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Book ; Online ; E-Book: Systems biology

Lei, Jinzhi

modeling, analysis, and simulation

(Lecture Notes on Mathematical Modelling in the Life Sciences,)

2021

Abstract: This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration. The diffusion of morphogens is addressed by introducing various reaction- ... ...

Author's details	Jinzhi Lei
Series title	Lecture Notes on Mathematical Modelling in the Life Sciences,
Abstract	This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and stem cell regeneration. The diffusion of morphogens is addressed by introducing various reaction-diffusion equations based on different hypotheses concerning the process of morphogen gradient formation. The robustness of steady-state gradients is also covered through boundary value problems. The introduction gives an overview of the relevant biological concepts (cells, DNA, organism development) and provides the requisite mathematical preliminaries on continuous dynamics and stochastic modeling. A basic understanding of calculus is assumed. The techniques described in this book encompass a wide range of mechanisms, from molecular behavior to population dynamics, and the inclusion of recent developments in the literature together with first-hand results make it an ideal reference for both new students and experienced researchers in the field of systems biology and applied mathematics.
Keywords	Systems biology/Mathematical models ; Biologia de sistemes ; Models matemàtics
Subject code	570.15
Language	English
Size	1 online resource (XII, 308 p. 95 illus., 69 illus. in color.)
Edition	1st ed. 2021.
Publisher	Springer
Publishing place	Cham, Switzerland
Document type	Book ; Online ; E-Book
Remark	Zugriff für angemeldete ZB MED-Nutzerinnen und -Nutzer
ISBN	3-030-73033-6 ; 3-030-73032-8 ; 978-3-030-73033-8 ; 978-3-030-73032-1
DOI	10.1007/978-3-030-73033-8
Database	ZB MED Catalogue: Medicine, Health, Nutrition, Environment, Agriculture

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Book ; Online: Mathematical modeling of heterogeneous stem cell regeneration

Lei, Jinzhi

from cell division to Waddington's epigenetic landscape

2023

Abstract: Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell division is ... ...

Abstract	Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell division is the core process connecting different scale biological processes and leading to changes in cell population number and the epigenetic state of cells. This chapter focuses on the primary strategies for modeling cell division in biological systems. The Lagrange coordinate modeling approach considers gene network dynamics within each cell and random changes in cell states and model parameters during cell division. In contrast, the Euler coordinate modeling approach formulates the evolution of cell population numbers with the same epigenetic state via a differential-integral equation. These strategies focus on different scale dynamics, respectively, and result in two methods of modeling Waddington's epigenetic landscape: the Fokker-Planck equation and the differential-integral equation approaches. The differential-integral equation approach formulates the evolution of cell population density based on simple assumptions in cell proliferation, apoptosis, differentiation, and epigenetic state transitions during cell division. Moreover, machine learning methods can establish low-dimensional macroscopic measurements of a cell based on single-cell RNA sequencing data. The low dimensional measurements can quantify the epigenetic state of cells and become connections between static single-cell RNA sequencing data with dynamic equations for tissue development processes. The differential-integral equation presented in this chapter provides a reasonable approach to understanding the complex biological processes of tissue development and tumor progression. Comment: 46pages, 1 figures
Keywords	Quantitative Biology - Quantitative Methods
Subject code	571
Publishing date	2023-09-14
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration.

Lei, Jinzhi

Journal of theoretical biology

2020 Volume 492, Page(s) 110196

Abstract: 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 ... ...

Abstract	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.
MeSH term(s)	Apoptosis ; Cell Cycle ; Cell Differentiation ; Cell Division ; Models, Biological ; Stem Cells
Language	English
Publishing date	2020-02-14
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2972-5
ISSN	1095-8541 ; 0022-5193
ISSN (online)	1095-8541
ISSN	0022-5193
DOI	10.1016/j.jtbi.2020.110196
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Article ; Online: Optimal treatment strategy of cancers with intratumor heterogeneity.

Zhang, Haifeng / Lei, Jinzhi

Mathematical biosciences and engineering : MBE

2023 Volume 19, Issue 12, Page(s) 13337–13373

Abstract: Intratumor heterogeneity hinders the success of anti-cancer treatment due to the interaction between different types of cells. To recapitulate the communication of different types of cells, we developed a mathematical model to study the dynamic ... ...

