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Supplementary Appendix from A Multiscale Mathematical Model for Oncolytic Virotherapy

Supplementary Parameter Estimates from A Multiscale Mathematical Model for Oncolytic Virotherapy

Supplementary Methods from A Multiscale Mathematical Model for Oncolytic Virotherapy

Supplementary Figure 1 from A Multiscale Mathematical Model for Oncolytic Virotherapy

One of the most promising strategies to treat cancer is attacking it with viruses. Oncolytic viruses can kill tumor cells specifically or induce anticancer immune response. A multiscale model for virotherapy of cancer is investigated through simulations. It was found that, for intratumoral virus administration, a solid tumor can be completely eradicated or keep growing after a transient remission. Furthermore, the model reveals undamped oscillatory dynamics of tumor cells and virus populations, which demands new in vivo and in vitro quantitative experiments aiming to detect this oscillatory response. The conditions for which each one of the different tumor responses dominates, as well as the occurrence probabilities for the other nondominant therapeutic outcomes, were determined. From a clinical point of view, our findings indicate that a successful, single agent virotherapy requires a strong inhibition of the host immune response and the use of potent virus species with a high intratumoral mobility. Moreover, due to the discrete and stochastic nature of cells and their responses, an optimal range for viral cytotoxicity is predicted because the virotherapy fails if the oncolytic virus demands either a too short or a very large time to kill the tumor cell. This result suggests that the search for viruses able to destroy tumor cells very fast does not necessarily lead to a more effective control of tumor growth. [Cancer Res 2009;69(3):1205–11]

Supplementary Video 1 from A Multiscale Mathematical Model for Oncolytic Virotherapy

Supplementary Video 2 from A Multiscale Mathematical Model for Oncolytic Virotherapy

Rumors have ignited revolutions, undermined the trust in political parties, or threatened the stability of human societies. Such destructive potential has been significantly enhanced by the development of on-line social networks. Several theoretical and computational studies have been devoted to understanding the dynamics and to control rumor spreading. In the present work, a model of rumor-telling in opinion polarized networks was investigated through extensive computer simulations. The key mechanism is the coupling between ones' opinions and their leaning to spread a given information, either by supporting or opposing its content. We report that a highly modular topology of polarized networks strongly impairs rumor spreading, but the couplings between agent's opinions and their spreading/stifling rates can either further inhibit or, conversely, foster information propagation, depending on the nature of those couplings. In particular, a controversy-seeking mechanism, in which agents are stimulated to postpone their transitions to the stiffer state upon interactions with other agents of confronting opinions, enhances the rumor spreading. Therefore such a mechanism is capable of overcoming the propagation bottlenecks imposed by loosely connected modular structures., 11 pages, 7 figures

Far beyond its relevance for commercial and political marketings, opinion formation and decision making processes are central for representative democracy, government functioning, and state organization. In the present report, a stochastic agent-based model is investigated. The model assumes that bounded confidence and homophily mechanisms drive both opinion dynamics and social network evolution through either rewiring or breakage of social contacts. In addition to the classical transition from global consensus to opinion polarization, our main findings are (i) a cascade of fragmentation of the social network into echo chambers (modules) holding distinct opinions and rupture of the bridges interconnecting these modules as the tolerance for opinion differences increases. There are multiple surviving opinions associated to these modules within which consensus is formed; and (ii) the adaptive social network exhibits a hysteresis-like behavior characterized by irreversible changes in its topology as the opinion tolerance cycles from radicalization towards consensus and backward to radicalization., Comment: 9 pages, 7 figures

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and in vitro drug testing. In the present paper, we characterize the aggregation kinetics of normal and cancer cells in culture by determining their cluster size distribution functions. Our experiments reveal that the complementary cumulative distributions for eight cell lines from epithelial and mesenchymal origins are described by stretched exponential functions. Also, we find that as time evolves and the cell density increases, a dynamical phase transition occurs from an aggregation regime described by monotonically decreasing cluster size distributions to another one in which these distributions are nonmonotonic, exhibiting local maxima at large cluster sizes. Subtly, the universality of the stretched exponential distributions admits distinct cluster growth processes controlled by motility and adhesion traits of the cells.

