A Microenvironment Based Model of Antimitotic Therapy of Gompertzian Tumor Growth

A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies—after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter λ, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.     

Inferring the effect of therapy on tumors showing stochastic Gompertzian growth

The present work deals with a Gompertz-type diffusion process, which includes in the drift term a time-dependent function C(t) representing the effect of a therapy able to modify the dynamics of the underlying process. However, in experimental studies is not immediate to deduce the functional form of C(t) from a treatment protocol. So a statistical approach is proposed in order to estimate this function when a control group and one or more treated groups are observed. In order to validate the proposed strategy a simulation study for several interesting functional forms of C(t) has been carried out. Finally, an application to infer the net effect of cisplatin and doxorubicin+cyclophosphamide in actual murine models is presented.     

Observer-based techniques for the identification and analysis of avascular tumor growth

Cancer represents one of the most challenging issues for the biomedical research, due its large impact on the public health state. For this reason, many mathematical methods have been proposed to forecast the time evolution of cancer size and invasion. In this paper, we study how to apply the Gompertz’s model to describe the growth of an avascular tumor in a realistic setting. To this aim, we introduce mathematical techniques to discretize the model, an important requirement when discrete-time measurements are available. Additionally, we describe observed-based techniques, borrowed from the field of automation theory, as a tool to estimate the model unknown parameters. This identification approach is a promising alternative to traditional statistical methods, and it can be easily extended to other models of cancer growth as well as to the evaluation of not measurable variables, on the basis of the available measurements. We show an application of this method to the analysis of solid tumor growth and parameters estimation in presence of a chemotherapy agent.     

Stochastic and deterministic simulations of heterogeneous cell population dynamics

A Monte Carlo algorithm, which can accurately simulate the dynamics of entire heterogeneous cell populations, was developed. The algorithm takes into account the random nature of cell division as well as unequal partitioning of cellular material at cell division. Moreover, it is general in the sense that it can accommodate a variety of single-cell, deterministic reaction kinetics as well as various stochastic division and partitioning mechanisms. The validity of the algorithm was assessed through comparison of its results with those of the corresponding deterministic cell population balance model in cases where stochastic behavior is expected to be quantitatively negligible. Both algorithms were applied to study: (a) linear intracellular kinetics and (b) the expression dynamics of a genetic network with positive feedback architecture, such as the lac operon. The effects of stochastic division as well as those of different division and partitioning mechanisms were assessed in these systems, while the comparison of the stochastic model with a continuum model elucidated the significance of cell population heterogeneity even in cases where only the prediction of average properties is of primary interest.     

A mathematical model to study the effects of drugs administration on tumor growth dynamics

A mathematical model for describing the cancer growth dynamics in response to anticancer agents administration in xenograft models is discussed. The model consists of a system of ordinary differential equations involving five parameters (three for describing the untreated growth and two for describing the drug action). Tumor growth in untreated animals is modelled by an exponential growth followed by a linear growth. In treated animals, tumor growth rate is decreased by an additional factor proportional to both drug concentration and proliferating cells. The mathematical analysis conducted in this paper highlights several interesting properties of this tumor growth model. It suggests also effective strategies to design in vivo experiments in animals with potential saving of time and resources. For example, the drug concentration threshold for the tumor eradication, the delay between drug administration and tumor regression, and a time index that measures the efficacy of a treatment are derived and discussed. The model has already been employed in several drug discovery projects. Its application on a data set coming from one of these projects is discussed in this paper.     

Stochastic Gompertz model of tumour cell growth

In this communication, based upon the deterministic Gompertz law of cell growth, a stochastic model in tumour growth is proposed. This model takes account of both cell fission and mortality too. The corresponding density function of the size of the tumour cells obeys a functional Fokker--Planck equation which can be solved analytically. It is found that the density function exhibits an interesting "multi-peak" structure generated by cell fission as time evolves. Within this framework the action of therapy is also examined by simply incorporating a therapy term into the deterministic cell growth term.     

An approximation method for estimating cell loss from a growing tumor

A simple self-consistent calculational scheme is developed for estimating cell loss for a growing tumor (or other population) when the growth fraction can be estimated at regular intervals. This is applied to published data for a particular much-studied Ehrlich ascites tumor. The loss rate is found to be substantially higher than that estimated by previous, less precise means.     

