The effect of the G1-S transition checkpoint on an age structured cell cycle model

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Mathematical analysis of a SIPC age-structured model of cervical cancer

Human Papillomavirus (HPV), which is the main causal factor of cervical cancer, infects normal cervical cells on the specific cell's age interval, i.e., between the G₁ to S phase of cell cycle. Hence, the spread of the viruses in cervical tissue not only depends on the time, but also the cell age. By this fact, we introduce a new model that shows the spread of HPV infections on the cervical tissue by considering the age of cells and the time. The model is a four dimensional system of the first order partial differential equations with time and age independent variables, where the cells population is divided into four sub-populations, i.e., susceptible cells, infected cells by HPV, precancerous cells, and cancer cells. There are two types of the steady state solution of the system, i.e., disease-free and cancerous steady state solutions, where the stability is determined by using Fatou's lemma and solving some integral equations. In this case, we use a non-standard method to calculate the basic reproduction number of the system. Lastly, we use numerical simulations to show the dynamics of the age-structured system.

Data Driven Cell Cycle Model to Quantify the Efficacy of Cancer Therapeutics Targeting Specific Cell-Cycle Phases From Flow Cytometry Results

Many chemotherapeutic drugs target cell processes in specific cell cycle phases. Determining the specific phases targeted is key to understanding drug mechanism of action and efficacy against specific cancer types. Flow cytometry experiments, combined with cell cycle phase and division round specific staining, can be used to quantify the current cell cycle phase and number of mitotic events of each cell within a population. However, quantification of cell interphase times and the efficacy of cytotoxic drugs targeting specific cell cycle phases cannot be determined directly. We present a data driven computational cell population model for interpreting experimental results, where in-silico populations are initialized to match observable results from experimental populations. A two-stage approach is used to determine the efficacy of cytotoxic drugs in blocking cell-cycle phase transitions. In the first stage, our model is fitted to experimental multi-parameter flow cytometry results from untreated cell populations to identify parameters defining probability density functions for phase transitions. In the second stage, we introduce a blocking routine to the model which blocks a percentage of attempted transitions between cell-cycle phases due to therapeutic treatment. The resulting model closely matches the percentage of cells from experiment in each cell-cycle phase and division round. From untreated cell populations, interphase and intermitotic times can be inferred. We then identify the specific cell-cycle phases that cytotoxic compounds target and quantify the percentages of cell transitions that are blocked compared with the untreated population, which will lead to improved understanding of drug efficacy and mechanism of action.

Radiation-induced cell cycle perturbations: a computational tool validated with flow-cytometry data

Cell cycle progression can be studied with computational models that allow to describe and predict its perturbation by agents as ionizing radiation or drugs. Such models can then be integrated in tools for pre-clinical/clinical use, e.g. to optimize kinetically-based administration protocols of radiation therapy and chemotherapy. We present a deterministic compartmental model, specifically reproducing how cells that survive radiation exposure are distributed in the cell cycle as a function of dose and time after exposure. Model compartments represent the four cell-cycle phases, as a function of DNA content and time. A system of differential equations, whose parameters represent transition rates, division rate and DNA synthesis rate, describes the temporal evolution. Initial model inputs are data from unexposed cells in exponential growth. Perturbation is implemented as an alteration of model parameters that allows to best reproduce cell-cycle profiles post-irradiation. The model is validated with dedicated in vitro measurements on human lung fibroblasts (IMR90). Cells were irradiated with 2 and 5 Gy with a Varian 6 MV Clinac at IRCCS Maugeri. Flow cytometry analysis was performed at the RadBioPhys Laboratory (University of Pavia), obtaining cell percentages in each of the four phases in all studied conditions up to 72 h post-irradiation. Cells show early \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{G}}_{2}$$\end{document}G2-phase block (increasing in duration as dose increases) and later \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{G}}_{1}$$\end{document}G1-phase accumulation. For each condition, we identified the best sets of model parameters that lead to a good agreement between model and experimental data, varying transition rates from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{G}}_{1}$$\end{document}G1- to S- and from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{G}}_{2}$$\end{document}G2- to M-phase. This work offers a proof-of-concept validation of the new computational tool, opening to its future development and, in perspective, to its integration in a wider framework for clinical use.