Evidence is mounting that the race of living organisms for adaptation to the chemicals synthesized by their neighbors may drive community structures. Here, an ecoevolutionary model for community assembly through resource competition, toxin-mediated interactions (allelopathy), and evolutionary branching is investigated. We found that stable communities with increasing biodiversity can emerge at weak allelopathic suppression, but strong chemical warfare drastically impairs diversity. For successive invasion events, the allelopathic interaction networks exhibit, respectively, Gaussian and Weibull degree distributions at weak and strong allelopathy. For the branching process dynamics, degrees scale as power laws truncated by stretched exponentials in both regimes. In addition, allelochemical interactions tend to be arranged in modules with low clustering coefficients and disassortative behavior to ensure community stability. So, in a homogeneous environment, species-rich communities can be assembled only at the context of a weak biochemical warfare between organisms, and even under this regime species interact with only a few others.

Microorganisms and plants very commonly release toxic secondary chemical compounds (allelochemicals) that inhibit or kill sensitive strains or individuals from their own or other species. In this work we study a model that describes two species interacting through allelopathic suppression and competing for resources. Employing linear stability analysis, the conditions for coexistence or extinction of species in spatially homogeneous systems were determined. We found that the borders between the regimes of bistability, coexistence, and the extinction of the weaker by the stronger competitor, are altered by allelopathic interactions. In addition, traveling wave solutions for one species invasion were obtained considering the spatially explicit nature of the model. Our findings indicate that the minimum speed of the invasion wavefronts depends primarily on the competition coefficients and the parameters characterizing the species' functional responses to their allelochemicals. As a general rule, the species provided with the most effective chemical weapons dominates the population dynamics. Finally, we found a tristability at the coexistence region due to the combination of allelopathy and patchy population distributions in space. So, our model provides a distinct mechanism, independent of social behaviors, that produces such unexpected tristability impossible in classical competition models involving one-to-one individual interactions.

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, the control of cell motion is a major demand in the creation of artificial tissues and organs. Here, cell migration assays on plastic 2D surfaces involving normal (MDCK) and tumoral (B16F10) epithelial cell lines were performed varying the initial density of plated cells. Through time-lapse microscopy quantities such as speed distributions, velocity autocorrelations and spatial correlations, as well as the scaling of mean-squared displacements were determined. We find that these cells exhibit anomalous diffusion with q-Weibull speed distributions that evolves non-monotonically to a Maxwellian distribution as the initial density of plated cells increases. Although short-ranged spatial velocity correlations mark the formation of small cell clusters, the emergence of collective motion was not observed. Finally, simulational results from a correlated random walk and the Vicsek model of collective dynamics evidence that fluctuations in cell velocity orientations are sufficient to produce q-Weibull speed distributions seen in our migration assays.

Exotic plants threaten the biodiversity of natural habitats and the integrity of agricultural systems throughout the World. Therefore, understanding, predicting and controlling plant invasions became issues of great practical importance. In the present paper, a model for plant invasion based on allelopathic suppression is proposed and studied through analytical methods and numerical integration. Employing linear stability analysis the conditions for plant coexistence as well as one species extinction were determined for the spatially homogeneous system. These conditions demonstrate the advantage conferred to the alien plant by its phytotoxin. It was shown that the system exhibits bistability between two distinct fixed points, either associated to species coexistence or to the extinction of one species. Numerical simulation is also included to support such results. Further, the invasion spreading starting from a single, spatially localized initial focus was investigated by numerical integration of the model's equations. As obtained for the spatially homogeneous system, at strong interspecific competition the outcome is the extinction of one plant species. In contrast, at low interspecific competition, the rule is the coexistence between the invader and native plants. So, under weak competition alien species can invade, but genetic diversity can be sustained.

Made available in DSpace on 2018-11-26T16:33:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2016-08-15 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação para o Desenvolvimento da UNESP (FUNDUNESP) We present a mathematical model based on partial differential equations that is applied to understand tumor development and its response to chemotherapy. Our primary aim is to evaluate comparatively the efficacies of two chemotherapeutic protocols, Maximum Tolerated Dose (MTD) and metronomic, as well as two methods of drug delivery. Concerning therapeutic outcomes, the metronomic protocol proves more effective in prolonging the patient's life than MTD. Moreover, a uniform drug delivery method combined with the metronomic protocol is the most efficient strategy to reduce tumor density. (C) 2016 Elsevier B.V. All rights reserved. Univ Estadual Paulista, Dept Bioestat, BR-18618689 Botucatu, SP, Brazil Univ Fed Vicosa, Dept Fis, BR-36570900 Vicosa, MG, Brazil Univ Estadual Paulista, Dept Bioestat, BR-18618689 Botucatu, SP, Brazil FAPESP: 2013/08133-0 FAPESP: 2009/15098-0 FAPEMIG: APQ-04232-10 CNPq: 306024/2013-6 FUNDUNESP: 1886/009-13

