Dynamics of a network mediated by IL-36 and involved in the pathogenesis of psoriasis.

The pathogenesis of the inflammatory, chronic, and common skin disease psoriasis involves immune cells, skin cells (keratinocytes), and the cytokines they secrete. Hyperproliferation and abnormal differentiation of keratinocytes are hallmarks of the disease. The roles of cytokines such as TNFα, IL-15, IL-17, and IL-23 in psoriasis have been studied through mathematical/computational models as well as experiments. However, the role of proinflammatory cytokine IL-36 in the onset and progression of psoriasis is still elusive. To explore the role of IL-36, we construct a network embodying indirect cell-cell interactions of a few immune and skin cells mediated by IL-36 based on existing knowledge. We also develop a mathematical model for the network and perform a global sensitivity analysis. Our results suggest that the model is most sensitive to a parameter that represents the level of cytokine IL-36. In addition, a steady-state analysis of the model suggests that an increase in the level of IL-36 could lead to the hyperproliferation of keratinocytes and, thus, psoriasis. Our analysis also highlights that the plaque formation and progression of psoriasis could occur through either a gradual or a switch-like increase in the keratinocyte population. We propose that the switch-like increase would be due to a bistable behavior of the network toward either a psoriatic or healthy state and could be used as a novel treatment strategy.

Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences.

Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

Public health system sustainability assessment by Gaidai hypersurface approach.

BACKGROUND: to determine extreme cardiovascular and cancer diseases deathrate risks at any time in any region of interest. DESIGN: Apply modern novel statistical methods to raw clinical surveillance data. METHODS: multi-centre, population-based, medical survey data-based bio statistical approach. For this study, cardiovascular and cancer diseases annual recorded deaths numbers in all 195 world countries have been selected, constituting 390D (390-dimensional) biosystem. It is challenging to model such phenomena. RESULTS: this paper describes a novel bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient timelapse. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the advantage of dealing efficiently with extensive regional dimensionality. The suggested methodology coped with this challenge well. CONCLUSIONS: the suggested methodology may be used in various public health applications, based on raw clinical survey data.

Gaidai reliability method for high-dimensional spatio-temporal biosystems.

This study presents novel methodology for pandemic risks assessment for a national health system of interest. The 2019 coronavirus disease (COVID-19) is a contagious disease with certain potential for worldwide spread and potentially significant effects on public health globally. Suggested methodology enables risks assessment of an epidemic, that may happen in the near future at any time, and in any national region of interest. Traditional spatio-temporal reliability methodologies do not have benefit of easily handling health system's high-dimensionality and complex cross-correlations between regional observations. Contrarily, advocated Gaidaireliability approach successfully addresses spatiotemporal clinical observations, as well as multi-regional epidemiological dynamics. This study aimed at benchmarking of a novel bio-statistical technique, enabling national health risk assessment, based on available clinical surveys with dynamically observed patient numbers, while accounting for relevant territorial mappings. The method developed in this study opens up the possibility of accurate epidemiological risk forecast for multi-regional biological and health systems. Suggested bioinformatical methodology may be used in a wide range of public health applications.

Prediction of death rates for cardiovascular diseases and cancers.

Background: To estimate cardiovascular and cancer death rates by regions and time periods. Design: Novel statistical methods were used to analyze clinical surveillance data. Methods: A multicenter, population-based medical survey was performed. Annual recorded deaths from cardiovascular diseases were analyzed for all 195 countries of the world. It is challenging to model such data; few mathematical models can be applied because cardiovascular disease and cancer data are generally not normally distributed. Results: A novel approach to assessing the biosystem reliability is introduced and has been found to be particularly suitable for analyzing multiregion environmental and healthcare systems. While traditional methods for analyzing temporal observations of multiregion processes do not deal with dimensionality efficiently, our methodology has been shown to be able to cope with this challenge. Conclusions: Our novel methodology can be applied to public health and clinical survey data.

