Mathematics Is Biology's Next Microscope, Only Better; Biology Is Mathematics' Next Physics, Only Better

Joel Cohen offers a historical and prospective analysis of the relationship between mathematics and biolog

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Biological limits to reduction in rates of coronary heart disease: a punctuated equilibrium approach to immune cognition, chronic inflammation, and pathogenic social hierarchy

On both empirical and theoretical grounds we find that a particular form of social hierarchy, here characterized as 'pathogenic', can, from the earliest phases of life, exert a formal analog to evolutionary selection pressure, literally writing a permanent image of itself upon immune function as chronic vascular inflammation and its consequences. The staged nature of resulting disease emerges 'naturally' as an analog to punctuated equilibrium in evolutionary theory. Exposure differs according to the social constructs of race, class, and ethnicity, accounting in large measure for observed population-level differences in rates of coronary heart disease affecting industrialized societies. The system of American Apartheid, which enmeshes both majority and minority communities in a construct of pathogenic hierarchy, appears to present a severe biological limit to ultimate possible reductions in rates of coronary heart disease and related disorders for powerful as well as subordinate subgroups

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions

Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

Method for finding metabolic properties based on the general growth law. Liver examples. A General framework for biological modeling

We propose a method for finding metabolic parameters of cells, organs and whole organisms, which is based on the earlier discovered general growth law. Based on the obtained results and analysis of available biological models, we propose a general framework for modeling biological phenomena and discuss how it can be used in Virtual Liver Network project. The foundational idea of the study is that growth of cells, organs, systems and whole organisms, besides biomolecular machinery, is influenced by biophysical mechanisms acting at different scale levels. In particular, the general growth law uniquely defines distribution of nutritional resources between maintenance needs and biomass synthesis at each phase of growth and at each scale level. We exemplify the approach considering metabolic properties of growing human and dog livers and liver transplants. A procedure for verification of obtained results has been introduced too. We found that two examined dogs have high metabolic rates consuming about 0.62 and 1 gram of nutrients per cubic centimeter of liver per day, and verified this using the proposed verification procedure. We also evaluated consumption rate of nutrients in human livers, determining it to be about 0.088 gram of nutrients per cubic centimeter of liver per day for males, and about 0.098 for females. This noticeable difference can be explained by evolutionary development, which required females to have greater liver processing capacity to support pregnancy. We also found how much nutrients go to biomass synthesis and maintenance at each phase of liver and liver transplant growth. Obtained results demonstrate that the proposed approach can be used for finding metabolic characteristics of cells, organs, and whole organisms, which can further serve as important inputs for many applications in biology (protein expression), biotechnology (synthesis of substances), and medicine.Comment: 20 pages, 6 figures, 4 table

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

An agent-based model of anoikis in the colon crypt displays novel emergent behaviour consistent with biological observations

Colorectal cancer (CRC) is a major cause of cancer mortality. Colon crypts are multi-cellular flask-shaped invaginations of the colonic epithelium, with stem cells at their base which support the continual turnover of the epithelium with loss of cells by anoikis from the flat mucosa. Mutations in these stem cells can become embedded in the crypts, a process that is strongly implicated in CRC initiation. We describe a computational model which includes novel features, including an accurate representation of the geometry of the crypt mouth. Model simulations yield previously unseen emergent phenomena, such as localization of cell death to a small region of the crypt mouth which corresponds with that observed in vivo. A mechanism emerges in the model for regulation of crypt cellularity in response to changes in either cell proliferation rates or membrane adhesion strengths. We show that cell shape assumptions influence this behaviour, with cylinders recapitulating biology better than spheres. Potential applications of the model include determination of roles of mutations in neoplasia and exploring factors for altered crypt morphodynamics

A Multi-Scale Agent Based Model of Colon Carcinogenesis

Colorectal cancer (CRC) is a major cause of cancer mortality and there remain aspects of its formation which are not understood. The colon contains an epithelium punctuated by flask shaped invaginations called the crypts of Lieberkühn. These crypts are monoclonal in nature while adenomas are thought to be polyclonal, suggesting that multiple crypts are involved in carcinogenesis. It has been reported that fields of mutated tissue surround adenomas but the causes and growth of these fields are not well understood. There are two competing hypotheses regarding growth, the first being that mutated cells from one crypt invade neighbouring crypts, and the second that mutated crypts replicate themselves more often than wild-type crypts. To investigate these processes two agent based models were developed. The first model represents cells as agents and is similar to previous models in the field, but is novel in including the geometry of the crypt mouth. This is necessary to model multiple interacting crypts. This model is the first in the literature to be used to represent multiple crypts and is used to investigate invasion of neighbour crypts by mutated cells. The second model represents whole crypts as agents, which allows the entire colon to be simulated for multiple decades of biological time, as far as we are aware this is the first such model. The cell scale model predicts that crypt invasion does not occur, but that mutated cells can invade the flat mucosa above neighbouring crypts. Analysis of in-vivo data is consistent with this prediction. The crypt as agent model predicts fields of ~41,000 crypts, in agreement with data in the literature, this corresponds to a field ~23mm in diameter. This project models pre-cancerous fields for the first time over a variety of scales, making specific novel predictions which are in agreement with in-vivo data where such data exist. Two agent based models were created to study the development of precancerous fields, one a model with cells as agents to study cell scale phenomena and the other with crypts as agents to allow processes to be studied on larger spatial and temporal scales. These models could potentially be used to refine clinic practice by predicting the required frequency of post-intervention monitoring of patients or the necessity of further intervention

On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution