Peter Hinow - Academia.edu (original) (raw)
Papers by Peter Hinow
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009
Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior b... more Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo referred to as dynamic instability. We propose a general mathematical model that accounts for the growth, catastrophe, rescue, and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization. While attempting to use a minimal number of adjustable parameters, the proposed model covers a broad range of behaviors and has predictive features discussed in the paper. We have analyzed the range of resultant dynamical behavior of the microtubules by changing each of the parameter values at a time and observing the emergence of various dynamical regimes that agree well with the previously reported experimental data and behavior.
SIMULATION, 2014
Matrix tablets are drug delivery devices designed to release a drug in a controlled manner over a... more Matrix tablets are drug delivery devices designed to release a drug in a controlled manner over an extended period of time. We develop a cellular automaton (CA) model for the dissolution and release of a water-soluble drug and excipient from a matrix tablet of water-insoluble polymer. Cells of the CA are occupied by drug, excipient, water or polymer and the CA updating rules simulate the dissolution of drug and excipient and the subsequent diffusion of the dissolved substances. In addition we simulate the possible fracture of brittle drug and excipient powders during the tablet compression and the melting of the polymer during a possible thermal curing process. Different stirring mechanisms that facilitate the transport of dissolved drug in the fluid in which the tablet is immersed are modeled in the water cells adjacent to the boundary of the tablet. We find that our simulations can reproduce experimental drug release profiles. Our simulation tool can be used to streamline the formulation and production of sustained release tablets.
Journal of Liposome Research, 2012
We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membra... more We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membrane permeability is modified by the binding of different bile salts to the leaflets of the lipid bilayer. We find that the permeability of the liposomal bilayer depends on the difference in the concentrations of bile salt in the inner and outer leaflets and is only minimally influenced by the total concentration of bile salt in the bilayer. Deoxycholate and cholate are found to behave similarly in enhancing permeability for limited times, whereas the novel bile salt, 12-monoketocholate, flips from the outer to inner leaflet slowly, thereby enhancing membrane permeability for a prolonged time.
… methods in medicine, 2009
Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a ... more Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a tumour promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cellcell adhesion. Coupling mathematical modelling and experiments, we investigate ...
Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks... more Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks. An important example is the migration of tumour cells through collagen networks during the process of metastasis formation. We investigate the mesenchymal motion model proposed by T. Hillen in in higher dimensions. We formulate the problem as an evolution equation in a Banach space of measure-valued functions and use methods from semigroup theory to show the global existence of classical solutions. We investigate steady states of the model and show that patterns of network type exist as steady states. For the case of constant fibre distribution, we find an explicit solution and we prove the convergence to the parabolic limit.
We propose a hybrid dynamical system approach to model the evolution of a pathogen that experienc... more We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a version of the Fisher-Haldane-Wright equation while the switching between environments follows a Markov process with a given generator matrix. We investigate how the qualitative behavior of a simple single-host deterministic system changes when the stochastic switching process is added. In particular, we study the exchange of stability between monomorphic equilibria. Our results are consistent with the view that in a fluctuating environment, the genotype with the highest mean fitness will eventually become fixed. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.
![Research paper thumbnail of Corrigendum to “Pathogen evolution in switching environments: A hybrid dynamical system approach”[Math. Biosci. 240 (2012) 70–75]](https://attachments.academia-assets.com/43560946/thumbnails/1.jpg)
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We introduce and investigate a series of models for an infection of a diplodiploid host species b... more We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.
We consider a linear size-structured population model with diffusion in the size-space. Individua... more We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary conditions. This allows modelling of "adhesion" at extremely small or large sizes. We establish existence and positivity of solutions by showing that solutions are governed by a positive quasicontractive semigroup of linear operators on the biologically relevant state space. This is carried out via establishing dissipativity of a suitably perturbed semigroup generator. We also show that solutions of the model exhibit balanced exponential growth, that is our model admits a finite dimensional global attractor. In case of strictly positive fertility we are able to establish that solutions in fact exhibit asynchronous exponential growth.
We study the problem of transfer in a population structured by a continuum variable corresponding... more We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernels corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
In this paper we develop two mathematical models to predict the release kinetics of a water solub... more In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of partial differential equations. The predictions of both models show good qualitative agreement with experimental release curves. The models will provide tools for designing better controlled release devices.
We study the motility behavior of the unicellular protozoan Paramecium tetraurelia in a microflui... more We study the motility behavior of the unicellular protozoan Paramecium tetraurelia in a microfluidic device that can be prepared with a landscape of attracting or repelling chemicals. We investigate the spatial distribution of the positions of the individuals at different time points with methods from spatial statistics and Poisson random point fields. This makes quantitative the informal notion of ''uniform distribution'' (or lack thereof). Our device is characterized by the absence of large systematic biases due to gravitation and fluid flow. It has the potential to be applied to the study of other aquatic chemosensitive organisms as well. This may result in better diagnostic devices for environmental pollutants.
Mathematical Biosciences and Engineering, 2009
In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of... more In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.
