Narrow Results

The cells in a tissue occupying a region Ω_t are divided according to their cycling phase. The density p_i of cells in phase i depends on the spatial variable x, the time t, and the time s_i since the cells entered in phase i. The p_i(x, t, s_i) and the oxygen concentration w(x, t) satisfy a system of PDEs in Ω_t, and the boundary of Ω_t is a free boundary. We denote by the oxygen concentration on the free boundary and consider the radially symmetric case, so that Ω_t = {r < R(t)}. We prove that R(t) is always bounded; furthermore, if is small, then R(t) → 0 as t → ∞, and if is large, then R(t) ≥ c > 0 for all t. Finally, we prove the existence and uniqueness of a stationary solution in a special case.

In this paper, we construct a model to describe the spatial motion of a monolayer of cells occupying a two-dimensional dish. By taking care of nonlocal contact inhibition, quiescence phenomenon, and the cell cycle, we derive porous media-like equation with nonlocal reaction terms. The first part of this paper is devoted to the construction of the model. In the second part we study the well-posedness of the model. We conclude the paper by presenting some numerical simulations of the model and we observe the formation of colonies.

This paper presents a new stochastic model to describe the progression of cells subject to radiation damage, through their cell cycles. The expected number of cells in various phases in the transient and steady state are obtained. Several interesting cases like quiescence in tumor cell population, effects of split dose and holding time on cell survival are also discussed using the developed model. The phase structured model offers quiescence and variable cell cycle time as contributing factors for the retardation of cell growth and the ultimate cell population reaching a steady state.

A class of mathematical models for cancer chemotherapy which has been described in the literature takes the form of an optimal control problem with dynamics given by a bilinear system. In this paper we analyze a three-dimensional model in which the cell-cycle is broken into three compartments. The cytostatic agent used as control to kill the cancer cells is active in a compartment which combines the second growth phase and mitosis where cell-division occurs. A blocking agent is used as a second control to slow down the transit of cells during synthesis, but does not kill cells. The cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. It is shown that singular controls are not optimal. This eliminates treatments where during some time only a portion of the full drug dose is administered. Consequently only treatments which alternate between a full and no dose, i.e., so-called bang-bang controls, canbe optimal for this model. Both necessary and sufficient conditions for optimality of treatment schedules of this type are given.

The underlying biochemical mechanisms that drive the cell division cycle involve the interactions and feedback controls between the cytoplasmic proteins cdc2 and cyclin, and the activities of the cdc2-cyclin complex MPF. Alternation between interphase and mitosis is associated with oscillatory MPF and cyclin levels. This paper describes an ordinary differential equations (ODE) model and a functional differential equations (FDE) model of the cell cycle based on experimental work with the newly fertilized frog egg. One major difference of these models from previous ones is the use of nonspecific reaction terms in describing the interactions between cdc2, cyclin and MPF. This qualitative approach makes possible the evaluation of the roles of the various reactions and feedback mechanisms in the control of the cell cycle.

Cell proliferation is considered as a periodic process which is governed by a two-variable relaxation timer. The collective behavior of a system composed of three identical relaxation oscillators is numerically studied under the condition that diffusion of the slow mode (inhibitor) dominates. The phase diagrams for cyclic and linear configurations show unexpectable diversity of stable periodic regimes, some of them are only observable under intermediate but reasonable values of coupling and stiffness. For cyclic configuration we demonstrate: (1) the existence of three periodic regimes with different periods and phase relations and unsymmetrical stable steady state (USSS); (2) the coexistence of in-phase oscillations and USSS; (3) the coexistence of periodic attractors and (4) the emergence of special kind of rotating wave which is manifested as two-loop limit cycle. The natural asymmetry of linear configuration leads to the appearance of many periodic attractors. The most of them are characterized by the large period oscillations of the middle element which has the step-like dependence of period versus coupling. The qualitative reasons for such a diversity and its possible role in the generation of cell cycle variability are discussed.

In this work the dynamics of coupled nonlinear oscillators, which are ubiquitous in biology, is experimentally studied by using electrical relaxation oscillators. The results of this analog computation obtained with two and three coupled oscillators are in agreement with the results known from numerical approaches. Phase death, which is a mutual annihilation of oscillations, is a generic phenomenon. All modes known from approaches using identical oscillators have been found. Additionally we observed new generic modes that are caused by inhomogeneities of the oscillators, such differences being typical for biological cells. Simulations of excitable electrical oscillators yield similar results.

Most living organisms display many types of biological rhythms. We describe how a growing population of cells may be distributed between age classes or cell types, and define conditions necessary to produce synchronous population development. A probabilistic model describing the changes in cell numbers during proliferation is presented. The model predicts that during cell reproduction with constant parameters any cell population approaches a stationary behavior. According to this model, synchronization of cell growth is possible if there is a uniform parameter set for cell division. This point is illustrated by a set of graphs showing snapshots of model simulations with different parameter sets for transient and stationary behaviors.

