Dynamics of cell-type transition mediated by epigenetic modifications.

Maintaining tissue homeostasis requires appropriate regulation of stem cell differentiation. The Waddington landscape posits that gene circuits in a cell form a potential landscape of different cell types, wherein cells follow attractors of the probability landscape to develop into distinct cell types. However, how adult stem cells achieve a delicate balance between self-renewal and differentiation remains unclear. We propose that random inheritance of epigenetic states plays a pivotal role in stem cell differentiation and present a hybrid model of stem cell differentiation induced by epigenetic modifications. Our comprehensive model integrates gene regulation networks, epigenetic state inheritance, and cell regeneration, encompassing multi-scale dynamics ranging from transcription regulation to cell population. Through model simulations, we demonstrate that random inheritance of epigenetic states during cell divisions can spontaneously induce cell differentiation, dedifferentiation, and transdifferentiation. Furthermore, we investigate the influences of interfering with epigenetic modifications and introducing additional transcription factors on the probabilities of dedifferentiation and transdifferentiation, revealing the underlying mechanism of cell reprogramming. This in silico model provides valuable insights into the intricate mechanism governing stem cell differentiation and cell reprogramming and offers a promising path to enhance the field of regenerative medicine.

Data-based modeling of breast cancer and optimal therapy.

Excessive accumulation of ß-catenin proteins is a vital driver in the development of breast cancer. Many clinical assessments incorporating immunotherapy with targeted mRNA of ß-catenin are costly endeavor. This paper develops novel mathematical models for different treatments by invoking available clinical data to calibrate models, along with the selection and evaluation of therapy strategies in a faster manner with lower cost. Firstly, in order to explore the interactions between cancer cells and the immune system within the tumor microenvironment, we construct different types of breast cancer treatment models based on RNA interference technique and immune checkpoint inhibitors, which have been proved to be an effective combined therapy in pre-clinical trials associated with the inhibition of ß-catenin proteins to enhance intrinsic anti-tumor immune response. Secondly, various techniques including MCMC are adopted to estimate multiple parameters and thus simulations in agreement with experimental results sustain the validity of our models. Furthermore, the gradient descent method and particle swarm algorithm are designed to optimize therapy schemes to inhibit the growth of tumor and lower the treatment cost. Considering the mechanisms of drug resistance in vivo, simulations exhibit that therapies are ineffective resulting in cancer relapse in the prolonged time. For this reason, parametric sensitivity analysis sheds light on the choice of new treatments which indicate that, in addition to inhibiting ß-catenin proteins and improving self-immunity, the injection of dendritic cells promoting immunity may provide a novel vision for the future of cancer treatment. Overall, our study provides witness of principle from a mathematical perspective to guide clinical trials and the selection of treatment regimens.

Treatment of melanoma with dendritic cell vaccines and immune checkpoint inhibitors: A mathematical modeling study.

Dendritic cell (DC) vaccines and immune checkpoint inhibitors (ICIs) play critical roles in shaping the immune responses of tumor cells (TCs) and are widely used in cancer immunotherapies. Quantitatively evaluating the effectiveness of these therapies are essential for the optimization of treatment strategies. Here, based on the combined therapy of melanoma with DC vaccines and ICIs, we formulated a mathematical model to investigate the dynamic interactions between TCs and the immune system and understand the underlying mechanisms of immunotherapy. First, we obtained a threshold parameter for the growth of TCs, which is given by the ratio of spontaneous proliferation to immune inhibition. Next, we proved the existence and locally asymptotic stability of steady states of tumor-free, tumor-dominant, and tumor-immune coexistent equilibria, and identified the existence of Hopf bifurcation of the proposed model. Furthermore, global sensitivity analysis showed that the growth of TCs strongly correlates with the injection rate of DC vaccines, the activation rate of CTLs, and the killing rate of TCs. Finally, we tested the efficacy of multiple monotherapies and combined therapies with model simulations. Our results indicate that DC vaccines can decelerate the growth of TCs, and ICIs can inhibit the growth of TCs. Besides, both therapies can prolong the lifetime of patients, and the combined therapy of DC vaccines and ICIs can effectively eradicate TCs.

Modeling tumour heterogeneity of PD-L1 expression in tumour progression and adaptive therapy.