Cancer therapy requires anticancer agents capable of efficient and uniform systemic delivery. One promising route to their development is nanotechnology. Here, a previous model for cancer chemotherapy based on a nanosized drug carrier (Paiva et al., 2011) is extended by including tissue vasculature and a three-dimensional growth. We study through computer simulations the therapy against tumors demanding either large or small nutrient supplies growing under different levels of tissue vascularization. Our results indicate that highly vascularized tumors demand more aggressive therapies (larger injected doses administrated at short intervals) than poorly vascularized ones. Furthermore, nanoparticle endocytic rate by tumor cells, not its selectivity, is the major factor that determines the therapeutic success. Finally, our finds indicate that therapies combining cytotoxic agents with antiangiogenic drugs that reduce the abnormal tumor vasculature, instead of angiogenic drugs that normalize it, can lead to successful treatments using feasible endocytic rates and administration intervals.

In the present paper, we propose and study by numerical simulations a multiscale model for plant invasion based on allelopathic suppression in a homogeneous environment. The negative effects on seed production and germination, establishment and mortality of native plants generated by the root-secreted alien phytotoxin constitute the basic mechanism contributing to invasiveness. We obtained the invasion patterns, their success probabilities, the time evolution of plant populations, the gyration radius and the border roughness of the invaded region. As an important result, it was observed that, in addition to the phytotoxin nature (synthesis and degradation rates, diffusivity and phytotoxic threshold), invasive patterns and invasion success depend on the kind of native plants present in the area. In fact, both success and invasion speed decrease in the presence of resistant native plants. Also, self-affine invasion fronts are smooth (Hurst exponent H = 1) in the absence of resistant plants, but are rough (H ≠ 1) on the contrary. Furthermore, if the resistant native species are randomly distributed on the landscape, the invasion front exhibits long-range correlations (H ∼ 0.76), while its border is anti-correlated (H ∼ 0.20), if resistant plants are distributed in patches. Finally, the cluster size distribution functions of resistant plants are exponentials with characteristic cluster sizes increasing in time.

In the past 30 years we have witnessed an extraordinary progress on the research in the molecular biology of cancer, but its medical treatment, widely based on empirically established protocols, still has many limitations. One of the reasons for that is the limited quantitative understanding of the dynamics of tumor growth and drug response in the organism. In this review we shall discuss in general terms the use of mathematical modeling and computer simulations related to cancer growth and its applications to improve tumor therapy. Particular emphasis is devoted to multiscale models which permit integration of the rapidly expanding knowledge concerning the molecular basis of cancer and the complex, nonlinear interactions among tumor cells and their microenvironment that will determine the neoplastic growth at the tissue level.

The susceptible-infected-susceptible (SIS) epidemics in a scale-free network in which each node is a square lattice itself is investigated through large-scale computer simulations. The model combines a local contact process among individuals in a node (or city) with stochastic long-range infections due to people traveling between cities interconnected by the national transportation scale-free network. A nonzero epidemic threshold is found and it is approached with a power-law behavior by the density of infected individuals, as observed in the small-world network of Watts and Strogatz. Also, the epidemic propagation follows a 1 / f , hierarchical dynamics from the highly connected square lattices to the smaller degree nodes in outbreaks with sizes distributed accordingly a Gaussian function.

Apresentamos um modelo matematico baseado em equacoes diferenciais parciais que e aplicado na compreensao do desenvolvimento tumoral e em sua resposta a aplicacao de quimioterapia. Administracao do quimioterapico e em ciclos segundo dois protocolos, MTD e metronomico, bem como, em dois metodos de entrega da droga, convencional e uniforme. Atraves de simulacoes numericas concluimos que a combinacao protocolo metronomico e metodo de entrega uniforme e mais eficaz em reduzir a densidade do tumor durante o tratamento, mas favorece a reincidencia do tumor. A combinacao protocolo metronomico e metodo convencional acarreta em uma sobrevida maior ao paciente mesmo nao sendo tao eficiente em reduzir a densidade do tumor durante o tratamento quanto a combinacao anterior.

An individual-based model for the population dynamics of Spodoptera frugiperda in a homogeneous environment is proposed. The model involves moths feeding plants, mating through an anemotaxis search (i.e., oriented by odor dispersed in a current of air), and dying due to resource competition or at a maximum age. As observed in the laboratory, the females release pheromones at exponentially distributed time intervals, and it is assumed that the ranges of the male flights follow a power-law distribution. Computer simulations of the model reveal the central role of anemotaxis search for the persistence of moth population. Such stationary populations are exponentially distributed in age, exhibit random temporal fluctuations with 1 / f spectrum, and self-organize in disordered spatial patterns with long-range correlations. In addition, the model results demonstrate that pest control through pheromone mass trapping is effective only if the amounts of pheromone released by the traps decay much slower than the exponential distribution for calling female.

