Biomedical subjects

Franziska Michor

Publications and source records attributed to Franziska Michor.

At least 19 recordsLinked to original sources

PubMed2006

Dynamics of metastasis suppressor gene inactivation.

For most cancer cell types, the acquisition of metastatic ability leads to clinically incurable disease. Twelve metastasis suppressor genes (MSGs) have been identified that reduce the metastatic propensity of cancer cells. If these genes are inactivated in both alleles, metastatic ability is promoted. Here, we develop a mathematical model of the dynamics of MSG inactivation and calculate the expected number of metastases formed by a tumor. We analyse the effects of increased mutation rates and different fitness values of cells with one or two inactivated alleles on the ability of a tumor to form metastases. We find that mutations that are negatively selected in the main tumor are unlikely to be responsible for the majority of metastases produced by a tumor. Most metastases-causing mutations will be present in all (or most) cells in the main tumor.

Animals↗

PubMed2006

Genetic instability and clonal expansion.

Inactivation of tumor suppressor genes can lead to clonal expansion. We study the evolutionary dynamics of this process and calculate the probability that inactivation of a tumor suppressor gene is preceded by mutations in genes that confer genetic instability. Unstable cells might have a slower rate of clonal expansion than stable cells because of an increased probability of generating lethal mutations or inducing apoptosis. We show that the different growth rates of genetically stable and unstable cells during clonal expansion represent, in general, only a small disadvantage for genetic instability. The intuitive reason for this conclusion is that robust clonal expansion, where cellular birth rates are significantly greater than death rates, occurs on a much faster time scale than waiting for those mutations that allow clonal expansion. Moreover, in special cases where clonal expansion is very slow, genetically unstable cells have a higher probability to accumulate additional mutations during clonal expansion that confer a selective advantage. Clonal expansion represents a major disadvantage for genetic instability only when inactivation of the tumor suppressor gene leads to a very small increase of the cellular reproductive rate that is cancelled by the increased mortality of unstable cells.

Animals↗

PubMed2006

Genetic instability and the quasispecies model.

Genetic instability is a defining characteristic of cancers. Microsatellite instability (MIN) leads to by elevated point mutation rates, whereas chromosomal instability (CIN) refers to increased rates of losing or gaining whole chromosomes or parts of chromosomes during cell division. CIN and MIN are, in general, mutually exclusive. The quasispecies model is a very successful theoretical framework for the study of evolution at high mutation rates. It predicts the existence of an experimentally verified error catastrophe. This catastrophe occurs when the mutation rates exceed a threshold value, the error threshold, above which replicative infidelity is incompatible with cell survival. We analyse the semiconservative quasispecies model of both MIN and CIN tumors. We consider the role of post-methylation DNA repair in tumor cells and demonstrate that DNA repair is fundamental to the nature of the error catastrophe in both types of tumors. We find that CIN introduces a plateau in the maximum viable mutation rate for a repair-free model, which does not exist in the case of MIN. This provides a plausible explanation for the mutual exclusivity of CIN and MIN.

Chromosomal Instability↗

PubMed2006

Evolution of resistance during clonal expansion.

Acquired drug resistance is a major limitation for cancer therapy. Often, one genetic alteration suffices to confer resistance to an otherwise successful therapy. However, little is known about the dynamics of the emergence of resistant tumor cells. In this article, we consider an exponentially growing population starting from one cancer cell that is sensitive to therapy. Sensitive cancer cells can mutate into resistant ones, which have relative fitness alpha prior to therapy. In the special case of no cell death, our model converges to the one investigated by Luria and Delbrück. We calculate the probability of resistance and the mean number of resistant cells once the cancer has reached detection size M. The probability of resistance is an increasing function of the detection size M times the mutation rate u. If Mu << 1, then the expected number of resistant cells in cancers with resistance is independent of the mutation rate u and increases with M in proportion to M(1-1/alpha) for advantageous mutants with relative fitness alpha>1, to l nM for neutral mutants (alpha = 1), but converges to an upper limit for deleterious mutants (alpha<1). Further, the probability of resistance and the average number of resistant cells increase with the number of cell divisions in the history of the tumor. Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only.