Although PD-1/PD-L1 inhibitors show potent and durable anti-tumour effects in some refractory tumours, the response rate in overall patients is unsatisfactory, which in part due to the inherent heterogeneity of PD-L1. In order to establish an approach for predicting and estimating the dynamic alternation of PD-L1 heterogeneity during cancer progression and treatment, this study establishes a comprehensive modelling and computational framework based on a mathematical model of cancer cell evolution in the tumour-immune microenvironment, and in combination with epigenetic data and overall survival data of clinical patients from The Cancer Genome Atlas. Through PD-L1 heterogeneous virtual patients obtained by the computational framework, we explore the adaptive therapy of administering anti-PD-L1 according to the dynamic of PD-L1 state among cancer cells. Our results show that in contrast to the continuous maximum tolerated dose treatment, adaptive therapy is more effective for PD-L1 positive patients, in that it prolongs the survival of patients by administration of drugs at lower dosage.

Data-driven multi-scale mathematical modeling of SARS-CoV-2 infection reveals heterogeneity among COVID-19 patients.

Patients with coronavirus disease 2019 (COVID-19) often exhibit diverse disease progressions associated with various infectious ability, symptoms, and clinical treatments. To systematically and thoroughly understand the heterogeneous progression of COVID-19, we developed a multi-scale computational model to quantitatively understand the heterogeneous progression of COVID-19 patients infected with severe acute respiratory syndrome (SARS)-like coronavirus (SARS-CoV-2). The model consists of intracellular viral dynamics, multicellular infection process, and immune responses, and was formulated using a combination of differential equations and stochastic modeling. By integrating multi-source clinical data with model analysis, we quantified individual heterogeneity using two indexes, i.e., the ratio of infected cells and incubation period. Specifically, our simulations revealed that increasing the host antiviral state or virus induced type I interferon (IFN) production rate can prolong the incubation period and postpone the transition from asymptomatic to symptomatic outcomes. We further identified the threshold dynamics of T cell exhaustion in the transition between mild-moderate and severe symptoms, and that patients with severe symptoms exhibited a lack of naïve T cells at a late stage. In addition, we quantified the efficacy of treating COVID-19 patients and investigated the effects of various therapeutic strategies. Simulations results suggested that single antiviral therapy is sufficient for moderate patients, while combination therapies and prevention of T cell exhaustion are needed for severe patients. These results highlight the critical roles of IFN and T cell responses in regulating the stage transition during COVID-19 progression. Our study reveals a quantitative relationship underpinning the heterogeneity of transition stage during COVID-19 progression and can provide a potential guidance for personalized therapy in COVID-19 patients.

A mathematical model with aberrant growth correction in tissue homeostasis and tumor cell growth.

Cancer is usually considered a genetic disease caused by alterations in genes that control cellular behaviors, especially growth and division. Cancer cells differ from normal tissue cells in many ways that allow them to grow out of control and become invasive. However, experiments have shown that aberrant growth in many tissues burdened with varying numbers of mutant cells can be corrected, and wild-type cells are required for the active elimination of mutant cells. These findings reveal the dynamic cellular behaviors that lead to a tissue homeostatic state when faced with mutational and nonmutational insults. The current study was motivated by these observations and established a mathematical model of how a tissue copes with the aberrant behavior of mutant cells. The proposed model depicts the interaction between wild-type and mutant cells through a system of two delay differential equations, which include the random mutation of normal cells and the active extrusion of mutant cells. Based on the proposed model, we performed qualitative analysis to identify the conditions of either normal tissue homeostasis or uncontrolled growth with varying numbers of abnormal mutant cells. Bifurcation analysis suggests the conditions of bistability with either a small or large number of mutant cells, the coexistence of bistable steady states can be clinically beneficial by driving the state of mutant cell predominance to the attraction basin of the state with a low number of mutant cells. This result is further confirmed by the treatment strategy obtained from optimal control theory.

Data driven mathematical modeling reveals the dynamic mechanism of MSC-induced neovascularization.

Coculture of mesenchymal stem cells (MSCs) and vascular endothelial cells (ECs) in vitro leads to the formation of a capillary-like reticular structure by ECs, which has great potential as a better substitute for artificial blood vessels in terms of stability and functionality. To investigate the mechanisms of the early neovascularization induced by MSCs, we analyzed the kinematic features of the motion of ECs and concluded that the dynamic interaction between cells and the extracellular matrix would reveal the capillary-like structure formation. Based on this hypothesis, we proposed a mathematical model to simulate the vascular-like migration pattern of ECs in silico, which was confirmed by in vitro studies. These in vitro studies validated that the dynamic secretion and degradation of collagen I is the critical factor for capillary structure formation. The model proposed based on cell tracking, single cell sequencing, and mathematical simulation provides a better understanding of the neovascularization process induced by MSCs and a possible simple explanation guiding this important cellular behavior.-Yu, Y., Situ, Q., Jia, W., Li, J., Wu, Q., Lei, J. Data driven mathematical modeling reveals the dynamic mechanism of MSC-induced neovascularization.

