Insulin is a potent peptide hormone that regulates glucose levels in the blood. Insulin-sensitive cells respond to insulin stimulation with the translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM), enabling the clearance of glucose from the blood. Defects in this process can give rise to insulin resistance and ultimately diabetes. One widely cited model of insulin signalling leading to glucose transport is that of Sedaghat et al. (2002) Am. J. Physiol. Endocrinol. Metab.283, E1084–E1101. Consisting of 20 deterministic ordinary differential equations (ODEs), it is the most comprehensive model of insulin signalling to date. However, the model possesses some major limitations, including the non-conservation of key components. In the current work, we detail mathematical and sensitivity analyses of the Sedaghat model. Based on the results of these analyses, we propose a reduced state space model of the insulin receptor subsystem. This reduced model maintains the input–output relation of the original model but is computationally more efficient, analytically tractable and resolves some of the limitations of the Sedaghat model.
{"title":"A receptor state space model of the insulin signalling system in glucose transport","authors":"Catheryn W. Gray;Adelle C.F. Coster","doi":"10.1093/imammb/dqv003","DOIUrl":"10.1093/imammb/dqv003","url":null,"abstract":"Insulin is a potent peptide hormone that regulates glucose levels in the blood. Insulin-sensitive cells respond to insulin stimulation with the translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM), enabling the clearance of glucose from the blood. Defects in this process can give rise to insulin resistance and ultimately diabetes. One widely cited model of insulin signalling leading to glucose transport is that of Sedaghat et al. (2002) Am. J. Physiol. Endocrinol. Metab.283, E1084–E1101. Consisting of 20 deterministic ordinary differential equations (ODEs), it is the most comprehensive model of insulin signalling to date. However, the model possesses some major limitations, including the non-conservation of key components. In the current work, we detail mathematical and sensitivity analyses of the Sedaghat model. Based on the results of these analyses, we propose a reduced state space model of the insulin receptor subsystem. This reduced model maintains the input–output relation of the original model but is computationally more efficient, analytically tractable and resolves some of the limitations of the Sedaghat model.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"457-473"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33046889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study transition of the temporal behaviours of $p53$ and $MDM2$ in a stress p53-MDM2-NO regulatory network induced by a bioactive molecule $NO$ (Nitric Oxide). We further study synchronization among a group of identical stress systems arranged in a 3D array with nearest neighbour diffusive coupling. The role of $NO$ and the effect of noise are investigated. In the single system study, we found three distinct types of temporal behaviour of $p53$ , namely oscillation death, damped oscillation and sustained oscillation, depending on the amount of stress induced by $NO$ , indicating how $p53$ responds to incoming stress. The correlation among coupled systems increases as the value of the coupling constant ( $epsilon$ ) is increased ( $gamma$ increases) and becomes constant after a certain value of $epsilon$ . The permutation entropy spectra $H(epsilon )$ for $p53$ and $MDM2$ as a function of $epsilon$ are found to be different due to direct and indirect interaction of $NO$ with respective proteins. We find $gamma$ versus $epsilon$ for $p53$ and $MDM2$ to be similar in a deterministic approach but different in a stochastic approach, and the separation between $gamma$ of the respective proteins as a function of $epsilon$ decreases as system size increases. The role of $NO$ is found to be two-fold: stress induced by NO is prominent at small and large values of $epsilon$ but synchrony induced by it dominates in the moderate range of $epsilon$ . Excess stress induces apoptosis.