Mathematical Modelling of Natural Phenomena, 2010
Motivated by structured parasite populations in aquaculture we consider a class of size-structure... more Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then, we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In the case of a separable fertility function, we deduce a characteristic equation, and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.
Physical biology, Aug 12, 2011
We propose a stochastic model that accounts for the growth, catastrophe and rescue processes of s... more We propose a stochastic model that accounts for the growth, catastrophe and rescue processes of steady-state microtubules assembled from MAP-free tubulin in the possible presence of a microtubule-associated drug. As an example of the latter, we both experimentally and theoretically study the perturbation of microtubule dynamic instability by S-methyl-D-DM1, a synthetic derivative of the microtubule-targeted agent maytansine and a potential anticancer agent. Our model predicts that among the drugs that act locally at the ...
Theoretical Biology and Medical Modelling, 2006
Background: Regular," moderate", physical exercise is an established non-pharmacologica... more Background: Regular," moderate", physical exercise is an established non-pharmacological form of treatment for depressive disorders. Brain lateralization has a significant role in the progress of depression. External stimuli such as various stressors or exercise influence the higher functions of the brain (cognition and affect). These effects often do not follow a linear course. Therefore, nonlinear dynamics seem best suited for modeling many of the phenomena, and putative global pathways in the brain, attributable to such ...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009
Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior b... more Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo referred to as dynamic instability. We propose a general mathematical model that accounts for the growth, catastrophe, rescue, and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization. While attempting to use a minimal number of adjustable parameters, the proposed model covers a broad range of behaviors and has predictive features discussed in the paper. We have analyzed the range of resultant dynamical behavior of the microtubules by changing each of the parameter values at a time and observing the emergence of various dynamical regimes that agree well with the previously reported experimental data and behavior.
SIMULATION, 2014
Matrix tablets are drug delivery devices designed to release a drug in a controlled manner over a... more Matrix tablets are drug delivery devices designed to release a drug in a controlled manner over an extended period of time. We develop a cellular automaton (CA) model for the dissolution and release of a water-soluble drug and excipient from a matrix tablet of water-insoluble polymer. Cells of the CA are occupied by drug, excipient, water or polymer and the CA updating rules simulate the dissolution of drug and excipient and the subsequent diffusion of the dissolved substances. In addition we simulate the possible fracture of brittle drug and excipient powders during the tablet compression and the melting of the polymer during a possible thermal curing process. Different stirring mechanisms that facilitate the transport of dissolved drug in the fluid in which the tablet is immersed are modeled in the water cells adjacent to the boundary of the tablet. We find that our simulations can reproduce experimental drug release profiles. Our simulation tool can be used to streamline the formulation and production of sustained release tablets.
Journal of Liposome Research, 2012
We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membra... more We propose a mathematical model for the release of carboxyfluorescein from liposomes whose membrane permeability is modified by the binding of different bile salts to the leaflets of the lipid bilayer. We find that the permeability of the liposomal bilayer depends on the difference in the concentrations of bile salt in the inner and outer leaflets and is only minimally influenced by the total concentration of bile salt in the bilayer. Deoxycholate and cholate are found to behave similarly in enhancing permeability for limited times, whereas the novel bile salt, 12-monoketocholate, flips from the outer to inner leaflet slowly, thereby enhancing membrane permeability for a prolonged time.
… methods in medicine, 2009
Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a ... more Transforming growth factor (TGF)-β is known to have properties of both a tumour suppressor and a tumour promoter. While it inhibits cell proliferation, it also increases cell motility and decreases cellcell adhesion. Coupling mathematical modelling and experiments, we investigate ...
Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks... more Mesenchymal motion describes the movement of cells in biological tissues formed by fibre networks. An important example is the migration of tumour cells through collagen networks during the process of metastasis formation. We investigate the mesenchymal motion model proposed by T. Hillen in in higher dimensions. We formulate the problem as an evolution equation in a Banach space of measure-valued functions and use methods from semigroup theory to show the global existence of classical solutions. We investigate steady states of the model and show that patterns of network type exist as steady states. For the case of constant fibre distribution, we find an explicit solution and we prove the convergence to the parabolic limit.
We propose a hybrid dynamical system approach to model the evolution of a pathogen that experienc... more We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a version of the Fisher-Haldane-Wright equation while the switching between environments follows a Markov process with a given generator matrix. We investigate how the qualitative behavior of a simple single-host deterministic system changes when the stochastic switching process is added. In particular, we study the exchange of stability between monomorphic equilibria. Our results are consistent with the view that in a fluctuating environment, the genotype with the highest mean fitness will eventually become fixed. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.
We introduce and investigate a series of models for an infection of a diplodiploid host species b... more We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model.
We consider a linear size-structured population model with diffusion in the size-space. Individua... more We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary conditions. This allows modelling of "adhesion" at extremely small or large sizes. We establish existence and positivity of solutions by showing that solutions are governed by a positive quasicontractive semigroup of linear operators on the biologically relevant state space. This is carried out via establishing dissipativity of a suitably perturbed semigroup generator. We also show that solutions of the model exhibit balanced exponential growth, that is our model admits a finite dimensional global attractor. In case of strictly positive fertility we are able to establish that solutions in fact exhibit asynchronous exponential growth.