A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration.

Stem cell heterogeneity is essential for homeostasis in tissue development. This paper establishes a general mathematical framework to model the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The framework generalizes the classical G0 cell cycle model and incorporates the epigenetic states of individual cells represented by a continuous multidimensional variable. In the model, the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, are dependent on their epigenetic states, and the random transitions of epigenetic states between cell cycles are represented by an inheritance probability function that describes the conditional probability of cell state changes. Moreover, the model can be extended to include genotypic changes and describe the process of gene mutation-induced tumor development. The proposed mathematical framework provides a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.

Detecting the stable point of therapeutic effect of chronic myeloid leukemia based on dynamic network biomarkers.

BACKGROUND: Most researches of chronic myeloid leukemia (CML) are currently focused on the treatment methods, while there are relatively few researches on the progress of patients' condition after drug treatment. Traditional biomarkers of disease can only distinguish normal state from disease state, and cannot recognize the pre-stable state after drug treatment. RESULTS: A therapeutic effect recognition strategy based on dynamic network biomarkers (DNB) is provided for CML patients' gene expression data. With the DNB criteria, the DNB with 250 genes is selected and the therapeutic effect index (TEI) is constructed for the detection of individual disease. The pre-stable state before the disease condition becomes stable is 1 month. Through functional analysis for the DNB, some genes are confirmed as key genes to affect the progress of CML patients' condition. CONCLUSIONS: The results provide a certain theoretical direction and theoretical basis for medical personnel in the treatment of CML patients, and find new therapeutic targets in the future. The biomarkers of CML can help patients to be treated promptly and minimize drug resistance, treatment failure and relapse, which reduce the mortality of CML significantly.

Origins of oscillation patterns in cyclical thrombocytopenia.

Cyclical thrombocytopenia (CT) is a rare hematological disease characterized by periodic oscillations in circulating platelet counts. In almost all CT patients, other cell lines show no sign of oscillation, but recently a CT patient was reported with significant oscillations in circulating neutrophils (in the same period as the platelets). In this paper, we attempt to understand this phenomenon through a previously published model of human hematopoiesis. We have investigated a variety of possible oscillation patterns that may appear when alterations occur in the control parameters in the platelet regulatory dynamics. Our results indicate that the platelet maturation time and the differentiation rate from hematopoietic stem cells (HSCs) into the platelet cell line play important roles in the emergence of various types of CT like oscillations. Moreover, we find different oscillation patterns, including CT and cyclical neutropenia like oscillations, with certain parameter values in the platelet compartment. A bifurcation analysis revealed the different origins of these oscillation patterns. We also identified bistable dynamics which indicate the potential importance of system history in the treatment of these diseases. Together, these results demonstrate the possible origins for various oscillation patterns dependent on alterations in the platelet cell line control mechanisms. One of the important origins may be related to the regulation of apoptosis in platelet precursors.

A single-cell epigenetic model for paternal psychological stress-induced transgenerational reprogramming in offspring.

Experimental evidence shows that parental psychological stress affects the long-term health of offspring in an inheritable fashion. Although epigenetic mechanisms, including DNA methylation, miRNA, and histone modifications, are involved in transgenerational programming, the underlining mechanisms of transgenerational inheritance remain unsolved. Here, we present a single-cell-based computational model for transgenerational inheritance for investigating the long-term dynamics of phenotype changes in response to parental stress. The model is based on a recent study that has identified the imprinted sperm gene Sfmbt2 as a key target, and incorporates crosstalks among drastically different time scales in mammalian development, including DNA methylation, transcription, cell division, and population dynamics. Computational analysis of the model suggests a positive feedback to DNA methylation in the promoter region of sperm Sfmbt2 gene that provides a possible mechanism to mediate the parental psychological stress reprogramming in offspring. This approach provides a modeling framework for the understanding of the roles that epigenetics play in transgenerational inheritance.

Mathematical model of adult stem cell regeneration with cross-talk between genetic and epigenetic regulation.