Cell adhesion molecules, signal transduction and cell growth

Signals from dynamic cellular interactions between the extracellular matrix and neighboring cells ultimately input into the cellular decision-making process. These interactions form the basis of anchorage-dependent growth. Recent advances have provided the mechanistic details behind the ability of integrins, and other cell adhesion molecules (CAMs), to regulate both early signal transduction events initiated by soluble factors and downstream events more proximally involved in cell cycle progression. These actions appear to depend on the ability of CAMs to initiate the formation of organized structures that permit the efficient flow of information.     

Estrogen receptor beta in breast cancer—Diagnostic and therapeutic implications

More than 10 years have passed since the discovery of the second estrogen receptor, estrogen receptor β (ERβ). It is now evident that ERα is not the only ER in breast cancer cells; in fact, ERβ is expressed in the majority of breast cancers although at lower levels than in the normal breast. In addition, ERβ is expressed in breast cancer infiltrating lymphocytes, fibroblasts and endothelial cells, all known to influence tumor growth. By overexpressing or knocking-out ERβ in breast cancer cell lines, several researchers have investigated its function with respect to proliferation and tumor growth. It appears that ERβ is anti-proliferative, in many ways antagonising the function of ERα. Furthermore, phytoestrogens have a binding-preference for ERβ and several epidemiological studies indicate a breast cancer preventing effect of this class of compounds. Tamoxifen is one of the standard, adjuvant treatments for ERα positive breast cancer, classically thought to mediate its effect through ERα. However, in several recent studies, ERβ has been described as a potential marker for tamoxifen response. In summary, experimental, epidemiological as well as diagnostic studies point towards ERβ as an important factor in breast cancer, opening up the possibility for novel ERβ-selective therapies in the treatment of breast cancer.     

A proapoptotic peptide conjugated to penetratin selectively inhibits tumor cell growth

The peptide KLA (acetyl-(KLAKLAK)₂-NH₂), which is rather non toxic for eukaryotic cell lines, becomes active when coupled to the cell penetrating peptide, penetratin (Pen), by a disulfide bridge. Remarkably, the conjugate KLA–Pen is cytotoxic, at low micromolar concentrations, against a panel of seven human tumor cell lines of various tissue origins, including cells resistant to conventional chemotherapy agents but not to normal human cell lines. Live microscopy on cells possessing fluorescent labeled mitochondria shows that in tumor cells, KLA–Pen had a strong impact on mitochondria tubular organization instantly resulting in their aggregation, while the unconjugated KLA and pen peptides had no effect. But, mitochondria in various normal cells were not affected by KLA–Pen. The interaction with membrane models of KLA–Pen, KLA and penetratin were studied using dynamic light scattering, calorimetry, plasmon resonance, circular dichroism and ATR-FTIR to unveil the mode of action of the conjugate. To understand the selectivity of the conjugate towards tumor cell lines and its action on mitochondria, lipid model systems composed of zwitterionic lipids were used as mimics of normal cell membranes and anionic lipids as mimics of tumor cell and mitochondria membrane. A very distinct mode of interaction with the two model systems was observed. KLA–Pen may exert its deleterious and selective action on cancer cells by the formation of pores with an oblique membrane orientation and establishment of important hydrophobic interactions. These results suggest that KLA–Pen could be a lead compound for the design of cancer therapeutics.     

Endogenous fragment of hemoglobin, neokyotorphin, as cell growth factor

It is shown that neokyotorphin (the -globin fragment 137–141) stimulates proliferation of normal cells (murine embryonic fibroblasts, red bone marrow and spleen cells) and tumor cells (murine melanoma and transformed fibroblasts L929) in the absence or in the presence of fetal bovine serum. In contrast to serum deprivation conditions, the ability to potentiate L929 cell growth in the presence of fetal serum is strongly cell density dependent. The peptide also enhances the viability of L929 cells, murine embryonic fibroblasts and of the primary cultures of murine red bone marrow cells and splenocytes under serum-deprivation conditions for at least 72 h. The results of flow cytometry analysis suggest that the effect of neokyotorphin on survival of L929 cells in serum-free culture medium is due to maintenance of cell proliferation in the absence of growth factors. Along with cell cycle progression the peptide induces reversible reduction of L929 cell size.     