Population dynamics models for various forms of adaptation.

Adaptability to changing environments is one of the universal characteristics of living organisms. Because individual modes of adaptation are diverse, a unified understanding of these diverse modes is essential to comprehend adaptation. Adaptations can be categorized from at least two perspectives with respect to information. One is the passivity and activity of adaptation and the other is the type of information transmission. In Darwinian natural selection, organisms are selected among randomly generated traits under which individual organisms are passive in the sense that they do not process any environmental information. On the other hand, organisms can also adapt by sensing their environment and changing their traits. This is an active adaptation in that it makes use of environmental information. In terms of information transfer, adaptation through phenotypic heterogeneity, such as bacterial bet-hedging, is intragenerational in which traits are not passed on to the next generation. In contrast, adaptation through genetic diversity is intergenerational. The theory of population dynamics enables us to unify these various modes of adaptations and their properties can be analyzed qualitatively and quantitatively using techniques from quantitative genetics and information thermodynamics. In addition, such methods can be applied to situations where organisms can learn from past experiences and pass them on from generation to generation. In this work, we introduce the unified theory of biological adaptation based on population dynamics and show its potential applications to evaluate the fitness value of information and to analyze experimental lineage tree data. Finally, we discuss future perspectives for its development. This review article is an extended version of the Japanese article in SEIBUTSU BUTSURI Vol. 57, p. 287-290 (2017).

A modeling framework for adaptive collective defense: crisis response in social-insect colonies.

Living systems, from cells to superorganismic insect colonies, have an organizational boundary between inside and outside and allocate resources to defend it. Whereas the micro-scale dynamics of cell walls can be difficult to study, the adaptive allocation of workers to defense in social-insect colonies is more conspicuous. This is particularly the case for Tetragonisca angustula stingless bees, which combine different defensive mechanisms found across other colonial animals: (1) morphological specialization (distinct soldiers (majors) are produced over weeks); (2) age-based polyethism (young majors transition to guarding tasks over days); and (3) task switching (small workers (minors) replace soldiers within minutes under crisis). To better understand how these timescales of reproduction, development, and behavior integrate to balance defensive demands with other colony needs, we developed a demographic Filippov ODE system to study the effect of these processes on task allocation and colony size. Our results show that colony size peaks at low proportions of majors, but colonies die if minors are too plastic or defensive demands are too high or if there is a high proportion of quickly developing majors. For fast maturation, increasing major production may decrease defenses. This model elucidates the demographic factors constraining collective defense regulation in social insects while also suggesting new explanations for variation in defensive allocation at smaller scales where the mechanisms underlying defensive processes are not easily observable. Moreover, our work helps to establish social insects as model organisms for understanding other systems where the transaction costs for component turnover are nontrivial, as in manufacturing systems and just-in-time supply chains.

On inverse problems for several coupled PDE systems arising in mathematical biology.

In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems, we mainly consider the non-negative solutions of the coupled equations, which are consistent with realistic settings in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction of the measurement/observation data due to averaging effects, the nonlinear coupling of multiple equations, and the non-negative constraints on the solutions, which pose significant challenges to the inverse problems. We develop a new and effective scheme to tackle the inverse problems and achieve unique identifiability results by properly controlling the injection of different source terms to obtain multiple sets of mean flux data. The approach relies on certain monotonicity properties which are related to the intrinsic structures of the coupled PDE system. We also connect our study to biological applications of practical interest.

Ongoing HIV replication in lymph node sanctuary sites in treated individuals contributes to the total latent HIV at a very slow rate.

