Mathematical modelling of bone remodelling cycles including the NFκB signalling pathway

RANKL can promote the differentiation of osteoclast precursors into mature osteoclasts by binding to RANK expressed on the surfaces of osteoclast progenitor cells during bone remodelling. The NF-κB signalling pathway is downstream of RANKL and transmits the RANKL signal to nuclear promoter-bound protein complexes from cell surface receptors, which then regulates target gene expression to facilitate osteoclastogenesis. However, this important role of the NF-κB signalling pathway is usually ignored in published mathematical models of bone remodelling. This paper describes the construction of a mathematical model of bone remodelling in a normal bone microenvironment with inclusion of the NF-κB signalling pathway. The model consisted of a set of ordinary differential equations and reconstructed variations in the bone cells, resultant bone volume, and biochemical factors involved in the NF-κB signalling pathway over time. The model was used to investigate how the NF-κB pathway is activated in osteoclast precursors to promote osteoclastogenesis during bone remodelling. Model simulations agreed well with published experimental data. It is hoped that this model can improve our understanding of bone remodelling. It has the obvious potential to examine the influence of NF-κB dysregulation on bone remodelling, and even propose potential therapeutic strategies to combat related bone diseases in future research

The Regulation and Function of YAP1

Yes-associated protein 1 (YAP1) is a transcriptional regulator that was first described as part of the Hippo signalling cascade. In the last five years, several others regulators have been identified, placing YAP1 at the centre of a much more complex network. One common feature of these different regulatory mechanisms is that YAP1 localises either in the nucleus bound to transcription factors promoting the expression of target genes or in the cytoplasm sequestered into diverse complexes. In vivo studies reveal that YAP1 can promote tumour initiation, progression and metastasis by controlling proliferation and survival of cancer cells. In addition to cancer cells, tumours contain many other cell types such as cancer-associated fibroblasts (CAFs). These cells show a high ability to promote invasion of cancer cells by remodelling the extra-cellular matrix. One possible origin for CAFs is through the local conversion of resident NFs, however the mechanism of this conversion is not fully understood. This thesis aims to understand the function and regulation of YAP1 in fibroblasts during normal development and tumour progression. Analyses of gene expression showed that YAP1 transcriptional activity was upregulated in CAFs compared to NFs. Treatment with actomyosin inhibitors revealed that this upregulation was dependent on the actomyosin cytoskeleton network suggesting a role for mechanotransduction in YAP1 regulation. This high transcriptional activity was associated with a nuclear translocation of YAP1 in CAFs compared to NFs. In order to determine the dynamics of the protein sub-cellular localisation, YAP1 was fused to EYFP fluorescent protein. Photobleaching experiments revealed a high mobility of YAP1 in the nucleus and the cytoplasm in both NFs and CAFs. These experiments also highlighted a constant and fast nucleocytoplasmic shuttling of the protein. Mathematical modelling analyses suggested a difference in the export rates from the nucleus to the cytoplasm, NFs showing a higher export rate than CAFs. This approach was extended to study the localisation, dynamics, and function of five YAP1 mutants. Analyses of the mutants showed differences in nuclear mobility and in export rates compared to the WT protein. Overall these data suggest the major roles of nuclear binding partners as well as export machinery in the regulation of YAP1 dynamics in NF1 and CAF1. In parallel, the role of YAP1 in fibroblasts during mouse development was assessed. Deletion of YAP1 in PDGFRα+ cells led to a lethal phenotype appearing at E11.5 due to haemorrhage in the head suggesting a crucial role of YAP1 protein in mesenchymal cells during normal vasculature development

Monocyte subpopulations in patients following ST-elevation myocardial infarction:implications for post-infarction left ventricular remodelling and clinical outcomes

Despite improvements in interventional and pharmacological therapy of atherosclerotic disease,it is still the leading cause of death in the developed world. Hence there is a need for further development of effective therapeutic approaches. This requires better understanding of the molecular mechanisms and pathophysiology of the disease. Atherosclerosis has long been identified as having an inflammatory component contributing to its pathogenesis, whilst the available therapy primarily targets hyperlipidaemia and prevention of thrombosis. Acknowledging a pleotropic anti-inflammatory effect to some therapies, such as acetyl salicylic acid and the statins, none of the currently approved medicines for management of either stable or complicated atherosclerosis has inflammation as a primary target. Monocytes, as representatives of the innate immune system, play a major role in the initiation, propagation and progression of atherosclerosis from a stable to an unstable state. Animal study data support a role of monocytes in acute coronary syndromes and in outcome post infarction; however, limited research has been done in humans.  In this thesis I describe for the first time in a large cohort of ST elevation myocardial infarction(STEMI) patients followed up for three years that total monocyte count, monocyte subset 1(Mon 1), and monocyte subset 2 (Mon 2) are predictive of major adverse cardiac events (MACE)post STEMI (including death, new diagnosis of heart failure, recurrent acute coronary syndrome). Both the inflammatory function of monocyte subsets (via assessment and quantification of IKK as a surrogate for the NFB inflammatory pathway activation) as well as the phagocytic activity of monocytes were studied in order to describe the mechanism through which monocytes affect their action. There was no significant difference in the NFB pathway activity between those patients who developed an adverse event and those who did not. Also NFB activity was not predictive of MACE. However the phagocytic activity of Mon 1 and Mon 2 were predictive of MACE suggesting that phagocytic activity of monocytes is the mechanism through which monocytes implement their action. Also this supports that the newly described monocytes subset 2 (Mon 2) is predominantly an inflammatory monocyte subset, not reparative as Mon 3.  Major adverse cardiac events were driven mainly by heart failure diagnosis and echocardiographic findings. Hence the association between ventricular remodelling and phenotypic and functional characterisation of monocytes subsets was studied in this thesis. Total monocyte count, Mon 1 and Mon 2 were again predictive of negative ventricular remodelling with increase in end systolic indexed volume of >15% at 6 months follow up echocardiogram post infarction. Subclinical parameters of systolic dysfunction, namely global longitudinal strain and global circumferential strain were also significantly correlated with total monocyte count as well as Mon 1 levels.  Given the above, I studied the effect of incorporating total monocyte count in Thrombolysis in Myocardial Infarction (TIMI) STEMI score to predict patient outcome at 30 days post infraction.C- statistics indicated improved prognostication of the TIMI STEMI model after incorporation of the total monocyte count into the model with improved area under the curve from 0.67 (for TIMI STEMI score), to area under the curve of 0.77 (TIMIMon score). This allows individual tailoring of secondary preventative therapy in order to improve patient outcome post infarction.Having described a potential mechanism through which the innate immune system affects outcome in STEMI patients, namely Mon1 and Mon2 through their phagocytic activity, the results from this thesis could be a stepping stone into targeted anti-inflammatory therapy in management of myocardial infarction

Modelling the molecular mechanisms of ageing

This document is the Accepted Manuscript version of a published work that appeared in final form in Bioscience reports. To access the final edited and published work see http://www.bioscirep.org/content/37/1/BSR20160177.The ageing process is driven at the cellular level by random molecular damage which slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the ageing process. The complexity of the ageing process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards, and discusses many specific examples of models which have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field

The Role of Activated Protein C in Bone, Arthritis, and Fracture Healing

Activated protein C (APC) is a cytoprotective anticoagulant that stimulates cellular proliferation, suppresses inflammation, and enhances wound healing. These properties of APC are primarily modulated through its receptors, endothelial protein C receptor (EPCR) and protease-activated receptors (PAR)1/2, and subsequent activation of downstream proteins including ERK1/2, Akt, and p38. In this study, APC was investigated for its potential application in bone repair and arthritic bone conditions, including rheumatoid arthritis (RA) and osteoarthritis (OA), through its actions on osteoblasts. APC increased viability of MG-63 and MC3T3-E1 cells through a PAR1 dependent pathway and subsequently upregulated pERK, pAkt, and p-p38. APC augmented bone and tissue volume but not osteoclast numbers in a BMP-2 induced murine ectopic bone formation model. APC, however, did not enhance callus formation in a closed murine mid-tibial fracture model owing to several study limitations. In contrast with its effects in osteoblastic cell lines, APC suppressed cell viability through an EPCR/PAR1/PAR2 dependent mechanism in OA and RA bone derived cells. APC also decreased pERK, increased p27, and modulated IL-6 and MMP-2 secretion in arthritic cells. Collectively, these results demonstrate the diverse actions of APC in normal and arthritic bone biology including the novel potential of APC on bone formation

Reduced order modelling of bone resorption and formation.

