Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

Modelling travelling waves in spatially constrained environment solutions

In this study, we consider how Fractional Differential Equations (FDEs) can be used to study the travelling wave phenomena in parabolic equations. As our method is conducted under intracellular environments that are highly crowded, it was discovered that there is a simple relationship between the travelling wave speed and obstacle density.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Multiple types of data are required to identify the mechanisms influencing the spatial expansion of melanoma cell colonies

Background The expansion of cell colonies is driven by a delicate balance of several mechanisms including cell motility, cell-to-cell adhesion and cell proliferation. New approaches that can be used to independently identify and quantify the role of each mechanism will help us understand how each mechanism contributes to the expansion process. Standard mathematical modelling approaches to describe such cell colony expansion typically neglect cell-to-cell adhesion, despite the fact that cell-to-cell adhesion is thought to play an important role. Results We use a combined experimental and mathematical modelling approach to determine the cell diffusivity, D, cell-to-cell adhesion strength, q, and cell proliferation rate, ?, in an expanding colony of MM127 melanoma cells. Using a circular barrier assay, we extract several types of experimental data and use a mathematical model to independently estimate D, q and ?. In our first set of experiments, we suppress cell proliferation and analyse three different types of data to estimate D and q. We find that standard types of data, such as the area enclosed by the leading edge of the expanding colony and more detailed cell density profiles throughout the expanding colony, does not provide sufficient information to uniquely identify D and q. We find that additional data relating to the degree of cell-to-cell clustering is required to provide independent estimates of q, and in turn D. In our second set of experiments, where proliferation is not suppressed, we use data describing temporal changes in cell density to determine the cell proliferation rate. In summary, we find that our experiments are best described using the range D = 161 - 243 ?m2 hour-1, q = 0.3 - 0.5 (low to moderate strength) and ? = 0.0305 - 0.0398 hour-1, and with these parameters we can accurately predict the temporal variations in the spatial extent and cell density profile throughout the expanding melanoma cell colony. Conclusions Our systematic approach to identify the cell diffusivity, cell-to-cell adhesion strength and cell proliferation rate highlights the importance of integrating multiple types of data to accurately quantify the factors influencing the spatial expansion of melanoma cell colonies.

STI-GMaS : an open-source environment for simulation of sexually-transmitted infections

Background Sexually-transmitted pathogens often have severe reproductive health implications if treatment is delayed or absent, especially in females. The complex processes of disease progression, namely replication and ascension of the infection through the genital tract, span both extracellular and intracellular physiological scales, and in females can vary over the distinct phases of the menstrual cycle. The complexity of these processes, coupled with the common impossibility of obtaining comprehensive and sequential clinical data from individual human patients, makes mathematical and computational modelling valuable tools in developing our understanding of the infection, with a view to identifying new interventions. While many within-host models of sexually-transmitted infections (STIs) are available in existing literature, these models are difficult to deploy in clinical/experimental settings since simulations often require complex computational approaches. Results We present STI-GMaS (Sexually-Transmitted Infections – Graphical Modelling and Simulation), an environment for simulation of STI models, with a view to stimulating the uptake of these models within the laboratory or clinic. The software currently focuses upon the representative case-study of Chlamydia trachomatis, the most common sexually-transmitted bacterial pathogen of humans. Here, we demonstrate the use of a hybrid PDE–cellular automata model for simulation of a hypothetical Chlamydia vaccination, demonstrating the effect of a vaccine-induced antibody in preventing the infection from ascending to above the cervix. This example illustrates the ease with which existing models can be adapted to describe new studies, and its careful parameterisation within STI-GMaS facilitates future tuning to experimental data as they arise. Conclusions STI-GMaS represents the first software designed explicitly for in-silico simulation of STI models by non-theoreticians, thus presenting a novel route to bridging the gap between computational and clinical/experimental disciplines. With the propensity for model reuse and extension, there is much scope within STI-GMaS to allow clinical and experimental studies to inform model inputs and drive future model development. Many of the modelling paradigms and software design principles deployed to date transfer readily to other STIs, both bacterial and viral; forthcoming releases of STI-GMaS will extend the software to incorporate a more diverse range of infections.

