2222-0631.2020.01.01.
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The paper presents algebraic mathematical models of centrifugal mechanisms that operate in the power boiler gas-hydraulic circuit. The models have been built by means of head-flow curve approximation. The head-flow curve depends on the centrifugal mechanism blade rotating speed and guide vane angle. The least squares method has been applied for centrifugal mechanism head-curve approximation on the basis of experimental or numerical data. Different configurations for the connections of centrifugal mechanisms in the power boiler gas-hydraulic circuit have been considered, relationships for their performance assessment obtained, and efficiency factors for various methods of their capacity control introduced. The state equation for a complex gas-hydraulic network in the problem of its efficiency analysis has been obtained with application of Kirchhoff laws. Numerical algorithms have been developed to solve group control parameter optimization problems for the considered connections of centrifugal mechanisms. Features of mathematical models for groups of series-, parallel- and complex-connected centrifugal mechanisms with different head curves in the power boiler maintenance system have been specified. An optimal group control problem for a group of centrifugal mechanisms has been formulated and solved under various power boiler modes. For the feed pumps, individual frequency control proves to be the most effective method, while for the boiler draft mechanisms group frequency regulation turns out to be the most efficient. In a typical summer month, implementation of energy-efficient centrifugal mechanism capacity regulation method in a Thermal Power Plant is shown to result in auxiliary electricity consumption reduction by 10.96 % as compared with available actual data.
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Goryachev, Andrew B., and Marcin Leda. "Many roads to symmetry breaking: molecular mechanisms and theoretical models of yeast cell polarity." Molecular Biology of the Cell 28, no. 3 (February 2017): 370–80. http://dx.doi.org/10.1091/mbc.e16-10-0739.
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Mathematical modeling has been instrumental in identifying common principles of cell polarity across diverse systems. These principles include positive feedback loops that are required to destabilize a spatially uniform state of the cell. The conserved small G-protein Cdc42 is a master regulator of eukaryotic cellular polarization. Here we discuss recent developments in studies of Cdc42 polarization in budding and fission yeasts and demonstrate that models describing symmetry-breaking polarization can be classified into six minimal classes based on the structure of positive feedback loops that activate and localize Cdc42. Owing to their generic system-independent nature, these model classes are also likely to be relevant for the G-protein–based symmetry-breaking systems of higher eukaryotes. We review experimental evidence pro et contra different theoretically plausible models and conclude that several parallel and non–mutually exclusive mechanisms are likely involved in cellular polarization of yeasts. This potential redundancy needs to be taken into consideration when interpreting the results of recent cell-rewiring studies.
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Bayly, P. V., and K. S. Wilson. "Analysis of unstable modes distinguishes mathematical models of flagellar motion." Journal of The Royal Society Interface 12, no. 106 (May 2015): 20150124. http://dx.doi.org/10.1098/rsif.2015.0124.
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The mechanisms underlying the coordinated beating of cilia and flagella remain incompletely understood despite the fundamental importance of these organelles. The axoneme (the cytoskeletal structure of cilia and flagella) consists of microtubule doublets connected by passive and active elements. The motor protein dynein is known to drive active bending, but dynein activity must be regulated to generate oscillatory, propulsive waveforms. Mathematical models of flagellar motion generate quantitative predictions that can be analysed to test hypotheses concerning dynein regulation. One approach has been to seek periodic solutions to the linearized equations of motion. However, models may simultaneously exhibit both periodic and unstable modes. Here, we investigate the emergence and coexistence of unstable and periodic modes in three mathematical models of flagellar motion, each based on a different dynein regulation hypothesis: (i) sliding control; (ii) curvature control and (iii) control by interdoublet separation (the ‘geometric clutch’ (GC)). The unstable modes predicted by each model are used to critically evaluate the underlying hypothesis. In particular, models of flagella with ‘sliding-controlled’ dynein activity admit unstable modes with non-propulsive, retrograde (tip-to-base) propagation, sometimes at the same parameter values that lead to periodic, propulsive modes. In the presence of these retrograde unstable modes, stable or periodic modes have little influence. In contrast, unstable modes of the GC model exhibit switching at the base and propulsive base-to-tip propagation.
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Vukobratović, M. K., V. F. Filaretov, and A. I. Korzun. "A unified approach to mathematical modelling of robotic manipulator dynamics." Robotica 12, no. 5 (September 1994): 411–20. http://dx.doi.org/10.1017/s0263574700017963.
