Dynamic modelling of protein and oxidative metabolisms simulates the pathogenesis of Parkinson's disease.

Research into Parkinson's disease (PD) is difficult and time consuming. It is a complex condition that develops over many decades in the human brain. For such apparently intractable diseases, mathematical models can offer an additional means of investigation. As a contribution to this process, the authors have developed an ordinary differential equation model of the most important cellular processes that have been associated with PD. The model describes the following processes: (i) cellular generation and scavenging of reactive oxygen species; (ii) the possible damage and removal of the protein -synuclein and, (iii) feedback interactions between damaged α-synuclein and reactive oxygen species. Simulation results show that the Parkinsonian condition, with elevated oxidative stress and misfolded α-synuclein accumulation, can be induced in the model by known PD risk factors such as ageing, exposure to toxins and genetic defects. The significant outcome of the paper is the demonstration that it is possible to reproduce in silico the multi-factorial interactions that characterise the pathogenesis of PD. As such, the model provides a systematic explanation of the variability and heterogeneity of PD and provides the basis for computational studies of further facets of this complex multi-factorial condition. [Includes supplementary material].

Feedback motif for the pathogenesis of Parkinson's disease.

Previous article on the integrative modelling of Parkinson's disease (PD) described a mathematical model with properties suggesting that PD pathogenesis is associated with a feedback-induced biochemical bistability. In this article, the authors show that the dynamics of the mathematical model can be extracted and distilled into an equivalent two-state feedback motif whose stability properties are controlled by multi-factorial combinations of risk factors and genetic mutations associated with PD. Based on this finding, the authors propose a principle for PD pathogenesis in the form of the switch-like transition of a bistable feedback process from 'healthy' homeostatic levels of reactive oxygen species and the protein α-synuclein, to an alternative 'disease' state in which concentrations of both molecules are stable at the damagingly high-levels associated with PD. The bistability is analysed using the rate curves and steady-state response characteristics of the feedback motif. In particular, the authors show how a bifurcation in the feedback motif marks the pathogenic moment at which the 'healthy' state is lost and the 'disease' state is initiated. Further analysis shows how known risks (such as: age, toxins and genetic predisposition) modify the stability characteristics of the feedback motif in a way that is compatible with known features of PD, and which explain properties such as: multi-factorial causality, variability in susceptibility and severity, multi-timescale progression and the special cases of familial Parkinson's and Parkinsonian symptoms induced purely by toxic stress.

A plea for more theory in molecular biology.

The integrationist principles of systems theory have proven hugely successful in the physical sciences and engineering. It is an underlying assumption made in the systems approach to biology that they can also be used to understand biological phenomena at the level of an entire organism or organ. Within this holistic vision, the vast majority of systems biology research projects investigate phenomena at the level of the cell, with the belief that unifying principles established at the most basic level can establish a framework within which we may understand phenomena at higher levels of organization. In this spirit, and to use a celestial analogy, if a disease--effecting an organ or entire body--is our universe of discourse, then the cell is the star we gaze at. In building an understanding of disease and the effect of drugs, systems biology makes an implicit assumption about direct causal entailment between cell function and physiology. A skeptic might argue that this is about the same as trying to predict the world economy from observations made at a local supermarket. However, assuming for the moment that the money and hope we are investing in molecular biology, genomics, and systems biology is justified, how should this amazing intellectual achievement be possible? In this chapter we argue that an essential tool to progress is a systems theory that allows biological objects and their operational characteristics to be captured in a succinct yet general form. Armed with this conceptual framework, we construct mathematical representations of standard cellular and intercellular functions which can be integrated to describe more general processes of cell complexes, and potentially entire organs.

A systems- and signal-oriented approach to intracellular dynamics.

A mathematical understanding of regulation, and, in particular, the role of feedback, has been central to the advance of the physical sciences and technology. In this article, the framework provided by systems biology is used to argue that the same can be true for molecular biology. In particular, and using basic modular methods of mathematical modelling which are standard in control theory, a set of dynamic models is developed for some illustrative cell signalling processes. These models, supported by recent experimental evidence, are used to argue that a control theoretical approach to the mechanisms of feedback in intracellular signalling is central to furthering our understanding of molecular communication. As a specific example, a MAPK (mitogen-activated protein kinase) signalling pathway is used to show how potential feedback mechanisms in the signalling process can be investigated in a simulated environment. Such 'what if' modelling/simulation studies have been an integral part of physical science research for many years. Using tools of control systems analysis, as embodied in the disciplines of systems biology, similar predictive modelling/simulation studies are now bearing fruit in cell signalling research.

Defined bacterial populations in the rumens of gnotobiotic lambs.

Five gnotobiotic lambs were fed on sterile diets until they were killed at 13 to 21 weeks of age. They were dosed orally with different combinations of 11 species of rumen bacteria. The biochemical reactions of each of the bacteria inoculated had been determined in pure culture in vitro, and they were chosen to perform the main reactions known to be associated with digestion in the normal mature rumen. Two of the bacteria could not be reisolated, but the remainder had established readily in the rumen, forming stable, mixed, defined populations. The total numbers of bacteria in the rumen, and the viable counts of most of the individual species were comparable to those of normal sheep. The concentration of volatile fatty acids was lower, however, and in four of the lambs there was a higher proportion of butyric acid and a lower proportion of propionic acid than in normal sheep. Cellulolytic, ureolytic, and methanogenic activities appeared to be taking place and lactate-utilizing bacteria appeared to reverse the accumulation of lactate which resulted from the activity of lactate-producing bacteria. Some of the bacteria also established at high levels in the caecum.

Observations on the alimentary tract of gnotobiotic lambs.

Seventeen gnotobiotic lambs were reared up to 21 weeks of age on cows' milk followed by sterile solid diets similar to diets fed to conventional lambs. Seven were inoculated with limited defined populations of rumen bacteria, seven were left uninoculated and three were dosed with rumen contents from conventional sheep ('conventionalised'). Seven naturally-born lambs were reared for purposes of comparison. As with other species of gnotobiotic animals, both the inoculated and the uninoculated gnotobiotic lambs had small, poorly developed lymph nodes, soft colon contents and thin intestinal walls. Unlike other species the caeca of gnotobiotic lambs were of normal size. The overall size of the reticulo-rumen including contents relative to body weight was similar in gnotobiotic and conventional lambs. However, macroscopically, the musculature of the rumen seemed to be poorly developed and histological studies showed hypoplasia of the muscle tissue of both the rumen and reticulum. Rumination was noted only infrequently in gnotobiotic lambs. The epithelium of the rumen and reticulum of the uninoculated gnotobiotic lambs was similar to that of neonatal lambs, but there was normal development of papillae in gnotobiotic lambs inoculated with limited defined populations of rumen bacteria and in conventionalised lambs. Degenerative changes were observed histologically in some of the organs of gnotobiotic lambs which were consistent with nutritional deficiencies.