Antineoplastic Agents↗

PubMed2006

Evolution of resistance to cancer therapy.

Acquired drug resistance is a major limitation for successful treatment of cancer. Resistance emerges due to drug exclusion, drug metabolism and alteration of the drug target by mutation or overexpression. Depending on therapy, the type of cancer and its stage, one or several genetic or epigenetic alterations are necessary to confer resistance to treatment. The fundamental question is the following: if a genetically diverse population of replicating cancer cells is subjected to chemotherapy that has the potential to eradicate it, what is the probability of emergence of resistance? Here, we review a general mathematical framework based on multi-type branching processes designed to study the dynamics of escape of replicating organisms from selection pressures. We apply the general model to evolution of resistance of cancer cells and discuss examples for diverse mechanisms of resistance. Our theory shows how to estimate the probability of success for any treatment regimen.

Animals↗

PubMed2005

Stochastic dynamics of metastasis formation.

Tumor metastasis accounts for the majority of deaths in cancer patients. The metastatic behavior of cancer cells is promoted by mutations in many genes, including activation of oncogenes such as RAS and MYC. Here, we develop a mathematical framework to analyse the dynamics of mutations enabling cells to metastasize. We consider situations in which one mutation is necessary to confer metastatic ability to the cell. We study different population sizes of the main tumor and different somatic fitness values of metastatic cells. We compare mutations that are positively selected in the main tumor with those that are neutral or negatively selected, but faster at forming metastases. We study whether metastatic potential is the property of all (or the majority of) cells in the main tumor or only the property of a small subset. Our theory shows how to calculate the expected number of metastases that are formed by a tumor.

Computer Simulation↗

PubMed2005

Synergy and discounting of cooperation in social dilemmas.

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.

Animals↗

PubMed2005

Dynamics of chronic myeloid leukaemia.

The clinical success of the ABL tyrosine kinase inhibitor imatinib in chronic myeloid leukaemia (CML) serves as a model for molecularly targeted therapy of cancer, but at least two critical questions remain. Can imatinib eradicate leukaemic stem cells? What are the dynamics of relapse due to imatinib resistance, which is caused by mutations in the ABL kinase domain? The precise understanding of how imatinib exerts its therapeutic effect in CML and the ability to measure disease burden by quantitative polymerase chain reaction provide an opportunity to develop a mathematical approach. We find that a four-compartment model, based on the known biology of haematopoietic differentiation, can explain the kinetics of the molecular response to imatinib in a 169-patient data set. Successful therapy leads to a biphasic exponential decline of leukaemic cells. The first slope of 0.05 per day represents the turnover rate of differentiated leukaemic cells, while the second slope of 0.008 per day represents the turnover rate of leukaemic progenitors. The model suggests that imatinib is a potent inhibitor of the production of differentiated leukaemic cells, but does not deplete leukaemic stem cells. We calculate the probability of developing imatinib resistance mutations and estimate the time until detection of resistance. Our model provides the first quantitative insights into the in vivo kinetics of a human cancer.

Benzamides↗

PubMed2005

Chromosomal instability and human cancer.

Genetic instability is a defining feature of human cancer. The main type of genetic instability, chromosomal instability (CIN), enhances the rate of gross chromosomal changes during cell division. CIN is brought about by mutations of CIN genes, i.e. genes that are involved in maintaining the genomic integrity of the cell. A major question in cancer genetics is whether genetic instability is a cause and hence a driving force of tumorigenesis. A mathematical framework for studying the somatic evolution of cancer sheds light onto the causal relations between CIN and human cancer.

Chromosomal Instability↗

PubMed2005

Virus evolution within patients increases pathogenicity.

