Marcus Baaz , Tim Cardilin , Torbjörn Lundh , Mats Jirstrand
{"title":"Probabilistic analysis of tumor growth inhibition models to Support trial design","authors":"Marcus Baaz , Tim Cardilin , Torbjörn Lundh , Mats Jirstrand","doi":"10.1016/j.jtbi.2024.111969","DOIUrl":"10.1016/j.jtbi.2024.111969","url":null,"abstract":"<div><div>A large enough sample size of patients is required to statistically show that one treatment is better than another. However, too large a sample size is expensive and can also result in findings that are statistically significant, but not clinically relevant. How sample sizes should be chosen is a well-studied problem in classical statistics and analytical expressions can be derived from the appropriate test statistic. However, these expressions require information regarding the efficacy of the treatment, which may not be available, particularly for newly developed drugs. Tumor growth inhibition (TGI) models are frequently used to quantify the efficacy of newly developed anticancer drugs. In these models, the tumor growth dynamics are commonly described by a set of ordinary differential equations containing parameters that must be estimated using experimental data.</div><div>One widely used endpoint in clinical trials is the proportion of patients in different response categories determined using the Response Evaluation Criteria In Solid Tumors (RECIST) framework. From the TGI model, we derive analytical expressions for the probability of patient response to combination therapy. The probabilistic expressions are used together with classical statistics to derive a parametric model for the sample size required to achieve a certain significance level and test power when comparing two treatments.</div><div>Furthermore, the probabilistic expressions are used to generalize the Tumor Static Exposure concept to be more suitable for predicting clinical response. The derivatives of the probabilistic expressions are used to derive two additional expressions characterizing the exposure and its sensitivity. Finally, our results are illustrated using parameters obtained from calibrating the model to preclinical data.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142481170","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 bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions","authors":"David Hernandez-Aristizabal , Diego-Alexander Garzon-Alvarado , Carlos-Alberto Duque-Daza , Anotida Madzvamuse","doi":"10.1016/j.jtbi.2024.111966","DOIUrl":"10.1016/j.jtbi.2024.111966","url":null,"abstract":"<div><div>In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction–diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface) dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape deformation of the cell during migration.</div><div>Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic development to cancer invasion. Experimental, theoretical and computational studies have been key to elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques allow for detailed experimental measurements of cell migration pathways, while, on the other, computational approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface mechanobiochemical modelling approach presented in this work, set premises to study single cell migration through complex non-isotropic environments in two- and three-space dimensions.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142481167","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":"Bayesian parameter inference for epithelial mechanics","authors":"Xin Yan , Goshi Ogita , Shuji Ishihara , Kaoru Sugimura","doi":"10.1016/j.jtbi.2024.111960","DOIUrl":"10.1016/j.jtbi.2024.111960","url":null,"abstract":"<div><div>Cell-based mechanical models, such as the Cell Vertex Model (CVM), have proven useful for studying the mechanical control of epithelial tissue dynamics. We recently developed a statistical method called image-based parameter inference for formulating CVM model functions and estimating their parameters from image data of epithelial tissues. In this study, we employed Bayesian statistics to improve the utility and flexibility of image-based parameter inference. Tests on synthetic data confirmed that both our non-hierarchical and hierarchical Bayesian models provide accurate estimates of model parameters. By applying this method to <em>Drosophila</em> wings, we demonstrated that the reliability of parameter estimation is closely linked to the mechanical anisotropies present in the tissue. Moreover, we revealed that the cortical elasticity term is dispensable for explaining force-shape correlations <em>in vivo</em>. We anticipate that the flexibility of the Bayesian statistical framework will facilitate the integration of various types of information, thereby contributing to the quantitative dissection of the mechanical control of tissue dynamics.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142481173","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}
Mossa Merhi Reimert, Maya Katrin Gussmann, Anette Ella Boklund, Matt Denwood
