Biomedical subjects

Yoh Iwasa

Publications and source records attributed to Yoh Iwasa.

At least 19 recordsLinked to original sources

PubMed2006

The age incidence of chronic myeloid leukemia can be explained by a one-mutation model.

Chronic myeloid leukemia (CML) is associated with the Philadelphia chromosome, which arises by a reciprocal translocation between chromosomes 9 and 22 and harbors the BCR-ABL fusion oncogene. It is unknown whether any other mutations are needed for the chronic phase of the disease. The CML incidence increases as a function of age with an exponent of approximately 3. A slope of 3 could indicate that there are two mutations, in addition to the Philadelphia translocation, that have not yet been discovered. In this work, we explore an alternative hypothesis: We study a model of cancer initiation requiring only a single mutation. A mutated cell has a net reproductive advantage over normal cells and, therefore, might give rise to clonal expansion. The cancer is detected with a probability that is proportional to the size of the mutated cell clone. This model has three waiting times: (i) the time until a mutated cell is produced, (ii) the time of clonal expansion, and (iii) the time until the clone is detected. Surprisingly, this simple process can give rise to cancer incidence curves with exponents up to 3. Therefore, the CML incidence data are consistent with the hypothesis that the Philadelphia translocation alone is sufficient to cause chronic phase CML.

Adolescent↗

PubMed2006

Global analyses of evolutionary dynamics and exhaustive search for social norms that maintain cooperation by reputation.

Reputation formation is a key to understanding indirect reciprocity. In particular, the way to assign reputation to each individual, namely a norm that describes who is good and who is bad, greatly affects the possibility of sustained cooperation in the population. Previously, we have exhaustively studied reputation dynamics that are able to maintain a high level of cooperation at the ESS. However, this analysis examined the stability of monomorphic population and did not investigate polymorphic population where several strategies coexist. Here, we study the evolutionary dynamics of multiple behavioral strategies by replicator dynamics. We exhaustively study all 16 possible norms under which the reputation of a player in the next round is determined by the action of the self and the reputation of the opponent. For each norm, we explore evolutionary dynamics of three strategies: unconditional cooperators, unconditional defectors, and conditional cooperators. We find that only three norms, simple-standing, Kandori, and shunning, can make conditional cooperation evolutionarily stable, hence, realize sustained cooperation. The other 13 norms, including scoring, ultimately lead to the invasion by defectors. Also, we study the model in which private reputation errors exist to a small extent. In this case, we find the stable coexistence of unconditional and conditional cooperators under the three norms.

Biological Evolution↗

PubMed2006

Optimal conservation strategy in fluctuating environments with species interactions: resource-enhancement of the native species versus extermination of the alien species.

Alien species are often a major threat to native species. We consider optimal conservation strategies for a population whose viability is affected both by an alien species (such as a competitor, a predator, or a pathogen) and by random fluctuations of the environment (e.g. precipitation, temperature). We assume that the survivorship of the native population can be improved by providing resources such as food and shelter, and also by an extermination effort that decreases the abundance of the alien species. These efforts decrease the extinction probability of the native population, but they are accompanied by economic costs. We search for the optimal strategy that minimizes the weighted sum of the extinction probability and the economic costs over a single year. We derive conditions under which investment should be made in both resource-enhancement and extermination, and examine how the optimal effort levels change with parameters. When the optimal strategy includes both types of efforts, the optimal extermination effort level turns out to be independent of the density and economic value of the native species, or the variance of the environmental fluctuation. Furthermore, the optimal resource-enhancement effort is then independent of the density of the alien species. However, the parameter dependencies greatly change if one of the efforts becomes zero. We also examine the situation in which the impact of the alien species is uncertain. The optimal extermination effort increases with the uncertainty of this impact except when the cost of extermination is very high.

Animals↗

PubMed2006

A symmetry of fixation times in evoultionary dynamics.

In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies.

Animals↗

PubMed2006

A model for the circadian rhythm of cyanobacteria that maintains oscillation without gene expression.

An intriguing property of the cyanobacterial circadian clock is that endogenous rhythm persists when protein abundances are kept constant either in the presence of translation and transcription inhibitors or in the constant dark condition. Here we propose a regulatory mechanism of KaiC phosphorylation for the generation of circadian oscillations in cyanobacteria. In the model, clock proteins KaiA and KaiB are assumed to have multiple states, regulating the KaiC phosphorylation process. The model can explain 1), the sustained oscillation of gene expression and protein abundance when the expression of the kaiBC gene is regulated by KaiC protein, and 2), the sustained oscillation of phosphorylated KaiC when transcription and translation processes are inhibited and total protein abundance is fixed. Results of this work suggest that KaiA and KaiB strengthen the nonlinearity of KaiC phosphorylation, thereby promoting the circadian rhythm in cyanobacteria.

Bacterial Proteins↗

PubMed2006

How canalization can make loops: a new model of reticulated leaf vascular pattern formation.

Formation of the vascular system in plant leaves can be explained by the canalization hypothesis which states that veins are formed in an initially homogeneous field by a self-organizing process between the plant hormone auxin and auxin carrier proteins. Previous models of canalization can generate vein patterns with branching but fail to generate vein patterns with closed loops. However, closed vein loops are commonly observed in plant leaves and are important in making them robust to herbivore attacks and physical damage. Here we propose a new model which generates a vein system with closed loops. We postulate that the "flux bifurcator" level is enhanced in cells with a high auxin flux and that it causes reallocation of auxin carriers toward neighbouring cells also having a high bifurcator level. This causes the auxin flux to bifurcate, allowing vein tips to attach to other veins creating vein loops. We explore several alternative functional forms for the flux bifurcator affecting the reallocation of efflux carriers and examine parameter dependence of the resulting vein pattern.

Indoleacetic Acids↗

PubMed2006

Direction of regeneration waves in grid-based models for forest dynamics.

Progressing waves of regeneration are observed in forest ecosystems such as Shimagare fir forests. The patterns generated by lattice models for forest dynamics often show similar waves of disturbance and recovery. This paper introduces a method to detect and quantify the directional movement of these waves. The method is based only on the disturbance times of the sites and allows to distinguish three types of wave patterns: patterns with global direction, patterns with local direction, and patterns without direction. We apply this to several grid-based models for forest dynamics which are evaluated analytically or by simulation. The results reveal a clear distinction of the models which earlier studies were not able to detect.

Ecosystem↗

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

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

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↗