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SUMMARYA new method for computer forming of dynamic equations of open-chain mechanical robot configurations is presented. The algorithm used is of a numeric-iterative type, based on mathematical apparatus of screw theory, which has enabled elimination of the unnecessary computations in the process of dynamic model derivation. In addition to conventional kinematic schemes of robotic manipulators, the branched kinematic chains which have recently found their application in the locomotion of robotic mechanisms were also treated. Both the inverse and direct problems of dynamics were addressed. A comparative analysis was carried out of the numerical complexity of various existing algorithms of numeric-iterative type dealing with the problems of spatial active mechanisms dynamics. It has been shown that the proposed method regardless of its generality, approaches by its models complexity symbolic models, which are valid for particular robotic mechanisms only where they achieve a high degree of efficiency.
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Cicuttin, A., L. De Micco, M. L. Crespo, M. Antonelli, L. Garcia, and W. Florian. "Physical implementation of asynchronous cellular automata networks: mathematical models and preliminary experimental results." Nonlinear Dynamics 105, no. 3 (July 31, 2021): 2431–52. http://dx.doi.org/10.1007/s11071-021-06754-z.
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de Jong, Hidde, Stefano Casagranda, Nils Giordano, Eugenio Cinquemani, Delphine Ropers, Johannes Geiselmann, and Jean-Luc Gouzé. "Mathematical modelling of microbes: metabolism, gene expression and growth." Journal of The Royal Society Interface 14, no. 136 (November 2017): 20170502. http://dx.doi.org/10.1098/rsif.2017.0502.
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The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.
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Racković, Miloš, Miomir Vukobratović, and Dusan Surla. "Generation of dynamic models of complex robotic mechanisms in symbolic form." Robotica 16, no. 1 (January 1998): 23–36. http://dx.doi.org/10.1017/s0263574798000125.
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A system to control a database is used for modelling of robotic mechanisms. This brings up the modelling process of robotic mechanisms to a higher level of abstraction and reduces the problem of numerical complexity reduction of the robotic mechanism model to database updating. Structural System Analysis was used to describe the functionality of the system for modelling of robotic mechanisms. The database model is presented by Extended Model Object-Connections, and all the object types for representation of mathematical expressions in the form of calculating graph are described in detail. The complete system is implemented and tested on the example of a robotic mechanism with six degrees of freedom and on the example of anthropomorphic locomotion robotic mechanism.
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SCIALDONE, ANTONIO, and MARIO NICODEMI. "STATISTICAL MECHANICS MODELS FOR X-CHROMOSOME INACTIVATION." Advances in Complex Systems 13, no. 03 (June 2010): 367–76. http://dx.doi.org/10.1142/s0219525910002566.
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We present statistical mechanics models to understand the physical and molecular mechanisms of X-Chromosome Inactivation (XCI), the process whereby a female mammal cell inactivates one of its two X-chromosomes. During XCI, X-chromosomes undergo a series of complex regulatory processes. At the beginning of XCI, the X's recognize and pair, then only one X which is randomly chosen is inactivated. Afterwards, the two X's move to different positions in the cell nucleus according to their different status (active/silenced). Our models illustrate about the still mysterious physical bases underlying all these regulatory steps, i.e., X-chromosome pairing, random choice of inactive X, and "shuttling" of the X's to their post-XCI locations. Our models are based on general and robust thermodynamic roots, and their validity can go beyond XCI, to explain analogous regulatory mechanisms in a variety of cellular processes.
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Yahaya, B. "Understanding Cellular Mechanisms Underlying Airway Epithelial Repair: Selecting the Most Appropriate Animal Models." Scientific World Journal 2012 (2012): 1–12. http://dx.doi.org/10.1100/2012/961684.
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Understanding the mechanisms underlying the process of regeneration and repair of airway epithelial structures demands close characterization of the associated cellular and molecular events. The choice of an animal model system to study these processes and the role of lung stem cells is debatable since ideally the chosen animal model should offer a valid comparison with the human lung. Species differences may include the complex three-dimensional lung structures, cellular composition of the lung airway as well as transcriptional control of the molecular events in response to airway epithelium regeneration, and repair following injury. In this paper, we discuss issues related to the study of the lung repair and regeneration including the role of putative stem cells in small- and large-animal models. At the end of this paper, the author discuss the potential for using sheep as a model which can help bridge the gap between small-animal model systems and humans.
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Haurie, Caroline, David C. Dale, and Michael C. Mackey. "Cyclical Neutropenia and Other Periodic Hematological Disorders: A Review of Mechanisms and Mathematical Models." Blood 92, no. 8 (October 15, 1998): 2629–40. http://dx.doi.org/10.1182/blood.v92.8.2629.
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Abstract Although all blood cells are derived from hematopoietic stem cells, the regulation of this production system is only partially understood. Negative feedback control mediated by erythropoietin and thrombopoietin regulates erythrocyte and platelet production, respectively, but the regulation of leukocyte levels is less well understood. The local regulatory mechanisms within the hematopoietic stem cells are also not well characterized at this point. Because of their dynamic character, cyclical neutropenia and other periodic hematological disorders offer a rare opportunity to more fully understand the nature of these regulatory processes. We review the salient clinical and laboratory features of cyclical neutropenia (and the less common disorders periodic chronic myelogenous leukemia, periodic auto-immune hemolytic anemia, polycythemia vera, aplastic anemia, and cyclical thrombocytopenia) and the insight into these diseases afforded by mathematical modeling. We argue that the available evidence indicates that the locus of the defect in most of these dynamic diseases is at the stem cell level (auto-immune hemolytic anemia and cyclical thrombocytopenia seem to be the exceptions). Abnormal responses to growth factors or accelerated cell loss through apoptosis may play an important role in the genesis of these disorders. © 1998 by The American Society of Hematology.
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Haurie, Caroline, David C. Dale, and Michael C. Mackey. "Cyclical Neutropenia and Other Periodic Hematological Disorders: A Review of Mechanisms and Mathematical Models." Blood 92, no. 8 (October 15, 1998): 2629–40. http://dx.doi.org/10.1182/blood.v92.8.2629.420a35_2629_2640.
Full textAbstract:
Although all blood cells are derived from hematopoietic stem cells, the regulation of this production system is only partially understood. Negative feedback control mediated by erythropoietin and thrombopoietin regulates erythrocyte and platelet production, respectively, but the regulation of leukocyte levels is less well understood. The local regulatory mechanisms within the hematopoietic stem cells are also not well characterized at this point. Because of their dynamic character, cyclical neutropenia and other periodic hematological disorders offer a rare opportunity to more fully understand the nature of these regulatory processes. We review the salient clinical and laboratory features of cyclical neutropenia (and the less common disorders periodic chronic myelogenous leukemia, periodic auto-immune hemolytic anemia, polycythemia vera, aplastic anemia, and cyclical thrombocytopenia) and the insight into these diseases afforded by mathematical modeling. We argue that the available evidence indicates that the locus of the defect in most of these dynamic diseases is at the stem cell level (auto-immune hemolytic anemia and cyclical thrombocytopenia seem to be the exceptions). Abnormal responses to growth factors or accelerated cell loss through apoptosis may play an important role in the genesis of these disorders. © 1998 by The American Society of Hematology.
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Lin, Yen Ting, Eugene T. Y. Chang, Julie Eatock, Tobias Galla, and Richard H. Clayton. "Mechanisms of stochastic onset and termination of atrial fibrillation studied with a cellular automaton model." Journal of The Royal Society Interface 14, no. 128 (March 2017): 20160968. http://dx.doi.org/10.1098/rsif.2016.0968.
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Mathematical models of cardiac electrical excitation are increasingly complex, with multiscale models seeking to represent and bridge physiological behaviours across temporal and spatial scales. The increasing complexity of these models makes it computationally expensive to both evaluate long term (more than 60 s) behaviour and determine sensitivity of model outputs to inputs. This is particularly relevant in models of atrial fibrillation (AF), where individual episodes last from seconds to days, and interepisode waiting times can be minutes to months. Potential mechanisms of transition between sinus rhythm and AF have been identified but are not well understood, and it is difficult to simulate AF for long periods of time using state-of-the-art models. In this study, we implemented a Moe-type cellular automaton on a novel, topologically equivalent surface geometry of the left atrium. We used the model to simulate stochastic initiation and spontaneous termination of AF, arising from bursts of spontaneous activation near pulmonary veins. The simplified representation of atrial electrical activity reduced computational cost, and so permitted us to investigate AF mechanisms in a probabilistic setting. We computed large numbers (approx. 10 5 ) of sample paths of the model, to infer stochastic initiation and termination rates of AF episodes using different model parameters. By generating statistical distributions of model outputs, we demonstrated how to propagate uncertainties of inputs within our microscopic level model up to a macroscopic level. Lastly, we investigated spontaneous termination in the model and found a complex dependence on its past AF trajectory, the mechanism of which merits future investigation.