The bone remodelling process, performed by the Bone Multicellular Unit (BMU) is a key multi-hierarchically regulated process, which provides and supports various functionality of bone tissue. It is also plays a critical role in bone disorders, as well as bone tissue healing following damage. Improved modelling of bone turnover processes could play a significant role in helping to understand the underlying cause of bone disorders and thus develop more effective treatment methods. Moreover, despite extensive research in the field of bone tissue engineering, bonescaffold development is still very empirical. The development of improved methods of modelling the bone remodelling process should help to develop new implant designs which encourage rapid osteointegration. There are a number of limitations with respect to previous research in the field of mathematical modelling of the bone remodelling process, including the absence of an osteocyte loop of regulation. It is within this context that this research presented in this thesis utilises a range of modelling methods to develop a framework for bone remodelling which can be used to improve treatment methods for bone disorders. The study concentrated on dynamic and steady state variables that in perspective can be used as constraints for optimisation problem considering bone remodelling or tissue remodelling with the help of the grafts/scaffolds.The cellular and combined allosteric-regulation approaches to modelling of bone turnover, based on the osteocyte loop of regulation, have been studied. Both approaches have been studied different within wide range of rate parameters. The approach to the model validation has been considered, including a statistical approach and parameter reduction approach. From a validation perspective the cellular class of modes is preferable since it has fewer parameters to validate. The optimal control framework for regulation of remodelling has been studied. Future work in to improve the models and their application to bone scaffold design applications have been considered. The study illustrates the complexity of formalisation of the metabolic processes and the relations between hierarchical subsystems in hard tissue where a relatively small number of cells are active. Different types/modes of behaviour have been found in the study: relaxational, periodical and chaotic modes. All of these types of behaviour can be found, in bone tissue. However, a chaotic or periodic modes are ones of the hardest to verify although a number of periodical phenomena have been observed empirically in bone and skeletal development. Implementation of the allosteric loop into cellular model damps other types of behaviour/modes. In this sense it improves the robustness, predictability and control of the system. The developed models represent a first step in a hierarchical model of bone tissue (system versus local effects). The limited autonomy of any organ or tissue implies differentiation on a regulatory level as well as physiological functions and metabolic differences. Implementation into the cellular phenomenological model of allosteric-like loop of regulation has been performed. The results show that the robustness of regulation can be inherited from the phenomenological model. An attempt to correlate the main bone disorders with different modes of behaviour has been undertaken using Paget’s disorder in bone, osteoporosis and some more general skeleton disorders which lead to periodical changes in bone mass, reported by some authors. However, additional studies are needed to make this hypothesis significant. The study has revealed a few interesting techniques. When studying a multidimensional phenomenon, as a bone tissue is, the visualisation and data reduction is important for analysis and interpretation of results. In the study two novel technical methods have been proposed. The first is the graphical matrix method to visualise/project the multidimensional phase space of variables into diagonal matrix of regular combination of two-dimensional graphs. This significantly simplifies the analysis and, in principle, makes it possible to visualise the phase space higher than three-dimensional. The second important technical development is the application of the Monte-Carlo method in combination with the regression method to study the character and stability of the equilibrium points of a dynamic system. The advantage of this method is that it enables the most influential parameters that affect the character and stability of the equilibrium point to be identified from a large number of the rate parameters/constants of the dynamic system. This makes the interpretation of parameters and conceptual verification of the model much easier

Mathematical modelling of epithelium homeostasis

The body and organs of all animals are covered by epithelial tissues, such as the epidermis and the airway epithelium. Epithelial tissues play a key role in protecting the body from environmental aggressors. Failure to maintain a competent epithelium can lead to the onset of many diseases, including Atopic dermatitis (AD) and infection by Streptococcus pneumoniae. Treatment of AD is currently restricted to the relief of symptoms, mainly because the underlying mechanisms remain elusive. Antibiotic resistance threatens the effectiveness of the prevalent treatments for infection. Devising new and effective therapeutic strategies that halt the progression of these diseases requires an understanding of the different disease mechanisms that can cause loss of epithelial homeostasis in different patients. Intricate regulatory networks of several biochemical and cellular interactions maintain epithelium homeostasis in healthy individuals, but can also propagate different disturbances, resulting in a wide spectrum of possible disease phenotypes. In this thesis, we propose mathematical models of these regulatory networks to analyse the mechanisms that lead to the onset and progression of AD and pneumococcal infection from a systems-level perspective. Our mathematical model of AD reproduced, for the first time, the different stages of the disease that have been observed in the clinic. Moreover, we proposed different pathogenic mechanisms, triggered by different genetic and environmental risk factors that are known to predispose to AD. By assessing the effects of common treatments for AD, we suggested effective treatment strategies that can prevent the aggravation of the disease, in a patient-specific way. Our data-driven mathematical model of pneumococcal infection identified four qualitatively different mechanisms by which co-infection can drive the pathogenic process. They can be counteracted by distinctive treatment strategies that only partially involve antibiotics. Our work provides a theoretical framework for the integration and analysis of clinical and experimental data describing epithelial homeostasis.Open Acces

Mathematical modelling of cytokine dynamics in arthritic disease

Arthritic diseases, a group of degenerative joint diseases, cause pain, disability and the loss of independence. Research over the last 30 years has improved our understanding of these conditions. We now know that these conditions are pathological in nature, and are mediated by cytokines, cell signalling proteins. We still have much to learn about disease initiation, control and progression if we wish to develop reliable and effective disease-modifying treatments. In this thesis we use mathematical modelling to extend our understanding of arthritic disease. We focus our attention on two arthritic diseases, rheumatoid arthritis (RA), predominantly initiated in the synovium of joints, and osteoarthritis (OA), predominantly initiated in the cartilage of joints. We develop an ODE model of cytokine dynamics in the synovium and show that it contains some features associated with RA. We find that increases in cytokine production rates over time can lead to initiation of RA, including periods of relapsing-remitting disease. We find that dose timing and interval as well as dose size are all important to treatment outcome. We develop two models of cytokine dynamics in cartilage and use these to analyse OA initiation and progression. The first model is an ODE model, expanding on the synovium model, and the second model is a spatial Cellular Potts model. We use these to consider pathways that could lead to the development of OA, and show that combined treatment strategies are more effective than single target therapies in treating OA. We also show that diffusion in cartilage plays an important role in OA. We look briefly at the downstream signalling pathways of cytokines, which are also not fully understood. Here we focus on the binding of a family of transcription factors (STAT proteins) to DNA. We find that multiple high affinity binding sites are not a requirement for cooperative binding of STAT proteins