Mathematical Medicine and Biology-A Journal of the Ima最新文献

{"title":"The effect of stochasticity on repair of DNA double strand breaks throughout non-homologous end joining pathway.","authors":"Fazeleh S Mohseni-Salehi, Fatemeh Zare-Mirakabad, Soudeh Ghafouri-Fard, Mehdi Sadeghi","doi":"10.1093/imammb/dqx017","DOIUrl":"https://doi.org/10.1093/imammb/dqx017","url":null,"abstract":"DNA double strand breaks (DSBs) are the most lethal lesions of DNA induced by ionizing radiation, industrial chemicals and a wide variety of drugs used in chemotherapy. In the context of DNA damage response system modelling, uncertainty may arise in several ways such as number of induced DSBs, kinetic rates and measurement error in observable quantities. Therefore, using the stochastic approaches is imperative to gain further insight into the dynamic behaviour of DSBs repair process. In this article, a continuous-time Markov chain (CTMC) model of the non-homologous end joining (NHEJ) mechanism is formulated according to the DSB complexity. Additionally, a Metropolis Monte Carlo method is used to perform maximum likelihood estimation of the kinetic rate constants. Here, the effects of fluctuating kinetic rates and DSBs induction rate of the NHEJ mechanism are investigated. The stochastic realizations of the total yield of simple and complex DSBs ligation are simulated to compare their asymptotic dynamics. Furthermore, it has been proved that the total yield of DSBs has a normal distribution for sufficiently large number of DSBs. In order to estimate the expected duration of repairing DSBs, the probability distribution of DSBs lifetime is calculated based on the CTMC NHEJ model. Moreover, the variability of total yield of DSBs during constant low-dose radiation is evaluated in the presented model. The findings indicate that in stochastic NHEJ model, when there is no new DSBs induction through the repair process, all DSBs are eventually repaired. However, when DSBs are induced by constant low-dose radiation, a number of DSBs remains un-repaired.","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 4","pages":"517-539"},"PeriodicalIF":1.1,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35652941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Aqueous humour flow in the posterior chamber of the eye and its modifications due to pupillary block and iridotomy.","authors":"M Dvoriashyna,&nbsp;R Repetto,&nbsp;M R Romano,&nbsp;J H Tweedy","doi":"10.1093/imammb/dqx012","DOIUrl":"https://doi.org/10.1093/imammb/dqx012","url":null,"abstract":"<p><p>The anterior chamber (AC) and posterior chamber (PC) of the eye are connected through the pupil and are filled with aqueous humour. The aqueous flows from the posterior to the AC at an approximately constant rate, and the intraocular pressure is governed by this rate and the resistance to aqueous outflow. In some patients the iris and lens come into contact, leading to pressure build-up in the PC, peripheral axial shallowing of the AC and, possibly, to angle-closure glaucoma. This can lead to blindness, which may be prevented by surgically creating an iridotomy, that is a hole through the iris to facilitate the flow from the posterior to the AC. The problem of optimal size and location of an iridotomy is still poorly understood. In this article, we study aqueous flow in the PC and investigate how it is modified in the presence of an iridotomy. Our approach is based on the lubrication theory, which allows us to solve the problem semi-analytically. We treat the iridotomy as a point sink and assume that the flux through it is proportional to the pressure. We find that the ideal size and location of an iridotomy are influenced by various geometrical and fluid mechanical factors, the most relevant of which are the size of the hole and the length and height of the iris-lens channel. For certain iridotomy diameters, we find that the jet velocity through the iridotomy might be large enough to cause possible corneal damage.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 4","pages":"447-467"},"PeriodicalIF":1.1,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35216135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pathogen transfer through environment-host contact: an agent-based queueing theoretic framework.","authors":"Shi Chen,&nbsp;Suzanne Lenhart,&nbsp;Judy D Day,&nbsp;Chihoon Lee,&nbsp;Michael Dulin,&nbsp;Cristina Lanzas","doi":"10.1093/imammb/dqx014","DOIUrl":"https://doi.org/10.1093/imammb/dqx014","url":null,"abstract":"<p><p>Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes between environments and hosts and potential nosocomial pathogen transfer, where environments are servers and hosts are customers. Two types of servers with different parameters but the same utilization are investigated. We consider various forms of transfer functions that map contact duration to the amount of pathogen transfer based on existing literature. We propose a case study of simulated in-hospital contact processes and apply stochastic queues to analyse the amount of pathogen transfer under different transfer functions, and assume that pathogen amount decreases during the inter-arrival time. Different host behaviour (feedback and non-feedback) as well as initial pathogen distribution (whether in environment and/or in hosts) are also considered and simulated. We assess pathogen transfer and circulation under these various conditions and highlight the importance of the nonlinear interactions among contact processes, transfer functions and pathogen demography during the contact process. Our modelling framework can be readily extended to more complicated queueing networks to simulate more realistic situations by adjusting parameters such as the number and type of servers and customers, and adding extra subroutines.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"409-425"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35578899","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Flow in the anterior chamber of the eye with an implanted iris-fixated artificial lens.","authors":"Jennifer H Tweedy,&nbsp;Jan O Pralits,&nbsp;Rodolfo Repetto,&nbsp;Paolo Soleri","doi":"10.1093/imammb/dqx007","DOIUrl":"https://doi.org/10.1093/imammb/dqx007","url":null,"abstract":"<p><p>Flow in the aqueous humour that fills the anterior chamber of the eye occurs in response to the production and drainage of the aqueous humour, and also due to buoyancy effects produced by thermal gradients. Phakic intraocular lenses are manufactured lenses that are surgically inserted in the eyes of patients to correct refractive errors. Their presence has a dramatic effect on the circulation of the aqueous humour, resulting a very different flow in the anterior chamber, the effects of which have not been extensively investigated. In this article we use a simplified mathematical model to analyse the flow, in order to assess the effect of the implanted lens on the pressure drop required to drive the flow and also on the wall shear stress experienced by the corneal endothelial cells and the cells of the iris. A high pressure drop could result in an increased risk of glaucoma, whilst raised shear stress on the cornea could result in a reduction in the density of endothelial cells there, and on the iris it could result in the detachment of pigment cells, which block the outflow of the eye, also leading to glaucoma. Our results confirm those of previous fully numerical studies, and show that, although the presence of the lens causes significant differences in the flow topology and direction, the typical magnitudes of the shear stress are not significantly changed from the natural case. Our semi-analytical solution allows us to perform a thorough study of the dependence of the results on the controlling parameters and also to understand the basic physical mechanisms underlying flow characteristics.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"363-385"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35481116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysing the dynamics of a model for alopecia areata as an autoimmune disorder of hair follicle cycling.","authors":"Atanaska Dobreva,&nbsp;Ralf Paus,&nbsp;N G Cogan","doi":"10.1093/imammb/dqx009","DOIUrl":"https://doi.org/10.1093/imammb/dqx009","url":null,"abstract":"<p><p>Alopecia areata (AA) is a CD8$^{+}$ T cell-dependent autoimmune disease that disrupts the constantly repeating cyclic transformations of hair follicles (HFs). Among the three main HF cycle stages-growth (anagen), regression (catagen) and relative quiescence (telogen)-only anagen HFs are attacked and thereby forced to prematurely enter into catagen, thus shortening active hair growth substantially. After having previously modelled the dynamics of immune system components critically involved in the disease development (Dobreva et al., 2015), we here present a mathematical model for AA which incorporates HF cycling and illustrates the anagen phase interruption in AA resulting from an inflammatory autoimmune response against HFs. The model couples a system describing the dynamics of autoreactive immune cells with equations modelling the hair cycle. We illustrate states of health, disease and treatment as well as transitions between them. In addition, we perform parameter sensitivity analysis to assess how different processes, such as proliferation, apoptosis and input from stem cells, impact anagen duration in healthy versus AA-affected HFs. The proposed model may help in evaluating the effectiveness of existing treatments and identifying new potential therapeutic targets.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"387-407"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35585064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling and mathematical analysis of the M$_{2}$ receptor-dependent joint signalling and secondary messenger network in CHO cells.","authors":"Benjamin Engelhardt,&nbsp;Janine Holze,&nbsp;Christina Elliott,&nbsp;George S Baillie,&nbsp;Maik Kschischo,&nbsp;Holger Fröhlich","doi":"10.1093/imammb/dqx003","DOIUrl":"https://doi.org/10.1093/imammb/dqx003","url":null,"abstract":"<p><p>The muscarinic M$_{2}$ receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M$_{2}$ receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M$_{2}$ receptor-dependent signalling pathway combined with relevant secondary messenger molecules using mass action. In our literature-based joint signalling and secondary messenger model, all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stoichiometric matrix analysis. We propose constraint flux sampling (CFS) as a method to characterize the expected shift of the steady state reaction flux distribution due to the known amount of cAMP production and PDE4 activation. CFS correctly predicts an experimentally observable influence on the cytoskeleton structure (marked by actin and tubulin) and in consequence a change of the optical density of cells. In a second step, we use CFS to simulate the effect of knock-out experiments within our biological system, and thus to rank the influence of individual molecules on the observed change of the optical cell density. In particular, we confirm the relevance of the protein RGS14, which is supported by current literature. A combination of CFS with Elementary Flux Mode analysis enabled us to determine the possible underlying mechanism. Our analysis suggests that mathematical tools developed for metabolic network analysis can also be applied to mixed secondary messenger and signalling models. This could be very helpful to perform model checking with little effort and to generate hypotheses for further research if parameters are not known.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"279-297"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34995292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Finite-time parametric identification for the model representing the metabolic and genetic regulatory effects of sequential aerobic respiration and anaerobic fermentation processes in Escherichia coli.","authors":"Alfonso Sepúlveda-Gálvez,&nbsp;Jesús Agustín Badillo-Corona,&nbsp;Isaac Chairez","doi":"10.1093/imammb/dqx004","DOIUrl":"https://doi.org/10.1093/imammb/dqx004","url":null,"abstract":"<p><p>Mathematical modelling applied to biological systems allows for the inferring of changes in the dynamic behaviour of organisms associated with variations in the environment. Models based on ordinary differential equations are most commonly used because of their ability to describe the mechanisms of biological systems such as transcription. The disadvantage of using this approach is that there is a large number of parameters involved and that it is difficult to obtain them experimentally. This study presents an algorithm to obtain a finite-time parameter characterization of the model used to describe changes in the metabolic behaviour of Escherichia coli associated with environmental changes. In this scheme, super-twisting algorithm was proposed to recover the derivative of all the proteins and mRNA of E. coli associated to changes in the concentration of oxygen available in the growth media. The 75 identified parameters in this study maintain the biological coherence of the system and they were estimated with no more than 20% error with respect to the real ones included in the proposed model.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"299-317"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34853550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pattern formation in multiphase models of chemotactic cell aggregation.","authors":"J E F Green,&nbsp;J P Whiteley,&nbsp;J M Oliver,&nbsp;H M Byrne,&nbsp;S L Waters","doi":"10.1093/imammb/dqx005","DOIUrl":"https://doi.org/10.1093/imammb/dqx005","url":null,"abstract":"<p><p>We develop a continuum model for the aggregation of cells cultured in a nutrient-rich medium in a culture well. We consider a 2D geometry, representing a vertical slice through the culture well, and assume that the cell layer depth is small compared with the typical lengthscale of the culture well. We adopt a continuum mechanics approach, treating the cells and culture medium as a two-phase mixture. Specifically, the cells and culture medium are treated as fluids. Additionally, the cell phase can generate forces in response to environmental cues, which include the concentration of a chemoattractant that is produced by the cells within the culture medium. The model leads to a system of coupled nonlinear partial differential equations for the volume fraction and velocity of the cell phase, the culture medium pressure and the chemoattractant concentration, which must be solved subject to appropriate boundary and initial conditions. To gain insight into the system, we consider two model reductions, appropriate when the cell layer depth is thin compared to the typical length scale of the culture well: a (simple) 1D and a (more involved) thin-film extensional flow reduction. By investigating the resulting systems of equations analytically and numerically, we identify conditions under which small amplitude perturbations to a homogeneous steady state (corresponding to a spatially uniform cell distribution) can lead to a spatially varying steady state (pattern formation). Our analysis reveals that the simpler 1D reduction has the same qualitative features as the thin-film extensional flow reduction in the linear and weakly nonlinear regimes, motivating the use of the simpler 1D modelling approach when a qualitative understanding of the system is required. However, the thin-film extensional flow reduction may be more appropriate when detailed quantitative agreement between modelling predictions and experimental data is desired. Furthermore, full numerical simulations of the two model reductions in regions of parameter space when the system is not close to marginal stability reveal significant differences in the evolution of the volume fraction and velocity of the cell phase, and chemoattractant concentration.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"319-346"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35008228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modelling recurrence and second cancer risks induced by proton therapy.","authors":"V S K Manem,&nbsp;A Dhawan","doi":"10.1093/imammb/dqx006","DOIUrl":"10.1093/imammb/dqx006","url":null,"abstract":"<p><p>In the past few years, proton therapy has taken the centre stage in treating various tumour types. The primary contribution of this study is to investigate the tumour control probability (TCP), relapse time and the corresponding secondary cancer risks induced by proton beam radiation therapy. We incorporate tumour relapse kinetics into the TCP framework and calculate the associated second cancer risks. To calculate proton therapy-induced secondary cancer induction, we used the well-known biologically motivated mathematical model, initiation-inactivation-proliferation formalism. We used the available in vitro data for the linear energy transfer (LET) dependence of cell killing and mutation induction parameters. We evaluated the TCP and radiation-induced second cancer risks for protons in the clinical range of LETs, i.e. approximately 8 $mathrm{keV/mu m}$ for the tumour volume and 1-3 $mathrm{keV/mu m}$ for the organs at risk. This study may serve as a framework for further work in this field and elucidates proton-induced TCP and the associated secondary cancer risks, not previously reported in the literature. Although studies with a greater number of cell lines would reduce uncertainties within the model parameters, we argue that the theoretical framework presented within is a sufficient rationale to assess proton radiation TCP, relapse and carcinogenic effects in various treatment plans. We show that compared with photon therapy, proton therapy markedly reduces the risk of secondary malignancies and for equivalent dosing regimens achieves better tumour control as well as a reduced primary recurrence outcome, especially within a hypo-fractionated regimen.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 3","pages":"347-361"},"PeriodicalIF":1.1,"publicationDate":"2018-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqx006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35227815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A stochastic model for tumour control probability that accounts for repair from sublethal damage.","authors":"Ana Victoria Ponce Bobadilla,&nbsp;Philip K Maini,&nbsp;Helen Byrne","doi":"10.1093/imammb/dqw024","DOIUrl":"https://doi.org/10.1093/imammb/dqw024","url":null,"abstract":"<p><p>The tumour control probability (TCP) is the probability that a treatment regimen of radiation therapy (RT) eradicates all tumour cells in a given tissue. To decrease the toxic effects on healthy cells, RT is usually delivered over a period of weeks in a series of fractions. This allows tumour cells to repair sublethal damage (RSD) caused by radiation. In this article, we introduce a stochastic model for tumour response to radiotherapy which accounts for the effects of RSD. The tumour is subdivided into two cell types: 'affected' cells which have been damaged by RT and 'unaffected' cells which have not. The model is formulated as a birth-death process for which we can derive an explicit formula for the TCP. We apply our model to prostate cancer, and find that the radiosensitivity parameters and the probability of sublethal damage during radiation are the parameters to which the TCP predictions are most sensitive. We compare our TCP predictions to those given by Zaider and Minerbo's one-class model (Zaider & Minerbo, 2000) and Dawson and Hillen's two-class model (Dawson & Hillen, 2006) and find that for low doses of radiation, our model predicts a lower TCP. Finally, we find that when the probability of sublethal damage during radiation is large, the mean field assumption overestimates the TCP.</p>","PeriodicalId":49863,"journal":{"name":"Mathematical Medicine and Biology-A Journal of the Ima","volume":"35 2","pages":"181-202"},"PeriodicalIF":1.1,"publicationDate":"2018-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqw024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"34852667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}