## System Robustness in Biological Systems (pt.1)

ystem robustness as well as systems stability are two important properties that control engineers often consider in the analysis of dynamical systems. Although these are concepts that have long been considered only part of the engineering domain, it seems that systems biology is moving toward the investigation of such properties even in biological systems.

Today I would like to bring you some considerations about two papers that I found really interesting in this field. They are:

H. Kitano, Biological Robustness. Nat Genetics. 2004

H. Kitano, Towars a Theory of Biological Robustness. Molecular Systems Biology 3:137. 2007.

In order to define the “Robustness” of a System I will borrow Kitano’s statement:

“Robustness is a property that allows a system to maintain its functions despite external and internal perturbations. It is one of the fundamental and ubiquitously observed systems-level phenomena that cannot be understood by looking at the individual components.A system must be robust to function in unpredictable environments using unreliable components.”

It is evident that robustness, as described herein, should be considered a fundamental part of any higher level biological system. In particular Kitano proposes a very interesting perspective: according to his idea, in fact, robustness is among the the directions that evolution tends to push organisms towards. From this perspective robustness and evolution should be considered highly tied together. Moreover robustness intended as the ability of a systems to face external or internal perturbations (or attacks) should be considered a key factor in the description of the way cancer finds its way in attacking our body; in fact robust mechanisms (like DNA reparing ones) allow our body to react to e.g. potentially deleterious point mutation in our genetic code or other exogenous events.

Our body could be thought of as a highly complex (nonlinear and, maybe, chaotic) system, but nonetheless a system, which is able to work in particular working condition in a stable way. In control theory we say that a linear system is stable if even only one of its state (working point) is stable, this is true nomore for nonlinear systems in which the stability property of each of the point of the state space should be verified using mathematical methods. Moreover nonlinear systems, are often characterized by several equilibrium points (or sets of points) (on the contrary we can observe that a linear system has zero or infinite equilibrium points) with very different characteristics. This aspect of nonlinear system allows them to show different “behaviors” according to the state they are in. The same “system” (the stability quality in nonlinear system is better referred to the single state) can be stable (given a an initial working point and a pertubartion it tends to return to the original working point after some time) or unstable (if we consider a different starting point). The behavior of a non linear system described by the equations:

$x'_{1}=2x - y + 3(x^{2}-y^{2}) + 2xy$
$x'_{2}=x - 3y - 3(x^{2}-y^{2}) + 3xy$

is presented below:

In this figure we can observe one of the most characteristic behaviors of nonlinear systems: a cyclic orbit (the orbit in thick blue line). From a biological point of view this means that our system, when perturbed after a long stay in an equilibrium point, can:

1. Go out of the previous equilibrium point looking for another point with the same characteristics but different from this one;
2. Go out of the previous equilibrium point e tend to return in it asymptotically;
3. Go out of the preovius equilibrium point and tend to cycle among the set of point described by an orbit.

These are the main characteristics of equilibrium points in nonlinear systems.

This is all for now! The next time we will face system control, alternative mechanisms, modularity and
decoupling principles in biological systems.

Annunci
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