We study the problem of transfer in a population structured by a continuum variable corresponding... more We study the problem of transfer in a population structured by a continuum variable corresponding to the quantity being transferred. The transfer of the quantity occurs between individuals according to specified rules. The model is of Boltzmann type with kernels corresponding to the transfer process. We prove that the transfer process preserves total mass of the transferred quantity and the solutions of the simple model converge weakly to Radon measures. We generalize the model by introducing proliferation of individuals and production and diffusion of the transferable quantity. It is shown that the generalized model admits a globally asymptotically stable steady state, provided that transfer is sufficiently small. We discuss an application of our model to cancer cell populations, in which individual cells exchange the surface protein P-glycoprotein, an important factor in acquired multidrug resistance against cancer chemotherapy.
In this paper we develop two mathematical models to predict the release kinetics of a water solub... more In this paper we develop two mathematical models to predict the release kinetics of a water soluble drug from a polymer/excipient matrix tablet. The first of our models consists of a random walk on a weighted graph, where the vertices of the graph represent particles of drug, excipient and polymer, respectively. The graph itself is the contact graph of a multidisperse random sphere packing. The second model describes the dissolution and the subsequent diffusion of the active drug out of a porous matrix using a system of partial differential equations. The predictions of both models show good qualitative agreement with experimental release curves. The models will provide tools for designing better controlled release devices.
We study the motility behavior of the unicellular protozoan Paramecium tetraurelia in a microflui... more We study the motility behavior of the unicellular protozoan Paramecium tetraurelia in a microfluidic device that can be prepared with a landscape of attracting or repelling chemicals. We investigate the spatial distribution of the positions of the individuals at different time points with methods from spatial statistics and Poisson random point fields. This makes quantitative the informal notion of ''uniform distribution'' (or lack thereof). Our device is characterized by the absence of large systematic biases due to gravitation and fluid flow. It has the potential to be applied to the study of other aquatic chemosensitive organisms as well. This may result in better diagnostic devices for environmental pollutants.
Mathematical Biosciences and Engineering, 2009
In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of... more In this paper we consider chemotherapy in a spatial model of tumor growth. The model, which is of reaction-diffusion type, takes into account the complex interactions between the tumor and surrounding stromal cells by including densities of endothelial cells and the extra-cellular matrix. When no treatment is applied the model reproduces the typical dynamics of early tumor growth. The initially avascular tumor reaches a diffusion limited size of the order of millimeters and initiates angiogenesis through the release of vascular endothelial growth factor (VEGF) secreted by hypoxic cells in the core of the tumor. This stimulates endothelial cells to migrate towards the tumor and establishes a nutrient supply sufficient for sustained invasion. To this model we apply cytostatic treatment in the form of a VEGF-inhibitor, which reduces the proliferation and chemotaxis of endothelial cells. This treatment has the capability to reduce tumor mass, but more importantly, we were able to determine that inhibition of endothelial cell proliferation is the more important of the two cellular functions targeted by the drug. Further, we considered the application of a cytotoxic drug that targets proliferating tumor cells. The drug was treated as a diffusible substance entering the tissue from the blood vessels. Our results show that depending on the characteristics of the drug it can either reduce the tumor mass significantly or in fact accelerate the growth rate of the tumor. This result seems to be due to complicated interplay between the stromal and tumor cell types and highlights the importance of considering chemotherapy in a spatial context.
Mathematical Modelling of Natural Phenomena, 2010
Motivated by structured parasite populations in aquaculture we consider a class of size-structure... more Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral theory of semigroups to establish conditions for the existence of a positive equilibrium solution of our model. Then, we formulate conditions that guarantee that the linearised system is governed by a positive quasicontraction semigroup on the biologically relevant state space. We also show that the governing linear semigroup is eventually compact, hence growth properties of the semigroup are determined by the spectrum of its generator. In the case of a separable fertility function, we deduce a characteristic equation, and investigate the stability of equilibrium solutions in the general case using positive perturbation arguments.
Physical biology, Aug 12, 2011
We propose a stochastic model that accounts for the growth, catastrophe and rescue processes of s... more We propose a stochastic model that accounts for the growth, catastrophe and rescue processes of steady-state microtubules assembled from MAP-free tubulin in the possible presence of a microtubule-associated drug. As an example of the latter, we both experimentally and theoretically study the perturbation of microtubule dynamic instability by S-methyl-D-DM1, a synthetic derivative of the microtubule-targeted agent maytansine and a potential anticancer agent. Our model predicts that among the drugs that act locally at the ...
Theoretical Biology and Medical Modelling, 2006
Background: Regular," moderate", physical exercise is an established non-pharmacologica... more Background: Regular," moderate", physical exercise is an established non-pharmacological form of treatment for depressive disorders. Brain lateralization has a significant role in the progress of depression. External stimuli such as various stressors or exercise influence the higher functions of the brain (cognition and affect). These effects often do not follow a linear course. Therefore, nonlinear dynamics seem best suited for modeling many of the phenomena, and putative global pathways in the brain, attributable to such ...