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Xu, Xiang Rong, Qi Wang, Hao Xu, and Liang Liang Li. "Development of Mathematical Modeling and Dynamics for Biofilms." Advanced Materials Research 749 (August 2013): 93–98. http://dx.doi.org/10.4028/www.scientific.net/amr.749.93.
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Biofilm formation, structure and dynamics properties play an important role in the effective performance of biofilm wastewater treatment reactors. Biofilm models are commonly used as simulation tools in engineering applications and as research tools to study biofilm formation and dynamics. This paper briefly outlines the present and past status of research on biofilm modeling, dynamics and experimental results. Biofilms constitute a spectrum of dynamical microorganisms, whose interaction with the surrounding environment and thereby induced dynamics dominates the complex properties of the living microorganism. Modeling of biofilms began with a low dimensional continuum description first based on kinematics and translational diffusions; later, more sophisticated microscopic dynamical mechanisms are introduced leading to the anomalous diffusion and dissipation encountered by various components in biofilms. We classify the models into roughly four classes: the reaction-diffusion dynamics model, the Capdeville biofilm growth dynamics model, the Cellular automata (CA) model, and the Phase field biofilm dynamical model.
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Li, Zixiang, Mukund Nilakantan Janardhanan, Peter Nielsen, and Qiuhua Tang. "Mathematical models and simulated annealing algorithms for the robotic assembly line balancing problem." Assembly Automation 38, no. 4 (September 3, 2018): 420–36. http://dx.doi.org/10.1108/aa-09-2017-115.
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Purpose Robots are used in assembly lines because of their higher flexibility and lower costs. The purpose of this paper is to develop mathematical models and simulated annealing algorithms to solve the robotic assembly line balancing (RALB-II) to minimize the cycle time. Design/methodology/approach Four mixed-integer linear programming models are developed and encoded in CPLEX solver to find optimal solutions for small-sized problem instances. Two simulated annealing algorithms, original simulated annealing algorithm and restarted simulated annealing (RSA) algorithm, are proposed to tackle large-sized problems. The restart mechanism in the RSA methodology replaces the incumbent temperature with a new temperature. In addition, the proposed methods use iterative mechanisms for updating cycle time and a new objective to select the solution with fewer critical workstations. Findings The comparative study among the tested algorithms and other methods adapted verifies the effectiveness of the proposed methods. The results obtained by these algorithms on the benchmark instances show that 23 new upper bounds out of 32 tested cases are achieved. The RSA algorithm ranks first among the algorithms in the number of updated upper bounds. Originality/value Four models are developed for RALBP-II and their performance is evaluated for the first time. An RSA algorithm is developed to solve RALBP-II, where the restart mechanism is developed to replace the incumbent temperature with a new temperature. The proposed methods also use iterative mechanisms and a new objective to select the solution with fewer critical workstations.
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Siddall, Robert, Victor Ibanez, Greg Byrnes, Robert J. Full, and Ardian Jusufi. "Mechanisms for Mid-Air Reorientation Using Tail Rotation in Gliding Geckos." Integrative and Comparative Biology 61, no. 2 (June 18, 2021): 478–90. http://dx.doi.org/10.1093/icb/icab132.
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Abstract Arboreal animals face numerous challenges when negotiating complex three-dimensional terrain. Directed aerial descent or gliding flight allows for rapid traversal of arboreal environments, but presents control challenges. Some animals, such as birds or gliding squirrels, have specialized structures to modulate aerodynamic forces while airborne. However, many arboreal animals do not possess these specializations but still control posture and orientation in mid-air. One of the largest inertial segments in lizards is their tail. Inertial reorientation can be used to attain postures appropriate for controlled aerial descent. Here, we discuss the role of tail inertia in a range of mid-air reorientation behaviors using experimental data from geckos in combination with mathematical and robotic models. Geckos can self-right in mid-air by tail rotation alone. Equilibrium glide behavior of geckos in a vertical wind tunnel show that they can steer toward a visual stimulus by using rapid, circular tail rotations to control pitch and yaw. Multiple coordinated tail responses appear to be required for the most effective terminal velocity gliding. A mathematical model allows us to explore the relationship between morphology and the capacity for inertial reorientation by conducting sensitivity analyses, and testing control approaches. Robotic models further define the limits of performance and generate new control hypotheses. Such comparative analysis allows predictions about the diversity of performance across lizard morphologies, relative limb proportions, and provides insights into the evolution of aerial behaviors.