Abstract	Intratumor heterogeneity hinders the success of anti-cancer treatment due to the interaction between different types of cells. To recapitulate the communication of different types of cells, we developed a mathematical model to study the dynamic interaction between normal, drug-sensitive and drug-resistant cells in response to cancer treatment. Based on the proposed model, we first study the analytical conclusions, namely the nonnegativity and boundedness of solutions, and the existence and stability of steady states. Furthermore, to investigate the optimal treatment that minimizes both the cancer cells count and the total dose of drugs, we apply the Pontryagin's maximum(or minimum) principle (PMP) to explore the combination therapy strategy with either quadratic control or linear control functionals. We establish the existence and uniqueness of the quadratic control problem, and apply the forward-backward sweep method (FBSM) to solve the optimal control problems and obtain the optimal therapy scheme.
MeSH term(s)	Humans ; Models, Theoretical ; Combined Modality Therapy ; Neoplasms/drug therapy
Language	English
Publishing date	2023-01-18
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2265126-3
ISSN	1551-0018 ; 1551-0018
ISSN (online)	1551-0018
ISSN	1551-0018
DOI	10.3934/mbe.2022625
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Article ; Online: Computational modeling reveals key factors driving treatment-free remission in chronic myeloid leukemia patients.

Lai, Xiulan / Jiao, Xiaopei / Zhang, Haojian / Lei, Jinzhi

NPJ systems biology and applications

2024 Volume 10, Issue 1, Page(s) 45

Abstract: 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 ... ...

Abstract	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.
MeSH term(s)	Humans ; Leukemia, Myelogenous, Chronic, BCR-ABL Positive/drug therapy ; Tumor Microenvironment/drug effects ; Protein Kinase Inhibitors/therapeutic use ; Remission Induction ; Computer Simulation ; Neoplastic Stem Cells/drug effects ; Neoplastic Stem Cells/metabolism ; Models, Biological
Chemical Substances	Protein Kinase Inhibitors
Language	English
Publishing date	2024-04-27
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ISSN	2056-7189
ISSN (online)	2056-7189
DOI	10.1038/s41540-024-00370-4
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Article ; Online: Modelling COVID-19 epidemic with confirmed cases-driven contact tracing quarantine.

Wu, Fei / Liang, Xiyin / Lei, Jinzhi

Infectious Disease Modelling

2023 Volume 8, Issue 2, Page(s) 415–426

Abstract: The pandemic of novel coronavirus disease 2019 (COVID-19) has been a severe threat to public health. The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak. In this paper, we developed a ... ...

Abstract	The pandemic of novel coronavirus disease 2019 (COVID-19) has been a severe threat to public health. The policy of close contract tracing quarantine is an effective strategy in controlling the COVID-19 epidemic outbreak. In this paper, we developed a mathematical model of the COVID-19 epidemic with confirmed case-driven contact tracing quarantine, and applied the model to evaluate the effectiveness of the policy of contact tracing and quarantine. The model is established based on the combination of the compartmental model and individual-based model simulations, which results in a closed-form delay differential equation model. The proposed model includes a novel form of quarantine functions to represent the number of quarantine individuals following the confirmed cases every day and provides analytic expressions to study the effects of changing the quarantine rate. The proposed model can be applied to epidemic dynamics during the period of community spread and when the policy of confirmed cases-driven contact tracing quarantine is efficient. We applied the model to study the effectiveness of contact tracing and quarantine. The proposed delay differential equation model can describe the average epidemic dynamics of the stochastic-individual-based model, however, it is not enough to describe the diverse response due to the stochastic effect. Based on model simulations, we found that the policy of contact tracing and quarantine can obviously reduce the epidemic size, however, may not be enough to achieve zero-infectious in a short time, a combination of close contact quarantine and social contact restriction is required to achieve zero-infectious. Moreover, the effect of reducing epidemic size is insensitive to the period of quarantine, there are no significant changes in the epidemic dynamics when the quarantine days vary from 7 to 21 days.
Language	English
Publishing date	2023-04-14
Publishing country	China
Document type	Journal Article
ZDB-ID	3015225-2
ISSN	2468-0427 ; 2468-2152
ISSN (online)	2468-0427
ISSN	2468-2152
DOI	10.1016/j.idm.2023.04.001
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Article ; Online: Dynamics of cell-type transition mediated by epigenetic modifications.

