Predicting the safety and efficacy of butter therapy to raise tumour pHe: an integrative modelling study

Background: Clinical positron emission tomography imaging has demonstrated the vast majority of human cancers exhibit significantly increased glucose metabolism when compared with adjacent normal tissue, resulting in an acidic tumour microenvironment. Recent studies demonstrated reducing this acidity through systemic buffers significantly inhibits development and growth of metastases in mouse xenografts.\ud \ud Methods: We apply and extend a previously developed mathematical model of blood and tumour buffering to examine the impact of oral administration of bicarbonate buffer in mice, and the potential impact in humans. We recapitulate the experimentally observed tumour pHe effect of buffer therapy, testing a model prediction in vivo in mice. We parameterise the model to humans to determine the translational safety and efficacy, and predict patient subgroups who could have enhanced treatment response, and the most promising combination or alternative buffer therapies.\ud \ud Results: The model predicts a previously unseen potentially dangerous elevation in blood pHe resulting from bicarbonate therapy in mice, which is confirmed by our in vivo experiments. Simulations predict limited efficacy of bicarbonate, especially in humans with more aggressive cancers. We predict buffer therapy would be most effectual: in elderly patients or individuals with renal impairments; in combination with proton production inhibitors (such as dichloroacetate), renal glomular filtration rate inhibitors (such as non-steroidal anti-inflammatory drugs and angiotensin-converting enzyme inhibitors), or with an alternative buffer reagent possessing an optimal pK of 7.1–7.2.\ud \ud Conclusion: Our mathematical model confirms bicarbonate acts as an effective agent to raise tumour pHe, but potentially induces metabolic alkalosis at the high doses necessary for tumour pHe normalisation. We predict use in elderly patients or in combination with proton production inhibitors or buffers with a pK of 7.1–7.2 is most promising

Information Dynamics in Living Systems: Prokaryotes, Eukaryotes, and Cancer

BACKGROUND: Living systems use information and energy to maintain stable entropy while far from thermodynamic equilibrium. The underlying first principles have not been established. FINDINGS: We propose that stable entropy in living systems, in the absence of thermodynamic equilibrium, requires an information extremum (maximum or minimum), which is invariant to first order perturbations. Proliferation and death represent key feedback mechanisms that promote stability even in a non-equilibrium state. A system moves to low or high information depending on its energy status, as the benefit of information in maintaining and increasing order is balanced against its energy cost. Prokaryotes, which lack specialized energy-producing organelles (mitochondria), are energy-limited and constrained to an information minimum. Acquisition of mitochondria is viewed as a critical evolutionary step that, by allowing eukaryotes to achieve a sufficiently high energy state, permitted a phase transition to an information maximum. This state, in contrast to the prokaryote minima, allowed evolution of complex, multicellular organisms. A special case is a malignant cell, which is modeled as a phase transition from a maximum to minimum information state. The minimum leads to a predicted power-law governing the in situ growth that is confirmed by studies measuring growth of small breast cancers. CONCLUSIONS: We find living systems achieve a stable entropic state by maintaining an extreme level of information. The evolutionary divergence of prokaryotes and eukaryotes resulted from acquisition of specialized energy organelles that allowed transition from information minima to maxima, respectively. Carcinogenesis represents a reverse transition: of an information maximum to minimum. The progressive information loss is evident in accumulating mutations, disordered morphology, and functional decline characteristics of human cancers. The findings suggest energy restriction is a critical first step that triggers the genetic mutations that drive somatic evolution of the malignant phenotype

Interdisciplinary approaches to metastasis

Interdisciplinary research is making a significant contribution to understanding metastasis - one of the grand challenges in cancer research. Examples drawn from apparently unconnected areas of physics, and described at a recent workshop on metastasis, illustrate the value of interdiscplinary thinking

Cellular adaptations to hypoxia and acidosis during somatic evolution of breast cancer

Conceptual models of carcinogenesis typically consist of an evolutionary sequence of heritable changes in genes controlling proliferation, apoptosis, and senescence. We propose that these steps are necessary but not sufficient to produce invasive breast cancer because intraductal tumour growth is also constrained by hypoxia and acidosis that develop as cells proliferate into the lumen and away from the underlying vessels. This requires evolution of glycolytic and acid-resistant phenotypes that, we hypothesise, is critical for emergence of invasive cancer. Mathematical models demonstrate severe hypoxia and acidosis in regions of intraductal tumours more than 100 m from the basement membrane. Subsequent evolution of glycolytic and acid-resistant phenotypes leads to invasive proliferation. Multicellular spheroids recapitulating ductal carcinoma in situ (DCIS) microenvironmental conditions demonstrate upregulated glucose transporter 1 (GLUT1) as adaptation to hypoxia followed by growth into normoxic regions in qualitative agreement with model predictions. Clinical specimens of DCIS exhibit periluminal distribution of GLUT-1 and Na+/H+ exchanger (NHE) indicating transcriptional activation by hypoxia and clusters of the same phenotype in the peripheral, presumably normoxic regions similar to the pattern predicted by the models and observed in spheroids. Upregulated GLUT-1 and NHE-1 were observed in microinvasive foci and adjacent intraductal cells. Adaptation to hypoxia and acidosis may represent key events in transition from in situ to invasive cancer