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JIANG, YU, and WEIQUN WANG. "POTENTIAL MECHANISMS OF CANCER PREVENTION BY WEIGHT CONTROL." Biophysical Reviews and Letters 03, no. 03 (July 2008): 421–37. http://dx.doi.org/10.1142/s1793048008000824.
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Weight control via dietary caloric restriction and/or physical activity has been demonstrated in animal models for cancer prevention. However, the underlying mechanisms are not fully understood. Body weight loss due to negative energy balance significantly reduces some metabolic growth factors and endocrinal hormones such as IGF-1, leptin, and adiponectin, but enhances glucocorticoids, that may be associated with anti-cancer mechanisms. In this review, we summarized the recent studies related to weight control and growth factors. The potential molecular targets focused on those growth factors- and hormones-dependent cellular signaling pathways are further discussed. It appears that multiple factors and multiple signaling cascades, especially for Ras-MAPK-proliferation and PI3K-Akt-anti-apoptosis, could be involved in response to weight change by dietary calorie restriction and/or exercise training. Considering prevalence of obesity or overweight that becomes apparent over the world, understanding the underlying mechanisms among weight control, endocrine change and cancer risk is critically important. Future studies using "-omics" technologies will be warrant for a broader and deeper mechanistic information regarding cancer prevention by weight control.
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Albanese, Antonio, Limei Cheng, Mauro Ursino, and Nicolas W. Chbat. "An integrated mathematical model of the human cardiopulmonary system: model development." American Journal of Physiology-Heart and Circulatory Physiology 310, no. 7 (April 1, 2016): H899—H921. http://dx.doi.org/10.1152/ajpheart.00230.2014.
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Several cardiovascular and pulmonary models have been proposed in the last few decades. However, very few have addressed the interactions between these two systems. Our group has developed an integrated cardiopulmonary model (CP Model) that mathematically describes the interactions between the cardiovascular and respiratory systems, along with their main short-term control mechanisms. The model has been compared with human and animal data taken from published literature. Due to the volume of the work, the paper is divided in two parts. The present paper is on model development and normophysiology, whereas the second is on the model's validation on hypoxic and hypercapnic conditions. The CP Model incorporates cardiovascular circulation, respiratory mechanics, tissue and alveolar gas exchange, as well as short-term neural control mechanisms acting on both the cardiovascular and the respiratory functions. The model is able to simulate physiological variables typically observed in adult humans under normal and pathological conditions and to explain the underlying mechanisms and dynamics.
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Namani, Ravi, Yoram Lanir, Lik Chuan Lee, and Ghassan S. Kassab. "Overview of mathematical modeling of myocardial blood flow regulation." American Journal of Physiology-Heart and Circulatory Physiology 318, no. 4 (April 1, 2020): H966—H975. http://dx.doi.org/10.1152/ajpheart.00563.2019.
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The oxygen consumption by the heart and its extraction from the coronary arterial blood are the highest among all organs. Any increase in oxygen demand due to a change in heart metabolic activity requires an increase in coronary blood flow. This functional requirement of adjustment of coronary blood flow is mediated by coronary flow regulation to meet the oxygen demand without any discomfort, even under strenuous exercise conditions. The goal of this article is to provide an overview of the theoretical and computational models of coronary flow regulation and to reveal insights into the functioning of a complex physiological system that affects the perfusion requirements of the myocardium. Models for three major control mechanisms of myogenic, flow, and metabolic control are presented. These explain how the flow regulation mechanisms operating over multiple spatial scales from the precapillaries to the large coronary arteries yield the myocardial perfusion characteristics of flow reserve, autoregulation, flow dispersion, and self-similarity. The review not only introduces concepts of coronary blood flow regulation but also presents state-of-the-art advances and their potential to impact the assessment of coronary microvascular dysfunction (CMD), cardiac-coronary coupling in metabolic diseases, and therapies for angina and heart failure. Experimentalists and modelers not trained in these models will have exposure through this review such that the nonintuitive and highly nonlinear behavior of coronary physiology can be understood from a different perspective. This survey highlights knowledge gaps, key challenges, future research directions, and novel paradigms in the modeling of coronary flow regulation.