Huang, Rongsheng / Situ, Qiaojun / Lei, Jinzhi

Journal of theoretical biology

2023 Volume 577, Page(s) 111664

Abstract: 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 ... ...

Abstract	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.
MeSH term(s)	Cell Differentiation/genetics ; Cellular Reprogramming ; Epigenesis, Genetic ; Computer Simulation ; Transcription Factors/genetics
Chemical Substances	Transcription Factors
Language	English
Publishing date	2023-11-16
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	2972-5
ISSN	1095-8541 ; 0022-5193
ISSN (online)	1095-8541
ISSN	0022-5193
DOI	10.1016/j.jtbi.2023.111664
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Article ; Online: Modeling tumour heterogeneity of PD-L1 expression in tumour progression and adaptive therapy.

Ma, Shizhao / Lei, Jinzhi / Lai, Xiulan

Journal of mathematical biology

2023 Volume 86, Issue 3, Page(s) 38

Abstract: 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 ... ...

Abstract	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.
MeSH term(s)	Humans ; Neoplasms/drug therapy ; Neoplasms/genetics ; Tumor Microenvironment
Chemical Substances	CD274 protein, human
Language	English
Publishing date	2023-01-25
Publishing country	Germany
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	187101-8
ISSN	1432-1416 ; 0303-6812
ISSN (online)	1432-1416
ISSN	0303-6812
DOI	10.1007/s00285-023-01872-1
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Article ; Online: Quantitative Modeling of Stemness in Single-Cell RNA Sequencing Data: A Nonlinear One-Class Support Vector Machine Method.

Jiang, Hao / Liu, Jingxin / Song, You / Lei, Jinzhi

Journal of computational biology : a journal of computational molecular cell biology

2023 Volume 31, Issue 1, Page(s) 41–57

Abstract: 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 ...

Abstract	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.
MeSH term(s)	Humans ; Support Vector Machine ; Neoplasms/genetics ; Cell Differentiation ; Sequence Analysis, RNA/methods ; Single-Cell Analysis/methods
Language	English
Publishing date	2023-11-28
Publishing country	United States
Document type	Journal Article
ZDB-ID	2030900-4
ISSN	1557-8666 ; 1066-5277
ISSN (online)	1557-8666
ISSN	1066-5277
DOI	10.1089/cmb.2022.0484
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Book ; Online: Evolutionary dynamics of cancer

Lei, Jinzhi

from epigenetic regulation to cell population dynamics -- mathematical model framework, applications, and open problems

2019

Abstract: Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and heterogeneity in ...

Abstract	Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and heterogeneity in cancer cells. Cancer is a group of diseases involving abnormal cell growth, during which abnormal regulations in stem cell regeneration are essential for the dynamics of cancer development. In general, the dynamics of stem cell regeneration can be simplified as a $\mathrm{G_0}$ phase cell cycle model, which lead to a delay differentiation equation. When cell heterogeneity and plasticity are considered, we establish a differential-integral equation based on the random transition of epigenetic states of stem cells during cell division. The proposed model highlights cell heterogeneity and plasticity, and connects the heterogeneity with cell-to-cell variance in cellular behaviors, e.g. proliferation, apoptosis, and differentiation/senescence, and can be extended to include gene mutation-induced tumor development. Hybrid computations models are developed based on the mathematical model framework, and are applied to the process of inflammation-induced tumorigenesis and tumor relapse after CAR-T therapy. Finally, we give rise to several mathematical problems related to the proposed differential-integral equation. Answers to these problems are crucial for the understanding of the evolutionary dynamics of cancer. Comment: 19 pages, 3 figures
Keywords	Quantitative Biology - Cell Behavior
Subject code	612
Publishing date	2019-08-19
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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