{"title":"Synchronization in stress p53 network","authors":"Gurumayum Reenaroy Devi;Md. Jahoor Alam;R.K. Brojen Singh","doi":"10.1093/imammb/dqv002","DOIUrl":"10.1093/imammb/dqv002","url":null,"abstract":"We study transition of the temporal behaviours of \u0000<tex>$p53$</tex>\u0000 and \u0000<tex>$MDM2$</tex>\u0000 in a stress p53-MDM2-NO regulatory network induced by a bioactive molecule \u0000<tex>$NO$</tex>\u0000 (Nitric Oxide). We further study synchronization among a group of identical stress systems arranged in a 3D array with nearest neighbour diffusive coupling. The role of \u0000<tex>$NO$</tex>\u0000 and the effect of noise are investigated. In the single system study, we found three distinct types of temporal behaviour of \u0000<tex>$p53$</tex>\u0000, namely oscillation death, damped oscillation and sustained oscillation, depending on the amount of stress induced by \u0000<tex>$NO$</tex>\u0000, indicating how \u0000<tex>$p53$</tex>\u0000 responds to incoming stress. The correlation among coupled systems increases as the value of the coupling constant (\u0000<tex>$epsilon$</tex>\u0000) is increased (\u0000<tex>$gamma$</tex>\u0000 increases) and becomes constant after a certain value of \u0000<tex>$epsilon$</tex>\u0000. The permutation entropy spectra \u0000<tex>$H(epsilon )$</tex>\u0000 for \u0000<tex>$p53$</tex>\u0000 and \u0000<tex>$MDM2$</tex>\u0000 as a function of \u0000<tex>$epsilon$</tex>\u0000 are found to be different due to direct and indirect interaction of \u0000<tex>$NO$</tex>\u0000 with respective proteins. We find \u0000<tex>$gamma$</tex>\u0000 versus \u0000<tex>$epsilon$</tex>\u0000 for \u0000<tex>$p53$</tex>\u0000 and \u0000<tex>$MDM2$</tex>\u0000 to be similar in a deterministic approach but different in a stochastic approach, and the separation between \u0000<tex>$gamma$</tex>\u0000 of the respective proteins as a function of \u0000<tex>$epsilon$</tex>\u0000 decreases as system size increases. The role of \u0000<tex>$NO$</tex>\u0000 is found to be two-fold: stress induced by NO is prominent at small and large values of \u0000<tex>$epsilon$</tex>\u0000 but synchrony induced by it dominates in the moderate range of \u0000<tex>$epsilon$</tex>\u0000. Excess stress induces apoptosis.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"437-456"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33081827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peng Du;Niranchan Paskaranandavadivel;Greg O'Grady;Shou-Jiang Tang;Leo K. Cheng
Gastric slow wave dysrhythmias are associated with motility disorders. Periods of tachygastria associated with slow wave re-entry were recently recognized as one important dysrhythmia mechanism, but factors promoting and sustaining gastric re-entry are currently unknown. This study reports two experimental forms of gastric re-entry and presents a series of multi-scale models that define criteria for slow wave re-entry initiation, maintenance and termination. High-resolution electrical mapping was conducted in porcine and canine models and two spatiotemporal patterns of re-entrant activities were captured: single-loop rotor and double-loop figure-of-eight. Two separate multi-scale mathematical models were developed to reproduce the velocity and entrainment frequency of these experimental recordings. A single-pulse stimulus was used to invoke a rotor re-entry in the porcine model and a figure-of-eight re-entry in the canine model. In both cases, the simulated re-entrant activities were found to be perpetuated by tachygastria that was accompanied by a reduction in the propagation velocity in the re-entrant pathways. The simulated re-entrant activities were terminated by a single-pulse stimulus targeted at the tip of re-entrant wave, after which normal antegrade propagation was restored by the underlying intrinsic frequency gradient. Main findings: (i) the stability of re-entry is regulated by stimulus timing, intrinsic frequency gradient and conductivity; (ii) tachygastria due to re-entry increases the frequency gradient while showing decreased propagation velocity; (iii) re-entry may be effectively terminated by a targeted stimulus at the core, allowing the intrinsic slow wave conduction system to re-establish itself.
