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Biomedical subjects

Yoh Iwasa

Publications and source records attributed to Yoh Iwasa.

At least 19 recordsLinked to original sources
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↗
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

The coevolution of altruism and punishment: role of the selfish punisher.

Punishment is an important mechanism promoting the evolution of altruism among non-relatives. We investigate the coevolution of altruism and punitive behavior, considering four possible strategies: the altruist punisher (AP, a cooperator who punishes defectors), the altruist non-punisher (AN, a pure cooperator), the selfish punisher (SP, a defector who punishes defectors), and the selfish non-punisher (SN, a pure defector). The SP uses a paradoxical strategy as it punishes other defectors. We analyse the effects of SP and AN on the coevolution of altruism and punishment. We study both the score-dependent viability model (whereby the game's score affects survivorship only) and the score-dependent fertility model (whereby the score affects fertility only). In the viability model of a completely mixed population, SP first drives out SN, and hence it helps cooperators (AP and AN) to evolve. In contrast, in the fertility model of a completely mixed population, neither SP nor AN helps the evolution of cooperation. In both the viability and fertility models of a lattice-structured population, SP promotes the spread of AP. In contrast, AN discourages the evolution of AP. These results can be understood that punishment is a form of spite behavior, paying a cost to reduce the fitness of the opponents, and that different models give different magnitude of advantage to spite behavior.

Altruism↗
PubMed2005

Genetic addiction: selfish gene's strategy for symbiosis in the genome.

The evolution and maintenance of the phenomenon of postsegregational host killing or genetic addiction are paradoxical. In this phenomenon, a gene complex, once established in a genome, programs death of a host cell that has eliminated it. The intact form of the gene complex would survive in other members of the host population. It is controversial as to why these genetic elements are maintained, due to the lethal effects of host killing, or perhaps some other properties are beneficial to the host. We analyzed their population dynamics by analytical methods and computer simulations. Genetic addiction turned out to be advantageous to the gene complex in the presence of a competitor genetic element. The advantage is, however, limited in a population without spatial structure, such as that in a well-mixed liquid culture. In contrast, in a structured habitat, such as the surface of a solid medium, the addiction gene complex can increase in frequency, irrespective of its initial density. Our demonstration that genomes can evolve through acquisition of addiction genes has implications for the general question of how a genome can evolve as a community of potentially selfish genes.

Bacteria↗
PubMed2005

Labyrinthine versus straight-striped patterns generated by two-dimensional Turing systems.

Striped patterns are often observed on fish skin. Such patterns have been accounted for by reaction-diffusion (RD) Turing-type models, in which two substances can spontaneously form a spatially heterogeneous pattern in a homogeneous field. Among the striped patterns generated by Turing-type models, some are "straight-striped patterns," with many stripes running in parallel, while others are "labyrinthine patterns," in which the stripes often change direction, merge with each other, and frequently branch out. RD models differ in terms of their tendency to generate either labyrinthine or straight-striped patterns. Here, we studied the conditions under which either a labyrinthine or straight-striped pattern would emerge. First, we defined an index for stripe clearness, Sh. Straight-striped patterns (large Sh) are formed if only a narrow range of spatial periods corresponds to an unstable mode. Labyrinthine patterns (small Sh) are formed when a wide range of spatial periods is unstable. More specifically, labyrinthine patterns are formed when the maximum spatial period of unstable modes is more than twice that of the minimum spatial period of unstable modes; otherwise, straight-striped patterns are formed. We then examined RD models with nonlinear reaction terms, including both activator-inhibitor and substrate-depletion models, and we demonstrated that the same conclusions hold with respect to the conditions required for labyrinthine versus straight-striped patterns.

Animals↗
PubMed2005

The evolution of a Müllerian mimic in a spatially distributed community.

Strong positive density-dependence should lead to a loss of diversity, but warning-colour and Müllerian mimicry systems show extraordinary levels of diversity. Here, we propose an analytical model to explore the dynamics of two forms of a Müllerian mimic in a heterogeneous environment with two alternative model species. Two connected populations of a dimorphic, chemically defended mimic are allowed to evolve and disperse. The proportions of the respective model species vary spatially. We use a nonlinear approximation of Müller's number-dependent equations to model a situation where the mortality for either form of the mimic decreases hyberbolically when its local density increases. A first non-spatial analysis confirms that the positive density-dependence makes coexistence of mimetic forms unstable in a single isolated patch, but shows that mimicry of the rarer model can be stable once established. The two-patch analysis shows that when models have different abundance in different places, local mimetic diversity in the mimic is maintained only if spatial heterogeneity is strong, or, more interestingly, if the mimic is not too strongly distasteful. Therefore, mildly toxic species can become polymorphic in a wider range of ecological settings. Spatial dynamics thus reveal a region of Müllerian polymorphism separating classical Batesian polymorphism and Müllerian monomorphism along the mimic's palatability spectrum. Such polymorphism-palatability relationship in a spatial environment provides a parsimonious hypothesis accounting for the observed Müllerian polymorphism that does not require quasi-Batesian dynamics. While the stability of coexistence depends on all factors, only the migration rate and strength of selection appear to affect the level of diversity at the polymorphic equilibrium. Local adaptation is predicted in most polymorphic cases. These results are in very good accordance with recent empirical findings on the polymorphic butterflies Heliconius numata and H. cydno.

Adaptation, Physiological↗
PubMed2005

The leading eight: social norms that can maintain cooperation by indirect reciprocity.