The integration of cell proliferation and growth in leaf morphogenesis

A number of recent publications have assessed the outcome on leaf development of targeted manipulation of cell proliferation. The results of these investigations have awakened interest in the long-standing debate in plant biology on the precise role of cell division in morphogenesis. Does cell proliferation drive morphogenesis (cell theory) or is it subservient to a mechanism which acts at the whole organ level to regulate morphogenesis (organismal theory)? In this review, the central role of growth processes (distinct from cell proliferation) in morphogenesis is highlighted and the limitations in our understanding of the basic mechanisms of plant growth control are highlighted. Finally, an attempt is made to demonstrate how sequential local co-ordination of growth might provide an interpretation of some of the recent observations on cell proliferation and leaf morphogenesis.     

The relationship between cell and population growth

A steady-state model of cell volume frequency distribution using the method of Williams (1971) is derived. Results are compared to a Monte Carlo simulation of cell growth and division. It is suggested that the Monte Carlo method might be of value for investigating cell and population properties for which analytic methods are not currently available.     

LKB1, a protein kinase regulating cell proliferation and polarity

LKB1 is a serine-threonine protein kinase mutated in patients with an autosomal dominantly inherited cancer syndrome predisposing to multiple benign and malignant tumours, termed Peutz-Jeghers syndrome. Since its discovery in 1998, much research has focused on identification and characterisation of its cellular roles and analysing how LKB1 might be regulated. In this review we discuss exciting recent advances indicating that LKB1 functions as a tumour suppressor perhaps by controlling cell polarity. We also outline the current understanding of the molecular mechanisms by which LKB1 is regulated in vivo, through interaction with other proteins as well as by protein phosphorylation and prenylation.     

Modelling cell population growth with applications to cancer therapy in human tumour cell lines

In this paper we present an overview of the work undertaken to model a population of cells and the effects of cancer therapy. We began with a theoretical one compartment size structured cell population model and investigated its asymptotic steady size distributions (SSDs) (On a cell growth model for plankton, MMB JIMA 21 (2004) 49). However these size distributions are not similar to the DNA (size) distributions obtained experimentally via the flow cytometric analysis of human tumour cell lines (data obtained from the Auckland Cancer Society Research Centre, New Zealand). In our one compartment model, size was a generic term, but in order to obtain realistic steady size distributions we chose size to be DNA content and devised a multi-compartment mathematical model for the cell division cycle where each compartment corresponds to a distinct phase of the cell cycle (J. Math. Biol. 47 (2003) 295). We then incorporated another compartment describing the possible induction of apoptosis (cell death) from mitosis phase (Modelling cell death in human tumour cell lines exposed to anticancer drug paclitaxel, J. Math. Biol. 2004, in press). This enabled us to compare our model to flow cytometric data of a melanoma cell line where the anticancer drug, paclitaxel, had been added. The model gives a dynamic picture of the effects of paclitaxel on the cell cycle. We hope to use the model to describe the effects of other cancer therapies on a number of different cell lines.     

MicroRNA-210 regulates cancer cell proliferation through targeting fibroblast growth factor receptor-like 1 (FGFRL1)

The importance of microRNAs (miRNAs) in human malignancies has been well recognized. Here, we report that the expression of microRNA-210 (miR-210) is down-regulated in human esophageal squamous cell carcinoma and derived cell lines. Marked decreases in the level of miR-210 were observed especially in poorly differentiated carcinomas. We found that miR-210 inhibits cancer cell survival and proliferation by inducing cell death and cell cycle arrest in G(1)/G(0) and G(2)/M. Finally, we identified fibroblast growth factor receptor-like 1 (FGFRL1) as a target of miR-210 in esophageal squamous cell carcinoma and demonstrated that FGFRL1 accelerates cancer cell proliferation by preventing cell cycle arrest in G(1)/G(0). Taken together, our findings show an important role for miR-210 as a tumor-suppressive microRNA with effects on cancer cell proliferation.