Developmental processes generating spontaneously coordinated and inhomogeneous spatiotemporal patterns with differentiated cell types are one of the main problems in modern biology. In this paper a cellular automata model for cell differentiation is proposed. It takes into account the time evolution of the gene networks representing each cell, cell–cell interactions through gene couplings and cell division. Our computer simulations show that a society with differentiated cell types exhibiting the main features observed in biological morphogenesis emerges from a marginally stable regime at the edge of chaos.

In multicellular organisms, cell motility is central in all morphogenetic processes, tissue maintenance, wound healing and immune surveillance. Hence, failures in its regulation potentiates numerous diseases. Here, cell migration assays on plastic 2D surfaces were performed using normal (Melan A) and tumoral (B16F10) murine melanocytes in random motility conditions. The trajectories of the centroids of the cell perimeters were tracked through time-lapse microscopy. The statistics of these trajectories was analyzed by building velocity and turn angle distributions, as well as velocity autocorrelations and the scaling of mean-squared displacements. We find that these cells exhibit a crossover from a normal to a super-diffusive motion without angular persistence at long time scales. Moreover, these melanocytes move with non-Gaussian velocity distributions. This major finding indicates that amongst those animal cells supposedly migrating through Lévy walks, some of them can instead perform q-Gaussian walks. Furthermore, our results reveal that B16F10 cells infected by mycoplasmas exhibit essentially the same diffusivity than their healthy counterparts. Finally, a q-Gaussian random walk model was proposed to account for these melanocytic migratory traits. Simulations based on this model correctly describe the crossover to super-diffusivity in the cell migration tracks.

A review of the main results obtained by a cellular automata model recently proposed to analyze the progress of citrus variegated chlorosis epidemics is done. In this model epidemiological and environmental features, such as motility of sharpshooter vectors which perform Levy flights, hydric and nutritional level of plant stress and seasonal climatic effects, are included. The observed epidemics data were quantitatively reproduced by the proposed model varying the parameters controlling vectors motility, plant stress and initial population of diseased plants.

In the present paper we extend the analysis of another model recently proposed to simulate the growth of carcinoma “in situ”, which includes cell proliferation, motility and death, as well as chemotactic interactions among cells. The tumour patterns generated by two distinct growth rules are characterised by its gyration radius, surface roughness, total number of cancer cells, and number of cells on tumour periphery. Our results indicate that very distinct morphological patterns follow Gompertz growth curves and their gyration radii increase linearly in time and scale, in the asymptotic limit, as a square root of the total number of tumour cells. In contrast, these distinct tumour patterns exhibit different scaling laws for their surfaces. Thus, some biological features of malignant behaviour seem to influence particularly the structure of the tumour border, while its gyration radius and progress curve are described by more robust functions. Finally, for both rules used, morphology transitions as well as a transient behaviour up to the onset of the phase of rapid growth in the Gompertz curves are observed.

One of the most aggressive phenomena in biology is the growth of cancer cells. In this paper we propose a simple model to simulate the growth of carcinoma “in situ”, which includes cell proliferation, motility and death, as well as the reciprocal influence among cells. Every simulated growth pattern is characterized by its gyration radius, surface roughness, number of cells on tumour periphery and fractal dimension. Our results indicate that the patterns are compact, with gyration radius, surface roughness and number of peripherical cells scaling, in the asymptotic limit, as a square root of the total number of tumour cells. Also, a preliminary comparison between the simulated patterns and explants of primary tumours is done.

Cellular automata (CA) are discrete, spatially homogeneous, locally interacting dynamical systems of very simple construction, but which exhibit a rich intrinsic behavior. CA can, even starting from disordered initial configurations, evolve into ordered states with complex structures crystallized in its space-time patterns. In this paper we concentrate on the several Wolfram qualitative classes of CA behavior. In order to better characterize these classes we apply the roughness exponent method to the profiles generated by the spatiotemporal patterns of one-dimensional “elementary” CA rules. We find that this method can separate Wolfram class IV from other ones.