The theory of indirect reciprocation explains the evolution of cooperation among unrelated individuals, engaging in one-shot interaction. Using reputation, a player acquires information on who are worth cooperating and who are not. In a previous paper, we formalized the reputation dynamics, a rule to assign a binary reputation (good or bad) to each player when his action, his current reputation, and the opponent's reputation are given. We then examined all the possible reputation dynamics, and found that there exist only eight reputation dynamics named "leading eight" that can maintain the ESS with a high level of cooperation, even if errors are included in executing intended cooperation and in reporting the observation to the public. In this paper, we study the nature of these successful social norms. First, we characterize the role of each pivot of the reputation dynamics common to all of the leading eight. We conclude that keys to the success in indirect reciprocity are to be nice (maintenance of cooperation among themselves), retaliatory (detection of defectors, punishment, and justification of punishment), apologetic, and forgiving. Second, we prove the two basic properties of the leading eight, which give a quantitative evaluation of the ESS condition and the level of cooperation maintained at the ESS.

Biological Evolution↗
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

Extinction risk of a meta-population: aggregation approach.

Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.

Animals↗
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

Temperature compensation in circadian clock models.

Circadian clock of organisms has a free-running period that does not change much with ambient temperature. This property "temperature compensation" is studied when the rate of all reaction steps increase with temperature in the biochemical network generating the rhythm. The period becomes shorter when all the rate parameters are enhanced by the same factor. However, the period becomes longer as degradation rate of proteins and/or transcription rate of the clock gene increase (their elasticity is positive). This holds for a wide range of models, including N-variable model, and PER-TIM double oscillator model, provided that (1) branch reactions (e.g. degradation of proteins or mRNAs) are strongly saturated, and that (2) the cooperativity of transcription inhibition by nuclear proteins is not very large. A strong temperature sensitivity of degradation of PER proteins and/or temperature-sensitive alternative splicing of per gene, known for Drosophila, can be mechanisms for the temperature compensation of circadian clock.

Alternative Splicing↗
PubMed2004

Optimal growth pattern of defensive organs: the diversity of shell growth among mollusks.

Mollusks show a diversity of shell growth patterns. We develop a model for the dynamic resource allocation to defense organs and analyze it with the Pontryagin maximum principle. A typical optimal growth schedule is composed of the initial phase of soft-body growth without shell followed by a simultaneous growth of shell and soft body and finally the reproductive phase without growth (simultaneous shell growth). If the defensible predation risk is low or if the cost of defense is high, the optimal strategy is to have no shell (shell-less growth). If defensible predation pressure or general mortality differs before and after maturation, an additional three strategies, characteristic of the exclusive growth of shell or soft body, can be optimal (sequential shell growth, additional body-expansion growth, and additional callus-building growth). These optimal strategies are in accord with the patterns observed for mollusks. In particular, the growth strategies with exclusive growth phase of external shells are preferred when durophagous predation pressure after maturation is higher than that before maturation. This result explains the observation that many tropical gastropods with thickened shell lips spend their vulnerable juvenile phase in sheltered habitats.

Animals↗
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

How should we define goodness?--reputation dynamics in indirect reciprocity.

Theory of indirect reciprocity is important in explaining cooperation between humans. Since a partner of a social interaction often changes, an individual should assess his partner by using social information such as reputation and make decisions whether to help him or not. To those who have 'good' social reputation does a player give aid as reciprocation, whereas he has to refuse to help those who have 'bad' reputation. Otherwise benefits of altruism is easily exploited by them. Little has been known, however, about the definition of 'goodness' in reputation. What kind of actions are and should be regarded as good and what kind of actions bad? And what sort of goodness enables sustaining exchange of altruism? We herein challenge this question with an evolutionary perspective. We generalize social reputation as 'Honor-score' (H-score) and examine the conditions under which individuals in a group stably maintain cooperative relationships based on indirect reciprocity. We examine the condition for evolutionarily stable strategies (ESSs) over 4096 possible cases exhaustively. Mathematical analysis reveals that only eight cases called 'leading eight' are crucial to the evolution of indirect reciprocity. Each in the leading eight shares two common characteristics: (i) cooperation with good persons is regarded as good while defection against them is regarded as bad, and (ii) defection against bad persons should be regarded as a good behavior because it works as sanction. Our results give one solution to the definition of goodness from an evolutionary viewpoint. In addition, we believe that the formalism of reputation dynamics gives general insights into the way social information is generated, handled, and transmitted in animal societies.

Altruism↗
PubMed2004

On the emergence of multifocal cancers.

Several tumors can exist as multiple lesions within a tissue. The lesions may either arise independently, or they may be monoclonal. The importance of multiple lesions for tumor staging, progression, and treatment is subject to debate. Here we use mathematical models to analyze the emergence of multiple, clonally related lesions within a single tissue. We refer to them as multi-focal cancers. We find that multifocal cancers can arise through a dynamical interplay between tumor promoting and inhibiting factors. This requires that tumor promoters act locally, while tumor inhibitors act over a longer range. An example of such factors may be angiogenesis promoters and inhibitors. The model further suggests that multifocal cancers represent an intermediate stage in cancer progression as the tumor evolves away from inhibition and towards promotion. Different patterns of progression can be distinguished: (i) If tumor inhibition is strong, the initial growth occurs as a unifocal and self contained lesion; progression occurs through bifurcation of the lesion and this gives rise to multiple lesions. As the tumor continues to evolve and pushes the balance between inhibition and promotion further towards promotion, the multiple lesions eventually give rise to a single large mass which can invade the entire tissue. (ii) If tumor inhibition is weaker upon initiation, growth can occur as a single lesion without the occurrence of multiple lesions, until the entire tissue is invaded. The model suggests that the sum of the tumor sizes across all lesions is the best characteristic which correlates with the stage and metastatic potential of the tumor.

Journal Article↗