Lymph nodes (LNs) serve as a sanctuary site for HIV viruses due to the heterogeneous distribution of the antiretrovirals (ARVs) inside the LNs. There is an ongoing debate whether this represents ongoing cycles of viral replication in the LNs or merely residual virus production by latently infected cells. Previous work has claimed that the measured levels of genetic variation in proviruses sampled from the blood were inconsistent with ongoing replication. However, it is not clear what rate of variation is consistent with ongoing replication in small sanctuary sites. In this study, we used a spherically symmetric compartmental ODE model to track the HIV viral dynamics in the LN and predict the contribution of ongoing replication within the LN to the whole-body proviral pool in an ARV-suppressed person living with HIV. This model tracks the reaction-diffusion dynamics of uninfected, actively infected, and latently infected T-cells as well as free virus within the LN parenchyma and the blood, and distinguishes between latently infected cells created before ARV therapy and during ARV therapy. We simulated suppressive therapy beginning in year 5 post-infection. Each LN sanctuary site had a volume of 1 ml, and we considered cases of 1 ml, 30 ml, and 250 ml total volume, which represent a single active sanctuary site, moderate systemic involvement, and involvement of the total lymphoid tissue. Viral load in the blood rapidly dropped and remained below the limit of detection in all cases but remained high in the LN sanctuary sites. Novel latent cells increased systemically over time but very slowly, taking between 25 and 50 years to reach 5 % of the total latent pool, depending on the volume of lymphoid tissue involvement. Putative sanctuary sites in LNs are limited in volume and produce novel latent cells slowly. Assays to detect genetic drift due to such sites would require very deep sequencing if sampling only from the blood. Previous studies showing a lack of genetic drift are consistent with the expected contribution of ongoing replication in lymph node sanctuary sites.

Dementia death rates prediction.

BACKGROUND: Prevalence of dementia illness, causing certain morbidity and mortality globally, places burden on global public health. This study primary goal was to assess future risks of dying from severe dementia, given specific return period, within selected group of regions or nations. METHODS: Traditional statistical approaches do not have benefits of effectively handling large regional dimensionality, along with nonlinear cross-correlations between various regional observations. In order to produce reliable long-term projections of excessive dementia death rate risks, this study advocates novel bio-system reliability technique, that being particularly suited for multi-regional environmental, biological, and health systems. DATA: Raw clinical data has been used as an input to the suggested population-based, bio-statistical technique using data from medical surveys and several centers. RESULTS: Novel spatiotemporal health system reliability methodology has been developed and applied to dementia death rates raw clinical data. Suggested methodology shown to be capable of dealing efficiently with spatiotemporal clinical observations of multi-regional nature. Accurate disease risks multi-regional spatiotemporal prediction being done, relevant confidence intervals have been presented as well. CONCLUSIONS: Based on available clinical survey dataset, the proposed approach may be applied in a variety of clinical public health applications. Confidence bands, given for predicted dementia-associated death rate levels with return periods of interest, have been reasonably narrow, indicating practical values of advocated prognostics.

COVID-19 spatio-temporal forecast in England.

The 2019 novel coronavirus disease (COVID-19, SARS-CoV-2) being contagious illness with allegedly high potential for global transmission, low potential for morbidity and fatality, and certain impact on global public health. This study describes a novel bio-system reliability spatio-temporal approach, that is especially appropriate for multi-regional environmental, biological and health systems and that, when observed for a sufficient amount of time, produces a reliable long-term forecast of the likelihood of an outbreak of a highly pathogenic virus. Conventional statistical approaches do not have the benefit of effectively handling large regional dimensionality and cross-correlation between various regional observations. These methods deal with temporal observations of multi-regional phenomena. The most afflicted districts of England's COVID-19 daily counts of reported patients were used for this investigation. In order to extract the essential data from dynamically observed patient numbers while taking into consideration pertinent geographical mapping, this study utilized recently developed bio-reliability methodology. With the use of the spatio-temporal approach described in this study, future epidemic outbreak risks for multi-regional public health systems may be predicted with sufficient accuracy.

Dichotomy in TCR V-domain dynamics binding the opposed inclined planes of pMHC-II and pMHC-I α-helices.