In order to study the overall behavior of gene networks, we propose a simple cellular automata ~CA! model in which each binary gene is connected to K other inputs ~including itself! interacting through asymmetric short- and long-range couplings. Using numerical simulations and mean-field calculations, collective dynamical properties of this CA model were investigated. It is shown that the CA exhibits three different dynamical regimes: a frozen, a marginal, and a chaotic phase, where an initial damage vanishes, remains limited, and grows to a finite fraction of the lattice sites, respectively. The results presented are also consistent with the observed biological scaling laws for the number of differentiated cells and cell length cycles as a function of the number of genes in an organism. @S1063-651X~97!03303-5#

Submitted by Guilherme Lemeszenski (guilherme@nead.unesp.br) on 2013-08-22T19:02:16Z No. of bitstreams: 1 S0104-77602013000100018.pdf: 195769 bytes, checksum: 75ce3fd120faacf80a79aa720fb872e9 (MD5) Made available in DSpace on 2013-08-22T19:02:16Z (GMT). No. of bitstreams: 1 S0104-77602013000100018.pdf: 195769 bytes, checksum: 75ce3fd120faacf80a79aa720fb872e9 (MD5) Previous issue date: 2013-03-01 Made available in DSpace on 2013-09-30T20:03:05Z (GMT). No. of bitstreams: 2 S0104-77602013000100018.pdf: 195769 bytes, checksum: 75ce3fd120faacf80a79aa720fb872e9 (MD5) S0104-77602013000100018.pdf.txt: 22847 bytes, checksum: 5601512d194dbb036d871b6c29c0de55 (MD5) Previous issue date: 2013-03-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T13:12:03Z No. of bitstreams: 2 S0104-77602013000100018.pdf: 195769 bytes, checksum: 75ce3fd120faacf80a79aa720fb872e9 (MD5) S0104-77602013000100018.pdf.txt: 22847 bytes, checksum: 5601512d194dbb036d871b6c29c0de55 (MD5) Made available in DSpace on 2014-05-20T13:12:03Z (GMT). No. of bitstreams: 2 S0104-77602013000100018.pdf: 195769 bytes, checksum: 75ce3fd120faacf80a79aa720fb872e9 (MD5) S0104-77602013000100018.pdf.txt: 22847 bytes, checksum: 5601512d194dbb036d871b6c29c0de55 (MD5) Previous issue date: 2013-03-01 A caracterização anatômica, física, mecânica e química da madeira fornece informações importantes para sua melhor utilização. Contudo, para que madeiras se tornem boa opção para o mercado de pisos, adicionalmente é necessária a realização de ensaios que simulem suas reais condições em serviço. Esses ensaios simulam o pisoteio executado pelos sapatos de salto com pequenas áreas de pressão, o arraste e a queda de objetos, a resistência à abrasão da superfície e o atrito oferecido durante o deslocamento de pessoas que caminham sobre ele. Grande dificuldade da seleção de novas madeiras para pisos está na ausência de valores de referência físico-mecânicos. O presente trabalho visou a caracterizar as madeiras de Eucalyptus clöeziana F. Muell, de Eucalyptus microcorys F. Muell e de Corymbia maculata Hook, para as propriedades de densidade básica, retratibilidade, aplicação de carga rolante, de atrito estático e dinâmico, endentação causada por cargas aplicadas em pequenas áreas, impacto da esfera de aço cadente e resistência à abrasão. Foi observado que as madeiras estudadas podem ser utilizadas para a confecção de pisos, de acordo com seus resultados obtidos e por meio de comparações com resultados de literatura. The anatomic, physical, mechanical and chemical characterization of wood provides important information for the indication of its best usage. However, to make these woods possible to become a good option in the wooden floors market, it is necessary to perform tests that simulate the real conditions of their practical use. These tests simulate the stomping of high-heeled shoes with small pressure areas, the dragging and falling of objects, the resistance to the surface abrasion and the friction offered during the walking of people. The difficulty of selection of new wood to manufacture floors is in the absence of specific physical-mechanical reference values. The present work intended to characterize the Eucalyptus clöeziana F. Muell, Eucalyptus microcorys F. Muell and Corymbia maculata Hook woods, regarding the properties of basic density, shrinkage, application of rolling roll, of static and dynamic friction, denting caused by loads applied on small areas, impact of falling steel sphere and resistance to abrasion. It was noticed that the woods may be used to the manufacturing of floors, according to results obtained and through comparisons with literature results. Universidade Federal de Lavras (UFLA) Departamento de Ciências Florestais Universidade Estadual Paulista Júlio de Mesquita Filho Escola Agrotécnica Federal de Januária Instituto Federal de Educação Ciência e Tecnologia do Norte de Minas Gerais Universidade Estadual Paulista Júlio de Mesquita Filho