Reactive Oxygen Species and Reactive Nitrogen Species in Epigenetic Modifications

For the normal homeostasis of a cell, there must be a balance between radical oxygen species/radical nitrogen species (ROS/RNS) production and the neutralization of these species by antioxidant scavenging. In times of stress, this balance is not maintained, and the result is oxidative stress. This stress can affect many pathways in the body and result in pathological consequences. Recent evidence suggests that ROS/RNS can affect the epigenetic regulation of genes by affecting the function of histone and DNA modifying enzymes, thus affecting phenotypic changes within the cellular environment. In the following chapter, we provide a broad overview of how oxidative stress induced by ROS/RNS can affect epigenetics, and using lung disease as our model we link the connection between these processes.

Epigenetics and migraine; complex mitochondrial interactions contributing to disease susceptibility

Migraine is a common neurological disorder classified by the World Health Organisation (WHO) as one of the top twenty most debilitating diseases in the developed world. Current therapies are only effective for a proportion of sufferers and new therapeutic targets are desperately needed to alleviate this burden. Recently the role of epigenetics in the development of many complex diseases including migraine has become an emerging topic. By understanding the importance of acetylation, methylation and other epigenetic modifications, it then follows that this modification process is a potential target to manipulate epigenetic status with the goal of treating disease. Bisulphite sequencing and methylated DNA immunoprecipitation have been used to demonstrate the presence of methylated cytosines in the human D-loop of mitochondrial DNA (mtDNA), proving that the mitochondrial genome is methylated. For the first time, it has been shown that there is a difference in mtDNA epigenetic status between healthy controls and those with disease, especially for neurodegenerative and age related conditions. Given co-morbidities with migraine and the suggestive link between mitochondrial dysfunction and the lowered threshold for triggering a migraine attack, mitochondrial methylation may be a new avenue to pursue. Creative thinking and new approaches are needed to solve complex problems and a systems biology approach, where multiple layers of information are integrated is becoming more important in complex disease modelling.

Whole-Body Imaging with Single-Cell Resolution by Tissue Decolorization

The development of whole-body imaging at single-cell resolution enables system-level approaches to studying cellular circuits in organisms. Previous clearing methods focused on homogenizing mismatched refractive indices of individual tissues, enabling reductions in opacity but falling short of achieving transparency. Here, we show that an aminoalcohol decolorizes blood by efficiently eluting the heme chromophore from hemoglobin. Direct transcardial perfusion of an aminoalcohol-containing cocktail that we previously termed CUBIC coupled with a 10 day to 2 week clearing protocol decolorized and rendered nearly transparent almost all organs of adult mice as well as the entire body of infant and adult mice. This CUBIC-perfusion protocol enables rapid whole-body and whole-organ imaging at single-cell resolution by using light-sheet fluorescent microscopy. The CUBIC protocol is also applicable to 3D pathology, anatomy, and immunohistochemistry of various organs. These results suggest that whole-body imaging of colorless tissues at high resolution will contribute to organism-level systems biology.

Multi-parametric hydrogels support 3D in vitro bioengineered microenvironment models of tumour angiogenesis

Tumour microenvironment greatly influences the development and metastasis of cancer progression. The development of three dimensional (3D) culture models which mimic that displayed in vivo can improve cancer biology studies and accelerate novel anticancer drug screening. Inspired by a systems biology approach, we have formed 3D in vitro bioengineered tumour angiogenesis microenvironments within a glycosaminoglycan-based hydrogel culture system. This microenvironment model can routinely recreate breast and prostate tumour vascularisation. The multiple cell types cultured within this model were less sensitive to chemotherapy when compared with two dimensional (2D) cultures, and displayed comparative tumour regression to that displayed in vivo. These features highlight the use of our in vitro culture model as a complementary testing platform in conjunction with animal models, addressing key reduction and replacement goals of the future. We anticipate that this biomimetic model will provide a platform for the in-depth analysis of cancer development and the discovery of novel therapeutic targets.