Ligand recognition by the human α/ß T-cell antigen receptor (TCR) heterodimer protein, unlike the surface immunoglobulin (sIg) B-cell receptor, is not governed by relative binding affinity. Its interaction with the peptide (p) plus major histocompatibility complex (MHC) protein (abbrev. pMHC) likely involves some different molecular mechanism linking pMHC binding to T-cell functions. Recent analytical geometry of TCR:pMHC-II solved crystallographic structures (n = 40) revealed that each variable (V)-domain is bound in similar, yet mathematically unique orientations to its target pMHC groove. The relative position of the central cysteine of each V-domain was examined by multivariable calculus in spherical coordinates, where a simple volume element (dV) was found to describe clonotypic geometry with pMHC-II. Here, the study was expanded to include TCR:pMHC-I structures, and to model a physical mechanism, specifically involving the two directionally opposed inclined planes (IP) manifest by the two major α-helices prominent in both MHC-I and MHC-II proteins. Calculations for rotational torque of each V-domain, together with acceleration up and down the slopes of both MHC α-helices were used to estimate the time a given V-domain spends sliding down its cognate MHC IP. This V-domain rotation/sliding mechanism appears to be quantitatively unique for each TCR:pMHC V-domain (n = 40). However, there is an apparent and common dichotomy between the mobility of each V-domain with respect to the two classes of MHC proteins. Evolutionary motifs in the MHC helices support that the V-domains negotiate the opposed inclined planes of pMHC ligands in clonotypic fashion. Thus, this model is useful in understanding how mechanical forces are linked to TCR function.

A fractional mathematical model with nonlinear partial differential equations for transmission dynamics of severe acute respiratory syndrome coronavirus 2 infection.

This study presents a fractional mathematical model based on nonlinear Partial Differential Equations (PDEs) of fractional variable-order derivatives for the host populations experiencing transmission and evolution of the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) pandemic. Five host population groups have been considered, the Susceptible, Exposed, Infected, Recovered, and Deceased (SEIRD). The new model, not introduced before in its current formulation, is governed by nonlinear PDEs with fractional variable-order derivatives. As a result, the proposed model is not compared with other models or real scenarios. The advantage of the proposed fractional partial derivatives of variable orders is that they can model the rate of change of subpopulation for the proposed model. As an efficient tool to obtain the solution of the proposed model, a modified analytical technique based on the homotopy and Adomian decomposition methods is introduced. Then again, the present study is general and is applicable to a host population in any country.

Mitochondrial networks through the lens of mathematics.

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

Fifty shades of greenbeard: robust evolution of altruism based on similarity of complex phenotypes.

We study the evolution of altruistic behaviour under a model where individuals choose to cooperate by comparing a set of continuous phenotype tags. Individuals play a donation game and only donate to other individuals that are sufficiently similar to themselves in a multidimensional phenotype space. We find the generic maintenance of robust altruism when phenotypes are multidimensional. Selection for altruism is driven by the coevolution of individual strategy and phenotype; altruism levels shape the distribution of individuals in phenotype space. Low donation rates induce a phenotype distribution that renders the population vulnerable to the invasion of altruists, whereas high donation rates prime a population for cheater invasion, resulting in cyclic dynamics that maintain substantial levels of altruism. Altruism is therefore robust to invasion by cheaters in the long term in this model. Furthermore, the shape of the phenotype distribution in high phenotypic dimension allows altruists to better resist the invasion by cheaters, and as a result the amount of donation increases with increasing phenotype dimension. We also generalize previous results in the regime of weak selection to two competing strategies in continuous phenotype space, and show that success under weak selection is crucial to success under strong selection in our model. Our results support the viability of a simple similarity-based mechanism for altruism in a well-mixed population.

Interplay of p53 and XIAP protein dynamics orchestrates cell fate in response to chemotherapy.