{"title":"Choice of landscape discretisation method affects the inferred rate of spread in wildlife disease spread models","authors":"Mossa Merhi Reimert, Maya Katrin Gussmann, Anette Ella Boklund, Matt Denwood","doi":"10.1016/j.jtbi.2024.111963","DOIUrl":"10.1016/j.jtbi.2024.111963","url":null,"abstract":"<div><div>Disease modelling at the livestock-wildlife interface is an important topic for which discrete-space models are used for the wildlife component. One prominent example is African Swine Fever, where wild boar play an influential role as reservoirs of disease spillover into domestic pig farms. In this paper, we present a simulation study that demonstrates the impact of seemingly arbitrary choices of landscape discretisation method on the inferred rate of spread within the model. We use an ordinary differential equation model to implement a simplified model of disease transmission between discrete groups of wild boar with spillover into domestic pig farms contained within a homogeneous landscape. We examine a range of scenarios whereby the landscape is discretised into wild boar patches of varying size and shape, and compare the rate of spread between domestic pig farms placed at fixed points on the landscape. Our results demonstrate a non-monotonic relationship between patch size and rate of spread, which is particularly unstable and unpredictable for square and triangular shaped patches. Discretisation of the landscape into hexagons appears to produce a more stable relationship between patch size and rate of spread for the three types of transmission kernel we investigated. Although the rate of disease spread does converge to a stable value, this occurs at patch sizes that are much smaller than would be used in practice for wild boar. We conclude that outputs of disease models containing a wildlife component should not be considered to be robust to arbitrary choices for patch size and placement, but rather as a source of uncertainty to be examined using sensitivity analysis. Furthermore, we strongly recommend the use of hexagons rather than squares or right triangles for landscape discretisation.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142402022","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 model for transcription-dependent R-loop formation at double-stranded DNA breaks: Implications for their detection and biological effects","authors":"Boris P. Belotserkovskii, Philip C. Hanawalt","doi":"10.1016/j.jtbi.2024.111962","DOIUrl":"10.1016/j.jtbi.2024.111962","url":null,"abstract":"<div><div>R-loops are structures containing an RNA-DNA duplex and an unpaired DNA strand. During R-loop formation an RNA strand invades the DNA duplex, displacing the homologous DNA strand and binding the complementary DNA strand. Here we analyze a model for transcription-dependent R-loop formation at double-stranded DNA breaks (DSBs). In this model, R-loop formation is preceded by detachment of the non-template DNA strand from the RNA polymerase (RNAP). Then, strand exchange is initiated between the nascent RNA and the non-template DNA strand. During that strand exchange the length of the R-loop could either increase, or decrease in a biased random-walk fashion, in which the bias would depend upon the DNA sequence. Eventually, the restoration of the DNA duplex would completely displace the RNA. However, as long as the RNAP remains bound to the template DNA strand it prevents that displacement. Thus, according to the model, RNAPs stalled at DSBs can increase the lifespan of R-loops, increasing their detectability in experiments, and perhaps enhancing their biological effects.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142395390","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":"An immuno-epidemiological model with non-exponentially distributed disease stage on complex networks","authors":"Junyuan Yang , Xinyi Duan , Guiquan Sun","doi":"10.1016/j.jtbi.2024.111964","DOIUrl":"10.1016/j.jtbi.2024.111964","url":null,"abstract":"<div><div>Most of epidemic models assume that duration of the disease phase is distributed exponentially for the simplification of model formulation and analysis. Actually, the exponentially distributed assumption on the description of disease stages is hard to accurately approximate the interplay of drug concentration and viral load within host. In this article, we formulate an immuno-epidemiological epidemic model on complex networks, which is composed of ordinary differential equations and integral equations. The linkage of within- and between-host is connected by setting that the death caused by the disease is an increasing function in viral load within host. Mathematical analysis of the model includes the existence of the solution to the epidemiological model on complex networks, the existence and stability of equilibrium, which are completely determined by the basic reproduction number of the between-host system. Numerical analysis are shown that the non-exponentially distributions and the topology of networks have significant roles in the prediction of epidemic patterns.