Viruses like the human immunodeficiency virus (HIV), the hepatitis B virus (HBV), the hepatitis C virus (HCV) and many others undergo numerous rounds of inaccurate reproduction within an infected host. The resulting viral quasispecies is heterogeneous and sensitive to any selection pressure. Here we extend earlier work by showing that for a wide class of models describing the interaction between the virus population and the immune system, virus evolution has a well-defined direction toward increased pathogenicity. In particular, we study virus-induced impairment of the immune response and certain cross-reactive stimulation of specific immune responses. For eight different mathematical models, we show that virus evolution reduces the equilibrium abundance of uninfected cells and increases the rate at which uninfected cells are infected. Thus, in general, virus evolution makes things worse. An idea for combating HIV infection, however, is constructing a virus mutant that could outcompete the existing infection without being pathogenic itself.

Antigens, Viral↗

PubMed2005

Can chromosomal instability initiate tumorigenesis?

Cancers result from the accumulation of inherited and somatic mutations in oncogenes and tumor suppressor genes. These genes encode proteins that function in growth regulatory and differentiation pathways. Mutations in those genes increase the net reproductive rate of cells. Chromosomal instability (CIN) is a feature of most human cancers. Mutations in CIN genes increase the rate at which whole chromosomes or large parts of chromosomes are lost or gained during cell division. CIN causes an imbalance in chromosome number (aneuploidy) and an enhanced rate of loss of heterozygosity, which is an important mechanism of inactivating tumor suppressor genes. A crucial question of cancer biology is whether CIN is an early event and thus a driving force of tumorigenesis. Here we discuss mathematical models of situations where inactivation of one or two tumor suppressor genes is required for tumorigenesis. If two tumor suppressor genes have to be inactivated in rate-limiting steps, then CIN is likely to emerge before the inactivation of the first tumor suppressor gene.

Animals↗

PubMed2005

Dynamics of colorectal cancer.

Colorectal cancer results from an accumulation of mutations in tumor suppressor genes and oncogenes. An additional defining characteristic of colorectal cancer is its genetic instability. Two main types of genetic instability have been identified. Microsatellite instability leads to an increased point mutation rate, whereas chromosomal instability refers to an enhanced rate of accumulating gross chromosomal aberrations. All colon cancer cell lines are genetically unstable. An interesting question is whether genetic instability arises early in tumorigenesis. An early emergence of genetic instability could drive most of the somatic evolution of cancer. Here, we review mathematical models of colorectal tumorigenesis and discuss the role of genetic instability.

Colorectal Neoplasms↗

PubMed2004

Population genetics of tumor suppressor genes.

Cancer emerges when a single cell receives multiple mutations. For example, the inactivation of both alleles of a tumor suppressor gene (TSG) can imply a net reproductive advantage of the cell and might lead to clonal expansion. In this paper, we calculate the probability as a function of time that a population of cells has generated at least one cell with two inactivated alleles of a TSG. Different kinetic laws hold for small and large populations. The inactivation of the first allele can either be neutral or lead to a selective advantage or disadvantage. The inactivation of the first and of the second allele can occur at equal or different rates. Our calculations provide insights into basic aspects of population genetics determining cancer initiation and progression.

Alleles↗

PubMed2004

Determinants of human immunodeficiency virus type 1 escape from the primary CD8+ cytotoxic T lymphocyte response.