Oncolytic virotherapy - the use of viruses that specifically kill tumor cells - is an innovative and highly promising route for treating cancer. However, its therapeutic outcomes are mainly impaired by the host immune response to the viral infection. In the present work, we propose a multiscale mathematical model to study how the immune response interferes with the viral oncolytic activity. The model assumes that cytotoxic T cells can induce apoptosis in infected cancer cells and that free viruses can be inactivated by neutralizing antibodies or cleared at a constant rate by the innate immune response. Our simulations suggest that reprogramming the immune microenvironment in tumors could substantially enhance the oncolytic virotherapy in immune-competent hosts. Viable routes to such reprogramming are either in situ virus-mediated impairing of CD$8^+$ T cells motility or blockade of B and T lymphocytes recruitment. Our theoretical results can shed light on the design of viral vectors or new protocols with neat potential impacts on the clinical practice., Comment: 14 pages, 4 figures

A Boolean dynamical system integrating the main signaling pathways involved in cancer is constructed based on the currently known protein-protein interaction network. This system exhibits stationary protein activation patterns – attractors – dependent on the cell’s microenvironment. These dynamical attractors were determined through simulations and their stabilities against mutations were tested. In a higher hierarchical level, it was possible to group the network attractors into distinct cell phenotypes and determine driver mutations that promote phenotypic transitions. We find that driver nodes are not necessarily central in the network topology, but at least they are direct regulators of central components towards which converge or through which crosstalk distinct cancer signaling pathways. The predicted drivers are in agreement with those pointed out by diverse census of cancer genes recently performed for several human cancers. Furthermore, our results demonstrate that cell phenotypes can evolve towards full malignancy through distinct sequences of accumulated mutations. In particular, the network model supports routes of carcinogenesis known for some tumor types. Finally, the Boolean network model is employed to evaluate the outcome of molecularly targeted cancer therapies. The major find is that monotherapies were additive in their effects and that the association of targeted drugs is necessary for cancer eradication.

In the present paper we analyse the morphology of dendrites of cerebellar Purkinje cells and axon terminals in the cerebral cortex of rats. We find that these three-dimensional biostructures are fractal over at least one decade of length scales, with fractal dimension 1.68 ± 0.08 for the Purkinje cells and 1.28 ± 0.17 for the axon terminals. We also discuss the largelly unknown mechanisms underlying neurite outgrowth which frequently develops neuronal shapes with fractal dimensions very different from that predicted for diffusion-limited-aggregation model (DLA) in three dimensions.

The present study aims to understand the growth of human malignant tumours in vitro, using the geometry of fractals as a method of analysis. The fractal dimensions of HN-5 and MDCK cell growth patterns have been measured. The first results may suggest the possibility of distinct growth processes characterized by different (time-dependent) effective fractal dimensions for MDCK and HN-5 cells. If this is true, the fractal dimensions may yet prove to be a useful discriminant for comparing different diagnostic categories.

One of the most promising strategies to treat cancer is attacking it with viruses designed to exploit specific altered pathways. Here, the effects of oncolytic virotherapy on tumors having compact, papillary, and disconnected morphologies are investigated through computer simulations of a multiscale model coupling macroscopic reaction-diffusion equations for the nutrients with microscopic stochastic rules for the actions of individual cells and viruses. The interaction among viruses and tumor cells involves cell infection, intracellular virus replication, and the release of new viruses in the tissue after cell lysis. The evolution over time of both the viral load and cancer cell population, as well as the probabilities for tumor eradication, were evaluated for a range of multiplicities of infection, viral entries, and burst sizes. It was found that in immunosuppressed hosts, the antitumor efficacy of a virus is primarily determined by its entry efficiency, its replicative capacity within the tumor, and its ability to spread over the tissue. However, the optimal traits for oncolytic viruses depend critically on the tumor growth dynamics and do not necessarily include rapid replication, cytolysis, or spreading, currently assumed as necessary conditions for a successful therapeutic outcome. Our findings have potential implications on the design of new vectors for the viral therapy of cancer.

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and \textit{in vitro} drug testing. In the present paper, a cluster-cluster aggregation model with stochastic particle replication and chemotactically driven motility is investigated as a model for the growth of animal cells in culture. The focus is on the scaling laws governing the aggregation kinetics. Our simulations reveal that in the absence of chemotaxy the mean cluster size and the total number of clusters scale in time as stretched exponentials dependent on the particle replication rate. Also, the dynamical cluster size distribution functions are represented by a scaling relation in which the scaling function involves a stretched exponential of the time. The introduction of chemoattraction among the particles leads to distribution functions decaying as power laws with exponents that decrease in time. The fractal dimensions and size distributions of the simulated clusters are qualitatively discussed in terms of those determined experimentally for several normal and tumoral cell lines growing in culture. It is shown that particle replication and chemotaxy account for the simplest cluster size distributions of cellular aggregates observed in culture., 14 pages, 8 figures, to appear on Jstat

Life, amazingly rich in diversity of shapes and functions, explores the limits of extreme complexity in nature. In this review we shall discuss in general terms the use of multiscale mathematical and computer models to study the dynamics of biological systems. These models permit integration of the rapidly expanding knowledge concerning the molecular basis of biology and its complex, nonlinear relationship with the emerging shapes and functions of cells, tissues and organs in living organisms.