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142401942","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":"The development of drug resistance in metastatic tumours under chemotherapy: An evolutionary perspective","authors":"Federica Padovano , Chiara Villa","doi":"10.1016/j.jtbi.2024.111957","DOIUrl":"10.1016/j.jtbi.2024.111957","url":null,"abstract":"<div><div>We present a mathematical model of the evolutionary dynamics of a metastatic tumour under chemotherapy, comprising non-local partial differential equations for the phenotype-structured cell populations in the primary tumour and its metastasis. These equations are coupled with a physiologically-based pharmacokinetic model of drug administration and distribution, implementing a realistic delivery schedule. The model is carefully calibrated from the literature, focusing on BRAF-mutated melanoma treated with Dabrafenib as a case study. By means of long-time asymptotic and global sensitivity analyses, as well as numerical simulations, we explore the impact of cell migration from the primary to the metastatic site, physiological aspects of the tumour tissues and drug dose on the development of chemoresistance and treatment efficacy. Our findings provide a possible explanation for empirical evidence indicating that chemotherapy may foster metastatic spread and that metastases may be less impacted by the chemotherapeutic agent.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142382450","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":"Global stability of coexistence equilibria for n-species models of facultative mutualism","authors":"Paul Georgescu , Hong Zhang","doi":"10.1016/j.jtbi.2024.111961","DOIUrl":"10.1016/j.jtbi.2024.111961","url":null,"abstract":"<div><div>We further pursue an investigation on an abstract model characterizing the dynamics of a general class of <span><math><mi>n</mi></math></span>-species facultative mutualisms that was initiated in Georgescu et al. (2017), establishing biologically relevant sufficient conditions for the global asymptotic stability of the coexistence equilibria. These conditions are given in terms of per-species limits of growth-to-loss ratios computed at higher population densities, complemented by either monotonicity or sublinearity inequalities, and are observed to hold for <span><math><mi>n</mi></math></span>-species versions of mutualistic models in current use. The specific modeling details that require either of these conditions being satisfied are outlined and discussed. As mutualisms can enhance species diversification and facilitate stable coexistence via a plethora of mechanisms, it is then important to understand the stability of speciose mutualisms, our results being of potential interest to theoretical ecologists studying the coexistence of many interacting species and to conservationists aiming for rare species preservation.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142378625","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}
Nishnath Polavarapu , Madison Doty , Hana M. Dobrovolny
{"title":"Exploring the treatment of SARS-CoV-2 with modified vesicular stomatitis virus","authors":"Nishnath Polavarapu , Madison Doty , Hana M. Dobrovolny","doi":"10.1016/j.jtbi.2024.111959","DOIUrl":"10.1016/j.jtbi.2024.111959","url":null,"abstract":"<div><div>SARS-CoV-2 caused a global pandemic and is now an endemic virus that will require continued antiviral and vaccine development. A possible new treatment modality was recently suggested that would use vesicular stomatitis virus (VSV) modified to express the ACE2 receptor. Since the modified VSV expresses the cell surface receptor that is used by the SARS-CoV-2 spike protein, the thought is that SARS-CoV-2 virions would bind to the modified VSV and thus be neutralized. Additionally, since SARS-CoV-2 infected cells also express the spike protein, the modified VSV could potentially infect these cells, allowing for its own replication, but also potentially interfering with replication of SARS-CoV-2. This idea has not yet been tested experimentally, but we can investigate the feasibility of this possible treatment theoretically. In this manuscript, we develop a mathematical model of this suggested treatment and explore conditions under which it might be effective. We find that treatment with modified VSV does little to change the SARS-CoV-2 time course except when the treatment is applied at the onset of the SARS-CoV-2 infection at very high doses. In this case, VSV reduces the peak SARS-CoV-2 viral load, but lengthens the duration of the SARS-CoV-2 infection. Thus, we find that modified VSV treatment is unlikely to be effective largely because it does not prevent infection of cells by SARS-CoV-2.</div></div>","PeriodicalId":54763,"journal":{"name":"Journal of Theoretical Biology","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142376324","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}