Boolean models represent a drastic simplification of complex biomolecular systems, and yet accurately predict system properties, e.g., effective control strategies. Why is this? Parameter robustness has been highlighted as a general feature of biomolecular systems and may play an important role in the accuracy of Boolean models. We argue here that a useful way to view a system’s controllability properties is through its repertoire of self-sustaining positive circuits (stable motifs). We examine attractor control and self-sustaining circuits within the cell cycle restriction switch, a bistable regulatory circuit that allows or prevents entry into the cell cycle. We explore this system using three models: a previously published Boolean model, a Hill kinetics model that we construct from the Boolean model using the HillCube methodology, and a reaction-based model we construct from the literature. We highlight the robustness of stable motifs across these three levels of modeling detail. We also show how consideration of control-robust regulatory circuits can aid in parameter specification.

Cluster analysis has proven to be a valuable statistical method for analyzing whole genome expression data. Although clustering methods have great utility, they do represent a lower level statistical analysis that is not directly tied to a specific model. To extend such methods and to allow for more sophisticated lines of inference, we use cluster analysis in conjunction with a specific model of gene expression dynamics. This model provides phenomenological dynamic parameters on both linear and non-linear responses of the system. This analysis determines the parameters of two different transition matrices (linear and nonlinear) that describe the influence of one gene expression level on another. Using yeast cell cycle microarray data as test set, we calculated the transition matrices and used these dynamic parameters as a metric for cluster analysis. Hierarchical cluster analysis of this transition matrix reveals how a set of genes influence the expression of other genes activated during different cell cycle phases. Most strikingly, genes in different stages of cell cycle preferentially activate or inactivate genes in other stages of cell cycle, and this relationship can be readily visualized in a two-way clustering image. The observation is prior to any knowledge of the chronological characteristics of the cell cycle process. This method shows the utility of using model parameters as a metric in cluster analysis.

A breast cancer subtype classification scheme, PAM50, based on genetic information is widely accepted for clinical applications. On the other hands, experimental cancer biology studies have been successful in revealing the mechanisms of breast cancer and now the hallmarks of cancer have been determined to explain the core mechanisms of tumorigenesis. Thus, it is important to understand how the breast cancer subtypes are related to the cancer core mechanisms, but multiple studies are yet to address the hallmarks of breast cancer subtypes. Therefore, a new approach that can explain the differences among breast cancer subtypes in terms of cancer hallmarks is needed.

We developed an information theoretic sub-network mining algorithm, differentially expressed sub-network and pathway analysis (DeSPA), that retrieves tumor-related genes by mining a gene regulatory network (GRN) of transcription factors and miRNAs. With extensive experiments of the cancer genome atlas (TCGA) breast cancer sequencing data, we showed that our approach was able to select genes that belong to cancer core pathways such as DNA replication, cell cycle, p53 pathways while keeping the accuracy of breast cancer subtype classification comparable to that of PAM50. In addition, our method produces a regulatory network of TF, miRNA, and their target genes that distinguish breast cancer subtypes, which is confirmed by experimental studies in the literature.

Signaling pathways are responsible for the regulation of cell processes, such as monitoring the external environment, transmitting information across membranes, and making cell fate decisions. Given the increasing amount of biological data available and the recent discoveries showing that many diseases are related to the disruption of cellular signal transduction cascades, in silico discovery of signaling pathways in cell biology has become an active research topic in past years. However, reconstruction of signaling pathways remains a challenge mainly because of the need for systematic approaches for predicting causal relationships, like edge direction and activation/inhibition among interacting proteins in the signal flow. We propose an approach for predicting signaling pathways that integrates protein interactions, gene expression, phenotypes, and protein complex information. Our method first finds candidate pathways using a directed-edge-based algorithm and then defines a graph model to include causal activation relationships among proteins, in candidate pathways using cell cycle gene expression and phenotypes to infer consistent pathways in yeast. Then, we incorporate protein complex coverage information for deciding on the final predicted signaling pathways. We show that our approach improves the predictive results of the state of the art using different ranking metrics.

