Biological dissipative structures

In biological dissipative structures, self-oiganization may be related to the attractors in the phase space, which correspond to ordered motions of the involved biological elements (De la Fuenta, 1999). When the system is far from equilibrium, ordering in time or spontaneous rhythmic behavior may occur. The Lotka-Volterra model of the predator-prey interactions is a simple example of the rhythmic behavior. The interactions are described by the following kinetics... 

This complex process of dissipative structure-assisted self-assembly plays an important role for pattern formation in biological systems and many other artificial systems. So far as the authors know, this concept was firstly proposed by Lefever in 2000 (12), We may extend his idea to think of an alternative concept a self-assembly-assisted dissipative structure. It is obvious that most biological dissipative structures such as traveling waves along giant axons and... 

Goldbeter, A. (2007) Biological rhythms as temporal dissipative structures. Adv. Chem. Phys., 135, 253-295. 

TNC.25.1. Prigogine, Dissipative structures in biological systems, iaDe la physique theorique a la biologie, M. Marois, ed., Ed. CNRS, Paris, 1971. 

TNC.39. I. Prigogine and R. Lefever, Stability and thermodynamic properties of dissipative structures in biological systems, in Proceedings, 1st Aharon Katzir-Katchalsky Conference, I. R. Miller, ed., Wiley, New York, 1975, pp. 26-57. 

Since the onset of studies on dissipative structures at the end of the 1960s [12, 14, 15,18,189], the field devoted to the investigation of nonequihbrium structures in chemistry, physics, and the fife sciences has grown tremendously. In this chapter I focused on temporal dissipative structures in biology, a field where they... 

Remark. A great deal of attention has been paid in recent years to non-equilibrium stationary processes that are unstable and also extended in space. They can give rise to different phases that exist side by side, so that translation symmetry is broken. The name dissipative structures has been coined for them, and the prime examples are the Benard cells and the Zhabotinski reactions, but they also occur in biology and meteorology. However, these are features of the macroscopic equations. They are only relevant for fluctuation theory inasmuch as the fluctuation becomes very large at the point where the instability sets in. The critical fluctuations in XIII.5 are an example. There are many more varieties, in particular in the case of more variables. 

This different behavior of the two converters has two consequences which are of an immediate biological interest. As depicted in Fig. 13 the nonlinear energy converter can only maintain very small output forces ( 1 kcal/mole) at optimal efficiency at the physiological values of the input force. These small output forces, which are near equilibrium, could hardly ever be sufficient for the onset and maintenance of dissipative structures in the living cell.3 In contrast, the linear energy converter can easily maintain high output forces at optimal efficiency. 

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