CD8+ cytotoxic T lymphocytes (CTLs) play an important role in containment of virus replication in primary human immunodeficiency virus (HIV) infection. HIV's ability to mutate to escape from CTL pressure is increasingly recognized; but comprehensive studies of escape from the CD8 T cell response in primary HIV infection are currently lacking. Here, we have fully characterized the primary CTL response to autologous virus Env, Gag, and Tat proteins in three patients, and investigated the extent, kinetics, and mechanisms of viral escape from epitope-specific components of the response. In all three individuals, we observed variation beginning within weeks of infection at epitope-containing sites in the viral quasispecies, which conferred escape by mechanisms including altered peptide presentation/recognition and altered antigen processing. The number of epitope-containing regions exhibiting evidence of early CTL escape ranged from 1 out of 21 in a subject who controlled viral replication effectively to 5 out of 7 in a subject who did not. Evaluation of the extent and kinetics of HIV-1 escape from >40 different epitope-specific CD8 T cell responses enabled analysis of factors determining escape and suggested that escape is restricted by costs to intrinsic viral fitness and by broad, codominant distribution of CTL-mediated pressure on viral replication.

Amino Acid Sequence↗

PubMed2004

Some basic properties of immune selection.

We analyze models for the evolutionary dynamics of viral or other infectious agents within a host. We study how the invasion of a new strain affects the composition and diversity of the viral population. We show that--under strain-specific immunity--the equilibrium abundance of uninfected cells declines during viral evolution. In addition, for cytotoxic immunity the absolute force of infection, and for non-cytotoxic immunity the absolute cellular virulence increases during viral evolution. We prove global stability by means of Lyapunov functions. These unidirectional trends of virus evolution under immune selection do not hold for general cross-reactive immune responses, which introduce frequency-dependent selection among viral strains. Therefore, appropriate cross-reactive immunity can lead to a viral evolution within a host which limits the extent of the disease.

Animals↗

PubMed2004

Evolutionary dynamics of tumor suppressor gene inactivation.

Tumor suppressor genes (TSGs) are important gatekeepers that protect against somatic evolution of cancer. Losing both alleles of a TSG in a single cell represents a step toward cancer. We study how the kinetics of TSG inactivation depends on the population size of cells and the mutation rates for the first and second hit. We calculate the probability as function of time that at least one cell has been generated with two inactivated alleles of a TSG. We find three different kinetic laws: in small, intermediate, and large populations, it takes, respectively, two, one, and zero rate-limiting steps to inactivate a TSG. We also study the effect of chromosomal and other genetic instabilities. Small lesions without genetic instability can take a very long time to inactivate the next TSG, whereas the same lesions with genetic instability pose a much greater risk for cancer progression.

Alleles↗

PubMed2004

Linear model of colon cancer initiation.

Cancer results if regulatory mechanisms of cell birth and death are disrupted. Colorectal tumorigenesis is initiated by somatic or inherited mutations in the APC tumor suppressor gene pathway. Several additional genetic hits in other tumor suppressor genes and oncogenes drive the progression from polyps to malignant, invasive cancer. The majority of colorectal cancers present chromosomal instability, CIN, which is caused by mutations in genes that are required to maintain chromosomal stability. A major question in cancer genetics is whether CIN is an early event and thus a driving force of tumor progression. We present a new mathematical model of colon cancer initiation assuming a linear flow from stem cells to differentiated cells to apoptosis. We study the consequences of mutations in different cell types and calculate the conditions for CIN to precede APC inactivation. We find that early emergence of CIN is very likely in colorectal tumorigenesis.

Cell Transformation, Neoplastic↗

PubMed2004

Evolutionary dynamics of invasion and escape.

Whenever life wants to invade a new habitat or escape from a lethal selection pressure, some mutations may be necessary to yield sustainable replication. We imagine situations like (i) a parasite infecting a new host, (ii) a species trying to invade a new ecological niche, (iii) cancer cells escaping from chemotherapy, (iv) viruses or microbes evading anti-microbial therapy, and also (v) the repeated attempts of combinatorial chemistry in the very beginning of life to produce self-replicating molecules. All such seemingly unrelated situations have a common structure in terms of Darwinian dynamics: a replicator with a basic reproductive ratio less than one attempts to find some mutations that allow indefinite survival. We develop a general theory, based on multitype branching processes, to describe the evolutionary dynamics of invasion and escape.

Animals↗