{"title":"A theoretical study of the initiation, maintenance and termination of gastric slow wave re-entry","authors":"Peng Du;Niranchan Paskaranandavadivel;Greg O'Grady;Shou-Jiang Tang;Leo K. Cheng","doi":"10.1093/imammb/dqu023","DOIUrl":"10.1093/imammb/dqu023","url":null,"abstract":"Gastric slow wave dysrhythmias are associated with motility disorders. Periods of tachygastria associated with slow wave re-entry were recently recognized as one important dysrhythmia mechanism, but factors promoting and sustaining gastric re-entry are currently unknown. This study reports two experimental forms of gastric re-entry and presents a series of multi-scale models that define criteria for slow wave re-entry initiation, maintenance and termination. High-resolution electrical mapping was conducted in porcine and canine models and two spatiotemporal patterns of re-entrant activities were captured: single-loop rotor and double-loop figure-of-eight. Two separate multi-scale mathematical models were developed to reproduce the velocity and entrainment frequency of these experimental recordings. A single-pulse stimulus was used to invoke a rotor re-entry in the porcine model and a figure-of-eight re-entry in the canine model. In both cases, the simulated re-entrant activities were found to be perpetuated by tachygastria that was accompanied by a reduction in the propagation velocity in the re-entrant pathways. The simulated re-entrant activities were terminated by a single-pulse stimulus targeted at the tip of re-entrant wave, after which normal antegrade propagation was restored by the underlying intrinsic frequency gradient. Main findings: (i) the stability of re-entry is regulated by stimulus timing, intrinsic frequency gradient and conductivity; (ii) tachygastria due to re-entry increases the frequency gradient while showing decreased propagation velocity; (iii) re-entry may be effectively terminated by a targeted stimulus at the core, allowing the intrinsic slow wave conduction system to re-establish itself.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"405-423"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32944628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Back matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/8225155/08225164.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50330133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sequential monotherapy is the most widely used therapeutic approach in the treatment of hepatitis B virus (HBV) chronic infection. Unfortunately, under therapy, in some patients the hepatitis virus mutates and gives rise to variants which are drug resistant. We wonder whether those patients would have benefited from the choice of combination therapy instead of sequential monotherapy. To study the action of these two therapeutic approaches and to explain the emergence of drug resistance, we propose a stochastic model for the infection within a patient who is treated with two drugs, either sequentially or contemporaneously, and who, under the first kind of therapy develops a strain of the virus which is resistant to both drugs. Our stochastic model has a deterministic approximation which is a slight modification of a classic three-strain model. We discuss why stochastic simulations are more suitable than the study of the deterministic approximation, when modelling the rise of mutations (this is mainly due to the amplitude of the stochastic fluctuations). We run stochastic simulations with suitable parameters and compare the time when, under the two therapeutic approaches, the resistant strain first reaches detectability in the serum viral load. Our results show that the best choice is to start an early combination therapy, which allows one to stay drug resistance free for a longer time and in many cases leads to viral eradication.