Coulomb Interactions between Cytoplasmic Electric Fields and Phosphorylated Messenger Proteins Optimize Information Flow in Cells

Normal cell function requires timely and accurate transmission of information from receptors on the cell membrane (CM) to the nucleus. Movement of messenger proteins in the cytoplasm is thought to be dependent on random walk. However, Brownian motion will disperse messenger proteins throughout the cytosol resulting in slow and highly variable transit times. We propose that a critical component of information transfer is an intracellular electric field generated by distribution of charge on the nuclear membrane (NM). While the latter has been demonstrated experimentally for decades, the role of the consequent electric field has been assumed to be minimal due to a Debye length of about 1 nanometer that results from screening by intracellular Cl- and K+. We propose inclusion of these inorganic ions in the Debye-Huckel equation is incorrect because nuclear pores allow transit through the membrane at a rate far faster than the time to thermodynamic equilibrium. In our model, only the charged, mobile messenger proteins contribute to the Debye length.Using this revised model and published data, we estimate the NM possesses a Debye-Huckel length of a few microns and find this is consistent with recent measurement using intracellular nano-voltmeters. We demonstrate the field will accelerate isolated messenger proteins toward the nucleus through Coulomb interactions with negative charges added by phosphorylation. We calculate transit times as short as 0.01 sec. When large numbers of phosphorylated messenger proteins are generated by increasing concentrations of extracellular ligands, we demonstrate they generate a self-screening environment that regionally attenuates the cytoplasmic field, slowing movement but permitting greater cross talk among pathways. Preliminary experimental results with phosphorylated RAF are consistent with model predictions.This work demonstrates that previously unrecognized Coulomb interactions between phosphorylated messenger proteins and intracellular electric fields will optimize information transfer from the CM to the NM in cells

Niche inheritance: a cooperative pathway to enhance cancer cell fitness though ecosystem engineering

Cancer cells can be described as an invasive species that is able to establish itself in a new environment. The concept of niche construction can be utilized to describe the process by which cancer cells terraform their environment, thereby engineering an ecosystem that promotes the genetic fitness of the species. Ecological dispersion theory can then be utilized to describe and model the steps and barriers involved in a successful diaspora as the cancer cells leave the original host organ and migrate to new host organs to successfully establish a new metastatic community. These ecological concepts can be further utilized to define new diagnostic and therapeutic areas for lethal cancers.Comment: 8 pages, 1 Table, 4 Figure

3D modelling of angiogenesis and vascular tumour growth

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute

A general reaction-diffusion model of acidity in cancer invasion

We model the metabolism and behaviour of a developing cancer tumour in the context of its microenvironment, with the aim of elucidating the consequences of altered energy metabolism. Of particular interest is the Warburg Effect, a widespread preference in tumours for cytosolic glycolysis rather than oxidative phosphorylation for glucose breakdown, as yet incompletely understood. We examine a candidate explanation for the prevalence of the Warburg Effect in tumours, the acid-mediated invasion hypothesis, by generalising a canonical non-linear reaction–diffusion model of acid-mediated tumour invasion to consider additional biological features of potential importance. We apply both numerical methods and a non-standard asymptotic analysis in a travelling wave framework to obtain an explicit understanding of the range of tumour behaviours produced by the model and how fundamental parameters govern the speed and shape of invading tumour waves. Comparison with conclusions drawn under the original system—a special case of our generalised system—allows us to comment on the structural stability and predictive power of the modelling framework

Prisoner's Dilemma in Cancer Metabolism

As tumors outgrow their blood supply and become oxygen deprived, they switch to less energetically efficient but oxygen-independent anaerobic glucose metabolism. However, cancer cells maintain glycolytic phenotype even in the areas of ample oxygen supply (Warburg effect). It has been hypothesized that the competitive advantage that glycolytic cells get over aerobic cells is achieved through secretion of lactic acid, which is a by-product of glycolysis. It creates acidic microenvironment around the tumor that can be toxic to normal somatic cells. This interaction can be seen as a prisoner's dilemma: from the point of view of metabolic payoffs, it is better for cells to cooperate and become better competitors but neither cell has an incentive to unilaterally change its metabolic strategy. In this paper a novel mathematical technique, which allows reducing an otherwise infinitely dimensional system to low dimensionality, is used to demonstrate that changing the environment can take the cells out of this equilibrium and that it is cooperation that can in fact lead to the cell population committing evolutionary suicide