In this work, we study period control of the mammalian cell cycle via coupling with the cellular clock. For this, we make use of the oscillators’ synchronization dynamics and investigate methods of slowing down the cell cycle with the use of clock inputs. Clock control of the cell cycle is well established via identified molecular mechanisms, such as the CLOCK:BMAL1-mediated induction of the wee1 gene, resulting in the WEE1 kinase that represses the active form of mitosis promoting factor (MPF), the essential cell cycle component. To investigate the coupling dynamics of these systems, we use previously developed models of the clock and cell cycle oscillators and center our studies on unidirectional clock $\to$ cell cycle coupling. Moreover, we propose an hypothesis of a Growth Factor (GF)-responsive clock, involving a pathway of the non-essential cell cycle complex cyclin D/CDK4. We observe a variety of rational ratios of clock to cell cycle period, such as: 1:1, 3:2, 4:3, and 5:4. Finally, our protocols of period control are successful in effectively slowing down the cell cycle by the use of clock modulating inputs, some of which correspond to existing drugs.

We present a kinetic model describing the growth of eukaryotic cells or, more specifically, the dependence of the cell volume on time in terms of the global interplay of the mRNA and protein synthesis and degradation and lipid synthesis. Addressing two long-standing questions in this interdisciplinary field, we explain why the average protein concentration in growing cells is nearly constant and the growth can accurately be fitted by using a bilinear or exponential function.

Programmed cell death, or apoptosis, and controlled cell division, or mitosis, are two highly regulated processes in the cell cycle. A balance between apoptosis and mitosis is critical for multiple distinct states including embryonic development, immune cell activation, stem cell differentiation, tissue formation (wound healing), and tumor prevention, among others. A cell undergoing apoptosis shows a series of characteristic morphological changes similar to normal mitosis and an aberrant form of mitosis. During each of these processes, nuclear chromatin condenses, the nuclear lamina and cytoplasmic membranes disintegrate, and cells decrease in volume. The morphological resemblance among cells undergoing these processes suggests that the underlying intracellular signaling pathways influence the mitotic cell fate. In this paper, the relationship of intracellular signaling pathways, cell cycle dynamics, and apoptotic cell signaling pathways is discussed. The mitogen-activated protein kinases/extracellular signal-regulated kinases (MAPK/Ras/Raf/ERK), phosphatidylinositol 3-kinase/protein kinase B (PI3K/Akt), Janus kinase/signal transducer and activator of transcription (JAK/STAT), wingless-related integration site (Wnt), and transforming growth factor beta (TGF-$\beta )$ are major cell signaling pathways that transmit signals from multiple cell surface receptors to transcription factors in the nucleus. The pathways are stimulated by cytokines, growth factors, and external stimuli, i.e., reactive oxygen species which induce signal transduction pathways and regulate complex processes such as cell cycle progression, cell proliferation, cellular growth, differentiation, and apoptosis. Aberrant mutations in particular genes and proteins of these pathways contribute to cancers usually by inhibiting pro-apoptotic proteins (e.g., Bak, Bax, Noxa, Puma, etc.) and stimulating antiapoptotic proteins (e.g., Bcl-2, Bcl-XL, Mcl-1, etc.). The cell cycle is regulated by intracellular signaling pathways such as the MAPK/Ras/Raf/ERK and PI3K pathways to produce the synthesis of cyclin D and other mitosis regulating proteins (Myc and Jun). Cyclin D1 binds to cyclin-dependent kinase (CDK) 4 and CDK 6 (CDK4/6) to form an effective complex, activate several substrates, and initiate the cell cycle. The prominent molecules that regulate signaling pathways in normal and cancer cells are described.

Objective: The present study was designed to investigate the cytoprotective effects of ginsenoside Rg1 (GS-Rg1) against malondialdehyde (MDA)-suppressed proliferation of the mesenchymal stem cells (MSCs) and its possible mechanisms in vitro.

Methods: Murine bone marrow-derived MSCs were treated with GS-Rg1 (10, 50, 100mg/L) for 24h before being incubated with MDA in vitro, CFU-Fassay, the cell viability and BrdU incorporation assay were examined, the expression of cyclin-dependent kinase 2 (CDK2), p21 and cyclin E of MSC were examined by Q-RT-PCR and Western blotting.

Results: The results showed that the number and size of murine bone marrow MSC colonies, the number of colony-forming cells, methyl thiazolyltetrazolium (MTT) absorbed value greatly and percentage of BrdU-positive cells increased significantly in MSC pretreated with GS-Rg1. GS-Rgl pretreatment markedly decreased the expression level of p21 and increased the expression of CDK2 and cyclin E. GS-Rg1 protects MSCs from MDA-suppressed proliferation.

Conclusion: The protective mechanism could be related to its ability to increase the expression of CDK2 and cyclin E, and to reduce the expression of p21.