{"title":"Combination versus sequential monotherapy in chronic HBV infection: a mathematical approach","authors":"Daniela Bertacchi;Fabio Zucca;Sergio Foresti;Davide Mangioni;Andrea Gori","doi":"10.1093/imammb/dqu022","DOIUrl":"10.1093/imammb/dqu022","url":null,"abstract":"Sequential monotherapy is the most widely used therapeutic approach in the treatment of hepatitis B virus (HBV) chronic infection. Unfortunately, under therapy, in some patients the hepatitis virus mutates and gives rise to variants which are drug resistant. We wonder whether those patients would have benefited from the choice of combination therapy instead of sequential monotherapy. To study the action of these two therapeutic approaches and to explain the emergence of drug resistance, we propose a stochastic model for the infection within a patient who is treated with two drugs, either sequentially or contemporaneously, and who, under the first kind of therapy develops a strain of the virus which is resistant to both drugs. Our stochastic model has a deterministic approximation which is a slight modification of a classic three-strain model. We discuss why stochastic simulations are more suitable than the study of the deterministic approximation, when modelling the rise of mutations (this is mainly due to the amplitude of the stochastic fluctuations). We run stochastic simulations with suitable parameters and compare the time when, under the two therapeutic approaches, the resistant strain first reaches detectability in the serum viral load. Our results show that the best choice is to start an early combination therapy, which allows one to stay drug resistance free for a longer time and in many cases leads to viral eradication.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"383-403"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32815605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In 1991 Keiding published a relation between the age-specific prevalence and incidence of a chronic disease (in Age-specific incidence and prevalence: a statistical perspective. J. Roy. Stat. Soc. A, 154, 371–412). For special cases alternative formulations by differential equations were given recently in Brinks et al. (2013, Deriving age-specific incidence from prevalence with an ordinary differential equation. Statist. Med., 32, 2070–2078) and in Brinks & Landwehr (2014, Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany, Theor. Popul. Biol., 92, 62–68). From these works, we generalize formulations and discuss the advantages of the novel approach. As an implication, we obtain a new way of estimating the incidence rate of a chronic disease from prevalence data. This enables us to employ cross-sectional studies where otherwise expensive and lengthy follow-up studies are needed. This article illustrates and validates the novel method in a simulation study about dementia in Germany.
{"title":"A new relation between prevalence and incidence of a chronic disease","authors":"Ralph Brinks;Sandra Landwehr","doi":"10.1093/imammb/dqu024","DOIUrl":"10.1093/imammb/dqu024","url":null,"abstract":"In 1991 Keiding published a relation between the age-specific prevalence and incidence of a chronic disease (in Age-specific incidence and prevalence: a statistical perspective. J. Roy. Stat. Soc. A, 154, 371–412). For special cases alternative formulations by differential equations were given recently in Brinks et al. (2013, Deriving age-specific incidence from prevalence with an ordinary differential equation. Statist. Med., 32, 2070–2078) and in Brinks & Landwehr (2014, Age- and time-dependent model of the prevalence of non-communicable diseases and application to dementia in Germany, Theor. Popul. Biol., 92, 62–68). From these works, we generalize formulations and discuss the advantages of the novel approach. As an implication, we obtain a new way of estimating the incidence rate of a chronic disease from prevalence data. This enables us to employ cross-sectional studies where otherwise expensive and lengthy follow-up studies are needed. This article illustrates and validates the novel method in a simulation study about dementia in Germany.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"425-435"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32967276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Andrea Arnold;Daniela Calvetti;Albert Gjedde;Peter Iversen;Erkki Somersalo
We address the problem of estimating the unknown parameters of a model of tracer kinetics from sequences of positron emission tomography (PET) scan data using a statistical sequential algorithm for the inference of magnitudes of dynamic parameters. The method, based on Bayesian statistical inference, is a modification of a recently proposed particle filtering and sequential Monte Carlo algorithm, where instead of preassigning the accuracy in the propagation of each particle, we fix the time step and account for the numerical errors in the innovation term. We apply the algorithm to PET images of [1- $^{11}$ C]-acetate-derived tracer accumulation, estimating the transport rates in a three-compartment model of astrocytic uptake and metabolism of the tracer for a cohort of 18 volunteers from 3 groups, corresponding to healthy control individuals, cirrhotic liver and hepatic encephalopathy patients. The distribution of the parameters for the individuals and for the groups presented within the Bayesian framework support the hypothesis that the parameters for the hepatic encephalopathy group follow a significantly different distribution than the other two groups. The biological implications of the findings are also discussed.
