Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

Periodic Modulation Induced Increase of Reaction Rates in Autocatalytic Systems

We propose a new mechanism to increase the reactions ratesin multistable autocatalytic systems. The mechanism is based upon the possibility for the enhancement of the response of the system due to the cooperative behavior between the noise and an external periodic modulation. In order to illustrate this feature we compute the reaction velocities for the particular case of the Sel'Kov model, showing that they increase significantly when the periodic modulation is introduced. This behavior originates from the existence of a minimum in the mean first passage time, one of the signatures of stochastic resonance.Comment: Submitted to J. Chem. Phy

Mathematical modelling of angiogenesis and vascular adaptation

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The phi(1020) a0(980) S-wave scattering and hints for a new vector-isovector resonance

We have studied the phi(1020)a0(980) S-wave scattering at threshold energies employing chiral Lagrangians coupled to vector mesons by minimal coupling. The interaction is described without new free parameters by considering the scalar isovector a0(980) resonance as dynamically generated in coupled channels, and demanding that the recently measured e+ e- -> phi(1020) f0(980) cross section is reproduced. For some realistic choices of the parameters, the presence of a dynamically generated isovector companion of the Y(2175) is revealed. We have also investigated the corrections to the e+ e- -> phi(1020) pi0 eta reaction cross section that arise from phi(1020)a0(980) re-scattering in the final state. They are typically large and modify substantially the cross section. For a suitable choice of parameters, the presence of the resonance would manifest itself as a clear peak at sqrt{s}~2.03 GeV in e+ e- -> phi(1020) pi0 eta.Comment: 16 pages, 9 figures, 2 table

The enzymes LSD1 and Set1A cooperate with the viral protein HBx to establish an active hepatitis B viral chromatin state

Indexación: Web of ScienceWith about 350 million people chronically infected around the world hepatitis B is a major health problem. Template for progeny HBV synthesis is the viral genome, organized as a minichromosome (cccDNA) inside the hepatocyte nucleus. How viral cccDNA gene expression is regulated by its chromatin structure; more importantly, how the modulation of this structure impacts on viral gene expression remains elusive. Here, we found that the enzyme SetDB1 contributes to setting up a repressed cccDNA chromatin state. This repressive state is activated by the histone lysine demethylase-1 (LSD1). Consistently, inhibiting or reducing LSD1 levels led to repression of viral gene expression. This correlates with the transcriptionally repressive mark H3K9 methylation and reduction on the activating marks H3 acetylation and H3K4 methylation on viral promoters. Investigating the importance of viral proteins we found that LSD1 recruitment to viral promoters was dependent on the viral transactivator protein HBx. Moreover, the histone methyltransferase Set1A and HBx are simultaneously bound to the core promoter, and Set1A expression correlates with cccDNA H3K4 methylation. Our results shed light on the mechanisms of HBV regulation mediated by the cccDNA chromatin structure, offering new therapeutic targets to develop drugs for the treatment of chronically infected HBV patients.http://www.nature.com/articles/srep2590