One of the most promising strategies to treat cancer is attacking it with viruses. Oncolytic viruses can kill tumor cells specifically or induce anticancer immune response. A multiscale model for virotherapy of cancer is investigated through simulations. It was found that, for intratumoral virus administration, a solid tumor can be completely eradicated or keep growing after a transient remission. Furthermore, the model reveals undamped oscillatory dynamics of tumor cells and virus populations, which demands new in vivo and in vitro quantitative experiments aiming to detect this oscillatory response. The conditions for which each one of the different tumor responses dominates, as well as the occurrence probabilities for the other nondominant therapeutic outcomes, were determined. From a clinical point of view, our findings indicate that a successful, single agent virotherapy requires a strong inhibition of the host immune response and the use of potent virus species with a high intratumoral mobility. Moreover, due to the discrete and stochastic nature of cells and their responses, an optimal range for viral cytotoxicity is predicted because the virotherapy fails if the oncolytic virus demands either a too short or a very large time to kill the tumor cell. This result suggests that the search for viruses able to destroy tumor cells very fast does not necessarily lead to a more effective control of tumor growth. [Cancer Res 2009;69(3):1205–11]

We review some computer algorithms for the simulation of off-lattice clusters grown from a seed, with emphasis on the diffusion-limited aggregation, ballistic aggregation and Eden models. Only those methods which can be immediately extended to distinct off-lattice aggregation processes are discussed. The computer efficiencies of the distinct algorithms are compared., Comment: 6 pages, 7 figures and 3 tables; published at Brazilian Journal of Physics 38, march, 2008 (http://www.sbfisica.org.br/bjp/files/v38_81.pdf)

Within a real space renormalisation group approach, the authors study the phase diagram and the universality classes of the three-state chiral clock model in a self-dual planar hierarchical lattice. They find that the chiral field Delta is relevant at the pure Potts critical point with a crossover exponent phi approximately=0.32. The critical line which separates the ferromagnetic phase from the non-ferromagnetic ones is characterised by a multicritical (Lifshitz) point located at (K, Delta ) approximately= (1.452, 0.382).

Inspired by dengue and yellow fever epidemics, we investigated the contact process (CP) in a multiscale network constituted by one-dimensional chains connected through a Barab\'asi-Albert scale-free network. In addition to the CP dynamics inside the chains, the exchange of individuals between connected chains (travels) occurs at a constant rate. A finite epidemic threshold and an epidemic mean lifetime diverging exponentially in the subcritical phase, concomitantly with a power law divergence of the outbreak's duration, were found. A generalized scaling function involving both regular and SF components was proposed for the quasistationary analysis and the associated critical exponents determined, demonstrating that the CP on this hybrid network and nonvanishing travel rates establishes a new universality class.

Membrane ruffle fluctuations of amphibian epithelial cells A6 (CCL102) cultured in normal and upside down oriented plates have been analyzed through video microscopy. Our results reveal that their edge ruffle fluctuations exhibit a stochastic dynamics with $1∕{f}^{\ensuremath{\alpha}}$ power spectrum over at least two decades at low frequencies and long range correlated, self-affine lateral border profiles. In a few and small areas of the membrane, probably nearby focal contacts, we found periodic oscillations which could be induced by myosin driven contraction of stress fibers. Furthermore, whereas the different gravitational orientations had none or little effect on the structure (power spectra and surface roughness) of these membrane ruffle fluctuations, their dynamic parameters were differentially affected. Indeed, the decay time of ruffles remained unchanged, but the period of lamellipodia oscillations near the focal adhesion points was significantly altered in A6 cells cultured upside down.

We report some experimental results for quasi-two-dimensional electrocrystallization of copper under magnetic fields. Such results are theoretically investigated by large scale simulations of a DLA-like model in which random walkers can move along circular vortices enhanced by the Lorentz force. In addition, a sticking probability is used to take into account the complex reaction dynamics at the cathode surface. Our results indicate that the convective motion does not change the nature of the normal diffusive regime, but increases dramatically the diffusion constant by a factor of up to six. The characteristic features (morphology and scaling laws) of both random walks and growing electrodeposits under a perpendicular magnetic field are determined.

