Modelling the molecular mechanisms of aging

Abstract

The aging process is driven at the cellular level by random molecular damage that 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 aging process. The complexity of the aging 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 that 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.

Keywords: aging; computational models; computer simulation; modelling standards; molecular mechanisms.

Figure 1. The underlying mechanisms of aging

The rate of accumulation of stress-induced random molecular damage is dependent on the capacity of the antioxidant system and efficiency of repair systems. As these systems are not 100% efficient, cells always contain some unrepaired damage that leads to activation of a stress response and up-regulation of mechanisms to remove the damage or to prevent the cell division. However, these responses also become less efficient with age so that damaged components accumulate leading to cellular defects, which gives rise to tissue dysfunction and aging (redrawing of Kirkwood, T.B. [2]).

Figure 2. The interaction of the molecular mechanisms of aging

Individual mechanisms cannot explain aging alone, as each mechanism has many interactions. Some example mechanisms and their interactions are shown but there are many others that are described in the text.

Figure 3. A pragmatic classification of modelling frameworks

The first decision concerns whether the model must capture the behaviour of the system (Dynamic) or only its structure (Static). Because aging, health and disease are processes, dynamic modelling of biological systems is a common approach within computational modelling. The second decision addresses whether the time-evolving behaviour of the system can be broken down into discrete states (Discrete) or not (Continuous). Within both of these partitions, a model can have fixed trajectories for a given parameter set and initial conditions (Deterministic) or contain a degree of uncertainty that makes it probabilistic in nature (Stochastic). Within both of these approaches, one can account for the spatial dimension if deemed appropriate. Examples of commonly employed computational frameworks for each classification are shown in blue. Note that the development of many frameworks has resulted in the transcending of the traditional classification boundaries. Examples include stochastic Boolean networks or dynamic Bayesian networks. An important consideration is how well the biological system can be approximated by a given modelling framework, regardless of its underlying fundamental nature. This is exemplified by the Gillespie algorithm, which can simulate continuous-deterministic ordinary differential equation (ODE) models as discrete-stochastic models given a previous adjustment of rate constants and a unit conversion to particle numbers. Another example would be the conversion of continuous models from deterministic to stochastic by the addition of a noise factor to the differential equations. For a more detailed description of these and other modelling frameworks, see [23,24]. Within the technical realm, modelling frameworks can be broadly classified into mathematical models, algorithmic models and hybrid models [25].