DNA replication is restricted to a specific time window of the cell cycle, called S phase. Successful progression through S phase requires replication to be properly regulated to ensure that the entire genome is duplicated exactly once, without errors, in a timely fashion. As a result, DNA replication has evolved into a tightly regulated process involving the coordinated action of numerous factors that function in all phases of the cell cycle. Biochemical mechanisms driving the eukaryotic cell division cycle have been the subject of a number of mathematical models. However, cell cycle networks reported in literature so far have not addressed the steps of DNA replication events. In particular, the assembly of the replication machinery is crucial for the timing of S phase. This event, called "initiation", which occurs in late M / early G₁ of the cell cycle, starts with the assembly of the pre-replicative complex (pre-RC) at the origins of replication on the DNA. Its activation depends on the availability of different kinase complexes, cyclin-dependent kinases (CDKs) and Dbf-dependent kinase (DDK), which phosphorylate specific components of the pre-RC to convert it into the pre-initiation complex (pre-IC). We have developed an ODE-based model of the network responsible for this process in budding yeast by using mass-action kinetics. We considered all steps from the assembly of the first components at the DNA replication origin up to the active replisome that recruits the polymerases and verified the computational dynamics with the available literature data. Our results highlighted the link between activation of CDK and DDK and the step-by-step formation of both pre-RC and pre-IC, suggesting S-CDK (Cdk1-Clb5,6) to be the main regulator of the process.

To produce precise number of neurons and glial cells from neuroepithelial cells, the progeression and exit of the cell cycle should accurately be coordinated. In mammalian neuroepithelial cells, the molecular and cellular mechanisms coordinating the cell cycle progression and neuronal differentiation is yet unknown. Recently, we noticed that a certain cell cycle regulator protein localized in the basal endfeet of the mouse neuroepithelial cells. However, it is difficult to know in which cell cycle phase the protein localizes, because suitable cell cycle markers expressed at the endfeet of the neuroepithelial cells are missing. To address this issue, we performed sequential labeling of neuroepithelial cells by introducing EGFP-F cDNA into cultured mouse embryos using electroporation and short pulse labeling of S-phase cells by incorporating BrdU, and analyzed the cell cycle phase of EGFP-F labeled cells by using antibodies to BrdU and PH3 (a M-phase marker). We found that EGFP-F-labled cells were in S-phase to Gl-phase, but not in G2-phase to M-phase 6 hours after electroporation, and that both of the nucleus and the whole outline of neuroepithelial cell including bipolar processes were clearly visualized. These results suggest that our labeling strategy makes it possible to characterize the cell cycle of neuroepithelial cells, and therefore the cell cycle-dependent distribution of cytoplasmic proteins at the endfeet would be elucidated in the future.

This expository paper provides an introduction to computational methods for solving continuous models of certain biological systems. These systems have important behavior in space and within the age distribution of individuals. Very often, the spatial behavior depends critically on the age structure of the population. The different spatial scales induce different time scales in the problem, whereas age and time advance together.

Age- and space-structured multiscale systems arise in a wide variety of biological problems ranging from multicellular and tissue-level phenomena to problems in ecology and evolutionary biology. We describe a general modeling framework used to represent such biological systems. We then discuss computational methods used to solve the model equations, beginning with a treatment of the moving-grid Galerkin method used to decouple age and time while they advance together, introduce how this discretization in age works with discretizations in time and space, and then review how more complicated nonlinear problems would be treated. We close by presenting two example systems, swarm-colony development of the bacteria Proteus mirabilis and tumor invasion, which differ in some important respects from the general model, but which are effectively treated by the computational methods presented in this paper.

The testis-specific protein Y-encoded (TSPY) gene is one of the early genes identified on the human Y chromosome. It is tandemly repeated on the short arm of this chromosome, postulated to contain the gonadoblastoma locus responsible for predisposing dysfunctional germ cells to tumorigenesis. TSPY encodes a phosphoprotein harboring a conserved domain, termed SET/NAP, present in various proteins involved in cell cycle regulation, chromatin modeling, and transcription regulation. Six TSPY-like genes have been identified in different mammalian genomes. One in particular, designated as TSPX, is located on the syntenic region of the X chromosome. Both TSPY and TSPX maintain a similar gene organization with six and seven exons, respectively. TSPX encodes a protein with two additional domains, an N-terminal proline-rich domain and a carboxyl bipartite acidic domain, that are absent in TSPY. Both TSPY and TSPX possess contrasting properties in cell cycle regulation when they are ectopically expressed. Other autosomal members of this gene family are single-exon genes, postulated to be retrotransposons of TSPY. They encode similar-sized proteins that share high levels of homology at their SET/NAP domains, but diverge at the flanking regions. Specific mutations on the TSPY-Like 1 gene have been demonstrated to be responsible for the sudden infant death with dysgenesis of the testes syndrome. Hence, TSPY and TSPY-like genes are hypothesized to serve a variety of different physiological functions mediated by the conserved SET/NAP and unique domains in their respective proteins.