{"title":"Astrocytic tracer dynamics estimated from [1-11C]-acetate PET measurements","authors":"Andrea Arnold;Daniela Calvetti;Albert Gjedde;Peter Iversen;Erkki Somersalo","doi":"10.1093/imammb/dqu021","DOIUrl":"10.1093/imammb/dqu021","url":null,"abstract":"We address the problem of estimating the unknown parameters of a model of tracer kinetics from sequences of positron emission tomography (PET) scan data using a statistical sequential algorithm for the inference of magnitudes of dynamic parameters. The method, based on Bayesian statistical inference, is a modification of a recently proposed particle filtering and sequential Monte Carlo algorithm, where instead of preassigning the accuracy in the propagation of each particle, we fix the time step and account for the numerical errors in the innovation term. We apply the algorithm to PET images of [1-\u0000<tex>$^{11}$</tex>\u0000C]-acetate-derived tracer accumulation, estimating the transport rates in a three-compartment model of astrocytic uptake and metabolism of the tracer for a cohort of 18 volunteers from 3 groups, corresponding to healthy control individuals, cirrhotic liver and hepatic encephalopathy patients. The distribution of the parameters for the individuals and for the groups presented within the Bayesian framework support the hypothesis that the parameters for the hepatic encephalopathy group follow a significantly different distribution than the other two groups. The biological implications of the findings are also discussed.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"367-382"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32837462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Front matter","authors":"","doi":"","DOIUrl":"https://doi.org/","url":null,"abstract":"","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 4","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2015-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016811/8225155/08225162.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50417902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cover Page","authors":"","doi":"10.1093/imammb/dqv032","DOIUrl":"https://doi.org/10.1093/imammb/dqv032","url":null,"abstract":"","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 3","pages":"NP-NP"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqv032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49954500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The immune system is a complex system of chemical and cellular interactions that responds quickly to queues that signal infection and then reverts to a basal level once the challenge is eliminated. Here, we present a general, four-component model of the immune system's response to a Staphylococcal aureus (S. aureus) infection, using ordinary differential equations. To incorporate both the infection and the immune system, we adopt the style of compartmenting the system to include bacterial dynamics, damage and inflammation to the host, and the host response. We incorporate interactions not previously represented including cross-talk between inflammation/damage and the infection and the suppression of the anti-inflammatory pathway in response to inflammation/damage. As a result, the most relevant equilibrium of the system, representing the health state, is an all-positive basal level. The model is able to capture eight different experimental outcomes for mice challenged with intratibial osteomyelitis due to S. aureus, primarily involving immunomodulation and vaccine therapies. For further validation and parameter exploration, we perform a parameter sensitivity analysis which suggests that the model is very stable with respect to variations in parameters, indicates potential immunomodulation strategies and provides a possible explanation for the difference in immune potential for different mouse strains.
{"title":"Modelling the interaction between the host immune response, bacterial dynamics and inflammatory damage in comparison with immunomodulation and vaccination experiments","authors":"Angela M. Jarrett;N.G. Cogan;M.E. Shirtliff","doi":"10.1093/imammb/dqu008","DOIUrl":"10.1093/imammb/dqu008","url":null,"abstract":"The immune system is a complex system of chemical and cellular interactions that responds quickly to queues that signal infection and then reverts to a basal level once the challenge is eliminated. Here, we present a general, four-component model of the immune system's response to a Staphylococcal aureus (S. aureus) infection, using ordinary differential equations. To incorporate both the infection and the immune system, we adopt the style of compartmenting the system to include bacterial dynamics, damage and inflammation to the host, and the host response. We incorporate interactions not previously represented including cross-talk between inflammation/damage and the infection and the suppression of the anti-inflammatory pathway in response to inflammation/damage. As a result, the most relevant equilibrium of the system, representing the health state, is an all-positive basal level. The model is able to capture eight different experimental outcomes for mice challenged with intratibial osteomyelitis due to S. aureus, primarily involving immunomodulation and vaccine therapies. For further validation and parameter exploration, we perform a parameter sensitivity analysis which suggests that the model is very stable with respect to variations in parameters, indicates potential immunomodulation strategies and provides a possible explanation for the difference in immune potential for different mouse strains.","PeriodicalId":94130,"journal":{"name":"Mathematical medicine and biology : a journal of the IMA","volume":"32 3","pages":"285-306"},"PeriodicalIF":0.0,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imammb/dqu008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32330237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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