Age Structure Can Account for Delayed Logistic Proliferation of Scratch Assays

Scratch assays are in vitro methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. Typically, scratch assays are modelled by reaction diffusion equations depicting cell migration by Fickian diffusion and proliferation by a logistic term. In a recent paper (Jin et al. in Bull Math Biol 79(5):1028-1050, 2017), the authors observed experimentally that during the early stage of the recolonisation process, there is a disturbance phase where proliferation is not logistic, and this is followed by a growth phase where proliferation appears to be logistic. The authors did not identify the precise mechanism that causes the disturbance phase but showed that ignoring it can lead to incorrect parameter estimates. The aim of this work is to show that a nonlinear age-structured population model can account for the two phases of proliferation in scratch assays. The model consists of an age-structured cell cycle model of a cell population, coupled with an ordinary differential equation describing the resource concentration dynamics in the substrate. The model assumes a resource-dependent cell cycle threshold age, above which cells are able to proliferate. By studying the dynamics of the full system in terms of the subpopulations of cells that can proliferate and the ones that can not, we are able to find conditions under which the model captures the two-phase behaviour. Through numerical simulations, we are able to show that the interplay between the resource concentration in the substrate and the cell subpopulations dynamics can explain the biphasic dynamics.

A mathematical model of subpopulation kinetics for the deconvolution of leukaemia heterogeneity

Acute myeloid leukaemia is characterized by marked inter- and intra-patient heterogeneity, the identification of which is critical for the design of personalized treatments. Heterogeneity of leukaemic cells is determined by mutations which ultimately affect the cell cycle. We have developed and validated a biologically relevant, mathematical model of the cell cycle based on unique cell-cycle signatures, defined by duration of cell-cycle phases and cyclin profiles as determined by flow cytometry, for three leukaemia cell lines. The model was discretized for the different phases in their respective progress variables (cyclins and DNA), resulting in a set of time-dependent ordinary differential equations. Cell-cycle phase distribution and cyclin concentration profiles were validated against population chase experiments. Heterogeneity was simulated in culture by combining the three cell lines in a blinded experimental set-up. Based on individual kinetics, the model was capable of identifying and quantifying cellular heterogeneity. When supplying the initial conditions only, the model predicted future cell population dynamics and estimated the previous heterogeneous composition of cells. Identification of heterogeneous leukaemia clones at diagnosis and post-treatment using such a mathematical platform has the potential to predict multiple future outcomes in response to induction and consolidation chemotherapy as well as relapse kinetics.

Effects of p21 Gene Down-Regulation through RNAi on Antler Stem Cells In Vitro

Cell cycle is an integral part of cell proliferation, and consists mainly of four phases, G1, S, G2 and M. The p21 protein, a cyclin dependent kinase inhibitor, plays a key role in regulating cell cyclevia G1 phase control. Cells capable of epimorphic regeneration have G2/M accumulation as their distinctive feature, whilst the majority of somatic cells rest at G1 phase. To investigate the role played byp21 in antler regeneration, we studied the cell cycle distribution of antler stem cells (ASCs), via down-regulation of p21 in vitro using RNAi. The results showed that ASCs had high levels of p21 mRNA expression and rested at G1 phase, which was comparable to the control somatic cells. Down-regulation of p21 did not result in ASC cell cycle re-distribution toward G2/M accumulation, but DNA damage and apoptosis of the ASCs significantly increased and the process of cell aging was slowed. These findings suggest that the ASCs may have evolved to use an alternative, p21-independent cell cycle regulation mechanism. Also a unique p21-dependent inhibitory effect may control DNA damage as a protective mechanism to ensure the fast proliferating ASCs do not become dysplastic/cancerous. Understanding of the mechanism underlying the role played by p21 in the ASCs could give insight into a mammalian system where epimorphic regeneration is initiated whilst the genome stability is effectively maintained.