Os padrões de crescimento de linhagens estáveis de células normais e cancerosas, cultivadas em monocamada e em géis de colágeno, foram caracterizados utilizando-se a distribuição de tamanhos de agregados celulares. Células HN-5 (cancerosas) apresentam, tanto em monocamada quanto em gel, distribuições regidas por leis de potência durante todo o tempo que permaneceram em cultura, enquanto que nas células MDCK (normais) e HEp-2 (cancerosas) observa-se uma transição de um comportamento exponencial para um regido por uma distribuição em leis de potência. Estes resultados sugerem que as transições nos regimes de crescimento de MDCK e HEp-2 podem estar associadas a alterações no controle da replicação ou nos padrões de expressão de moléculas de adesividade celular de junções célula-célula ou célula-matriz extracelular, relacionadas com sinalização intracelular. Estas transições são irreversíveis e parecem corresponder a uma resposta adaptativa das células às restrições ao crescimento impostas por uma elevada densidade populacional ou por uma longa permanência em cultura. The growth patterns of established normal and cancer cell lines, cultured in monolayer and collagen gel, have been characterized using the cluster size distribution of cellular aggregates. HN-5 (cancer) cells exhibit, either in gel or in monolayer, power-law distributions at any time in culture, whereas for MDCK (normal) and HEp-2 (cancer) cells there is a transition from an exponential behavior to a power-law distribution after a transient time in culture. These results suggest that the transitions in growth regimes observed in MDCK and HEp-2 cell lines might be associated to changes in the control of replication or in the expression patterns of cell adhesion molecules of cell-cell and cell-matrix type related to intracellular signalling. These transitions are irreversible and seems to be an adaptative response to the growth constraints imposed by high cell population density or long permanence in culture.

Recently, we have proposed a nutrient-limited model for the avascular growth of tumors including cell proliferation, motility and death \cite{jr}, that, qualitatively reproduces commonly observed morphologies for carcinomas {\it in situ}. In the present work, we analyze the effects of distinct chemotherapeutic strategies on the patterns, scaling and growth laws obtained for such nutrient-limited model. Two kinds of chemotherapeutic strategies were considered, namely, those that kill cancer cells and those that block cell mitosis but allows the cell to survive for some time. Depending on the chemotherapeutic schedule used, the tumors are completely eliminated, reach a stationary size or grow following power laws. The model suggests that the scaling properties of the tumors are not affected by the mild cytotoxic treatments, although a reduction in growth rates and an increase in invasiveness are observed. For the strategies based on antimitotic drugs a morphological transition in which compact tumors become more fractal under aggressive treatments was seen., Comment: 9 pages, 9 figures

Nowadays, in societies threatened by atomization, selfishness, short-term thinking, and alienation from political life, there is a renewed debate about classical questions concerning the quality of democratic decision-making. In this work a cellular automata (CA) model for the dynamics of free elections based on the social impact theory is proposed. By using computer simulations, power law distributions for the size of electoral clusters and decision time have been obtained. The major role of broadcasted electoral surveys in guiding opinion formation and stabilizing the ``{\it status quo}'' was demonstrated. Furthermore, it was shown that in societies where these surveys are manipulated within the universally accepted statistical error bars, even a majoritary opposition could be hindered from reaching the power through the electoral path., Comment: 15 pages, 9 figures

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are characterized by its gyration radius, total number of cancer cells, and number of cells on tumor periphery. These very distinct morphological patterns follow Gompertz growth curves, but exhibit different scaling laws for their surfaces. Also, the simulated tumors incorporate a spatial structure composed of a central necrotic core, an inner rim of quiescent cells and a narrow outer shell of proliferating cells in agreement with biological data. Finally, our results indicate that the competition for nutrients among normal and cancer cells may be a determinant factor in generating papillary tumor morphology., 9 pages, 6 figures, to appear in PRE

We present a numerical study of the self-affine profiles obtained from configurations of the q-state Potts (with q=2,3 and 7) and p=10 clock models as well as from the occupation states for site-percolation on the square lattice. The first and second order static phase transitions of the Potts model are located by a sharp change in the value of the roughness exponent $\alpha$ characterizing those profiles. The low temperature phase of the Potts model corresponds to flat ($\alpha\simeq 1$) profiles, whereas its high temperature phase is associated to rough ($\alpha\simeq 0.5$) ones. For the p=10 clock model, in addition to the flat (ferromagnetic) and rough (paramagnetic) profiles, an intermediate rough ($0.5< \alpha, Comment: 8 pages, 9 figures, submitted to Phys. Rev. E