Process Algebra Models in Biology: The Case of Phagocytosis

Introduction

Systems biology is a relatively recent term, which is often used to describe the general interdisciplinary effort in using techniques from biology, mathematics, physics and computing to provide insight into the workings of biological systems (Boogerd et al., 2007). Thus, the paradigm of systems biology covers a broad range of approaches, including those for obtaining massive amounts of information about whole biology systems. Another line of research in systems biology aims at building, with such a data, a science of principles of operation that is based on the interactions between components of biological systems. In this chapter, we discuss this latter consideration from the point of view of computer science (Cardelli, 2005; Fisher & Henzinger, 2007), in particular, of process algebras (Priami et al., 2001; Regev & Shapiro, 2002; Priami, 2009).

Biological systems are evolutionarily engineered, highly structured systems (Oltvai & Barabási, 2002). The underlying mechanisms enjoy an immense complexity, which is necessary for their functioning and survival, but difficult to reverse engineer. One of the reasons for this difficulty lies in obtaining ‘complete’ and ‘accurate’ data on these systems or their components for conceptualizing the acquired knowledge in (formal or informal) models. Another difficulty is that, in the presence of such data, the principles and analysis techniques imported from other disciplines are often not directly applicable to cover their complexity in an obvious way, and require an adjustment to the characteristics of the particular biological system being studied.

One of the main stream approaches for modeling and simulating the dynamics of biological systems is using differential equations, which can be traced back to the sixties (Noble, 1960) and earlier (Lotka, 1927; Volterra, 1926), and has its roots in Newton’s physics. Being equipped with well understood analysis techniques, differential equations provide the ‘deterministic’ approach (as opposed to the stochastic approach) for modeling and simulating biological systems. In comparison to stochastic simulations, simulations with differential equation models are advantageous in terms of computational cost. However, differential equation models are inherently difficult to change, extend and upgrade, when modification to the model structure is required. For example, as new data about the modeled system is acquired, local changes in the structure of a model need to be carried over to all the equations that describe the structure of the model. Moreover, differential equations have limitations in expressivity when, for example, complexations of unbounded number of (diverse) entities are being modeled. Because of these reasons, differential equation models are better suited for models with a smaller size and fewer number of species (Danos et al., 2007). In addition, within the last few years, a general consensus has emerged that noise and stochastic effects, which are not directly captured by ordinary differential equations, are essential attributes of biological systems, especially when molecule numbers of certain species are smaller (Blossey et al, 2008; Shahrezaei & Swain, 2008).