Adult stem cells, which exist throughout the body, multiply by cell division to replenish dying cells or to promote regeneration to repair damaged tissues. To perform these functions during the lifetime of organs or tissues, stem cells need to maintain their populations in a faithful distribution of their epigenetic states, which are susceptible to stochastic fluctuations during each cell division, unexpected injury, and potential genetic mutations that occur during many cell divisions. However, it remains unclear how the three processes of differentiation, proliferation, and apoptosis in regulating stem cells collectively manage these challenging tasks. Here, without considering molecular details, we propose a genetic optimal control model for adult stem cell regeneration that includes the three fundamental processes, along with cell division and adaptation based on differential fitnesses of phenotypes. In the model, stem cells with a distribution of epigenetic states are required to maximize expected performance after each cell division. We show that heterogeneous proliferation that depends on the epigenetic states of stem cells can improve the maintenance of stem cell distributions to create balanced populations. A control strategy during each cell division leads to a feedback mechanism involving heterogeneous proliferation that can accelerate regeneration with less fluctuation in the stem cell population. When mutation is allowed, apoptosis evolves to maximize the performance during homeostasis after multiple cell divisions. The overall results highlight the importance of cross-talk between genetic and epigenetic regulation and the performance objectives during homeostasis in shaping a desirable heterogeneous distribution of stem cells in epigenetic states.

A hybrid model of molecular regulation and population dynamics for yeast autophagy.

Autophagy is an evolutionarily conserved lysosome-based degradation process that is involved in maintaining cellular homeostasis and stress responses. Dysregulation of autophagy is known to associate with many diseases. In this paper, we establish a Hybrid model of Molecular regulation and Population dynamics (HMP model) for yeast autophagy to study how autophagy regulation at molecular level affects the cell population dynamics under the stress of starvation. The model includes interactions between amino acids, TORC1, Atg1 complex, and Atg8 lipidation at the molecular level, and cell death and division at the cell behavior level. Two feedback loops are involved in autophagy induction, in which the negative feedback of TORC1 activation has been known previously, and the positive feedback between TORC1 and Atg1 complex formation is introduced according to the similarity of Drosophila and mammalian cells. We demonstrate that the two feedback loops play distinct roles in autophagy regulation. The positive feedback is pro-survival, whereas the negative feedback has little effect on the survival of population during starvation. In addition, autophagy deficient cells can be rescued from starvation by amino acid exchanges from their neighboring wild type cells.

PDCD5 functions as a regulator of p53 dynamics in the DNA damage response.

The tumor suppressor p53 plays a central role in cell fate decisions after DNA damage. Programmed Cell Death 5 (PDCD5) interacts with the p53 pathway to promote cell apoptosis. Recombinant human PDCD5 can significantly sensitize different cancers to chemotherapies. In the present paper, we construct a computational model that includes PDCD5 interactions in the p53 signaling network and study the effects of PDCD5 on p53-mediated cell fate decisions during the DNA damage response. Our results revealed that PDCD5 functions as a co-activator of p53 and regulates p53-dependent cell fate decisions via the mediation of p53 dynamics. The effects of PDCD5 are dose-dependent, such that p53 activity exhibits sustained low level, pulsed oscillations, or sustained high level dynamics depending on the PDCD5 level following DNA damage. Moreover, PDCD5 regulates caspase-3 activation via two mechanisms during the two phases of sustained and pulsed p53 dynamics. This study provides insights regarding how PDCD5 functions as a regulator of the p53 pathway and might be helpful for increasing our understanding of the molecular mechanisms by which PDCD5 can be used to treat cancers.

Bifurcation analysis and potential landscapes of the p53-Mdm2 module regulated by the co-activator programmed cell death 5.

The dynamics of p53 play important roles in the regulation of cell fate decisions in response to various stresses, and programmed cell death 5 (PDCD5) functions as a co-activator of p53 that modulates p53 dynamics. In the present paper, we investigated how p53 dynamics are modulated by PDCD5 during the deoxyribose nucleic acid damage response using methods of bifurcation analysis and potential landscape. Our results revealed that p53 activities display rich dynamics under different PDCD5 levels, including monostability, bistability with two stable steady states, oscillations, and the coexistence of a stable steady state (or two states) and an oscillatory state. The physical properties of the p53 oscillations were further demonstrated by the potential landscape in which the potential force attracts the system state to the limit cycle attractor, and the curl flux force drives coherent oscillation along the cyclic trajectory. We also investigated the efficiency with which PDCD5 induced p53 oscillations. We show that Hopf bifurcation can be induced by increasing the PDCD5 efficiency and that the system dynamics exhibited clear transition features in both barrier height and energy dissipation when the efficiency was close to the bifurcation point.

Adiabatic reduction of a model of stochastic gene expression with jump Markov process.