Chemotherapeutic drugs are used to treat almost all types of cancer, but the intended response, i.e., elimination, is often incomplete, with a subset of cancer cells resisting treatment. Two critical factors play a role in chemoresistance: the p53 tumour suppressor gene and the X-linked inhibitor of apoptosis (XIAP). These proteins have been shown to act synergistically to elicit cellular responses upon DNA damage induced by chemotherapy, yet, the mechanism is poorly understood. This study introduces a mathematical model characterising the apoptosis pathway activation by p53 before and after mitochondrial outer membrane permeabilisation upon treatment with the chemotherapy Doxorubicin (Dox). "In-silico" simulations show that the p53 dynamics change dose-dependently. Under medium to high doses of Dox, p53 concentration ultimately stabilises to a high level regardless of XIAP concentrations. However, caspase-3 activation may be triggered or not depending on the XIAP induction rate, ultimately determining whether the cell will perish or resist. Consequently, the model predicts that failure to activate apoptosis in some cancer cells expressing wild-type p53 might be due to heterogeneity between cells in upregulating the XIAP protein, rather than due to the p53 protein concentration. Our model suggests that the interplay of the p53 dynamics and the XIAP induction rate is critical to determine the cancer cells' therapeutic response.

The lost art of mathematical modelling.

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

COVID-19 Epidemic Forecast in Brazil.

This study advocates a novel spatio-temporal method for accurate prediction of COVID-19 epidemic occurrence probability at any time in any Brazil state of interest, and raw clinical observational data have been used. This article describes a novel bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient time period, resulting in robust long-term forecast of the virus outbreak probability. COVID-19 daily numbers of recorded patients in all affected Brazil states were taken into account. This work aimed to benchmark novel state-of-the-art methods, making it possible to analyse dynamically observed patient numbers while taking into account relevant regional mapping. Advocated approach may help to monitor and predict possible future epidemic outbreaks within a large variety of multi-regional biological systems. Suggested methodology may be used in various modern public health applications, efficiently using their clinical survey data.

Characterizing the Impact of Communication on Cellular and Collective Behavior Using a Three-Dimensional Multiscale Cellular Model.

Communication between cells enables the coordination that drives structural and functional complexity in biological systems. Both single and multicellular organisms have evolved diverse communication systems for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell-cell communication. While research has elucidated the form and function of cell-cell communication in many biological systems, our knowledge is still limited by the confounding effects of other biological phenomena at play and the bias of the evolutionary background. In this work, our goal is to push forward the context-free understanding of what impact cell-cell communication can have on cellular and population behavior to more fully understand the extent to which cell-cell communication systems can be utilized, modified, and engineered. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. We focus on two key communication parameters: the effective interaction distance at which cells are able to interact and the receptor activation threshold. We found that cell-cell communication can be divided into six different forms along the parameter axes, three asocial and three social. We also show that cellular behavior, tissue composition, and tissue diversity are all highly sensitive to both the general form and specific parameters of communication even when the cellular network has not been biased towards that behavior.

Modelling of indirect cell-cell interaction networks mediated by IFNγ/IL-4 cytokine involved in atopic dermatitis.

Atopic dermatitis (AD) is an immune-driven inflammatory skin disease that is known to have a significantly high life-time prevalence in the human population. T-helper (Th) immune cells play a key role in the pathogenesis of AD which is marked by defects in the skin barrier function along with a significant increase in the population of either Th1 or Th2 sub-types of Th cells. The progression of AD from the acute to chronic phase is still poorly understood, and here we explore the mechanism of this transition through the study of a mathematical model for indirect cell-cell interactions among Th and skin cells via the secreted cytokines IFNγ and IL-4, both known to have therapeutic potential. An increase in the level of cytokine IFN γ can catalyse the transition of AD from an acute to a chronic stage, while an increase in the level of cytokine IL-4 has the reverse effect. In our model, the transition of AD from the acute to chronic stage and vice versa can be abrupt (switch-like) with hysteresis: this bistable behaviour can potentially be used to keep AD in the acute phase since therapy based on suppression of IFNγ can retard the transition to the chronic phase.