This paper considers adiabatic reduction in a model of stochastic gene expression with bursting transcription considered as a jump Markov process. In this model, the process of gene expression with auto-regulation is described by fast/slow dynamics. The production of mRNA is assumed to follow a compound Poisson process occurring at a rate depending on protein levels (the phenomena called bursting in molecular biology) and the production of protein is a linear function of mRNA numbers. When the dynamics of mRNA is assumed to be a fast process (due to faster mRNA degradation than that of protein) we prove that, with appropriate scalings in the burst rate, jump size or translational rate, the bursting phenomena can be transmitted to the slow variable. We show that, depending on the scaling, the reduced equation is either a stochastic differential equation with a jump Poisson process or a deterministic ordinary differential equation. These results are significant because adiabatic reduction techniques seem to have not been rigorously justified for a stochastic differential system containing a jump Markov process. We expect that the results can be generalized to adiabatic methods in more general stochastic hybrid systems.

Understanding and treating cytopenia through mathematical modeling.

Here, we briefly review how the study of dynamic hematological diseases with mathematical modeling tools has led to a better understanding of the origin of some types of neutropenia and thrombocytopenia and to improved treatment strategies. In addition, we have briefly discussed how these models suggest improved ways to minimize and/or treat cytopenia induced by chemotherapy.

Quantitative Modeling of Stemness in Single-Cell RNA Sequencing Data: A Nonlinear One-Class Support Vector Machine Method.

Intratumoral heterogeneity and the presence of cancer stem cells are challenging issues in cancer therapy. An appropriate quantification of the stemness of individual cells for assessing the potential for self-renewal and differentiation from the cell of origin can define a measurement for quantifying different cell states, which is important in understanding the dynamics of cancer evolution, and might further provide possible targeted therapies aimed at tumor stem cells. Nevertheless, it is usually difficult to quantify the stemness of a cell based on molecular information associated with the cell. In this study, we proposed a stemness definition method with one-class Hadamard kernel support vector machine (OCHSVM) based on single-cell RNA sequencing (scRNA-seq) data. Applications of the proposed OCHSVM stemness are assessed by various data sets, including preimplantation embryo cells, induced pluripotent stem cells, or tumor cells. We further compared the OCHSVM model with state-of-the-art methods CytoTRACE, one-class logistic regression, or one-class SVM methods with different kernels. The computational results demonstrate that the OCHSVM method is more suitable for stemness identification using scRNA-seq data.

Computational modeling reveals key factors driving treatment-free remission in chronic myeloid leukemia patients.

Patients with chronic myeloid leukemia (CML) who receive tyrosine kinase inhibitors (TKIs) have been known to achieve treatment-free remission (TFR) upon discontinuing treatment. However, the underlying mechanisms of this phenomenon remain incompletely understood. This study aims to elucidate the mechanism of TFR in CML patients, focusing on the feedback interaction between leukemia stem cells and the bone marrow microenvironment. We have developed a mathematical model to explore the interplay between leukemia stem cells and the bone marrow microenvironment, allowing for the simulation of CML progression dynamics. Our proposed model reveals a dichotomous response following TKI discontinuation, with two distinct patient groups emerging: one prone to early molecular relapse and the other capable of achieving long-term TFR after treatment cessation. This finding aligns with clinical observations and underscores the essential role of feedback interaction between leukemic cells and the tumor microenvironment in sustaining TFR. Notably, we have shown that the ratio of leukemia cells in peripheral blood (PBLC) and the tumor microenvironment (TME) index can be a valuable predictive tool for identifying patients likely to achieve TFR after discontinuing treatment. This study provides fresh insights into the mechanism of TFR in CML patients and underscores the significance of microenvironmental control in achieving TFR.

ROBUSTNESS OF MORPHOGEN GRADIENTS WITH "BUCKET BRIGADE" TRANSPORT THROUGH MEMBRANE-ASSOCIATED NON-RECEPTORS.

Robust multiple-fate morphogen gradients are essential for embryo development. Here, we analyze mathematically a model of morphogen gradient (such as Dpp in Drosophila wing imaginal disc) formation in the presence of non-receptors with both diffusion of free morphogens and the movement of morphogens bound to non-receptors. Under the assumption of rapid degradation of unbound morphogen, we introduce a method of functional boundary value problem and prove the existence, uniqueness and linear stability of a biologically acceptable steady-state solution. Next, we investigate the robustness of this steady-state solution with respect to significant changes in the morphogen synthesis rate. We prove that the model is able to produce robust biological morphogen gradients when production and degradation rates of morphogens are large enough and non-receptors are abundant. Our results provide mathematical and biological insight to a mechanism of achieving stable robust long distance morphogen gradients. Key elements of this mechanism are rapid turnover of morphogen to non-receptors of neighoring cells resulting in significant degradation and transport of non-receptor-morphogen complexes, the latter moving downstream through a "bucket brigade" process.