11 - Stability, complexity and non-linear systems

Summary

One of the hallmarks of physiological systems is homeostasis. Homeostatic systems maintain a steady-state set point over time using negative feedback. Negative feedback activates recovery processes when there is deviation from the set point. While some states are always tightly maintained, some changes can occur during the lifetime of the individual. These changes take two forms: adjustment of the homeostatic set point, or a step change to a new set point by a positive feedback mechanism. Positive feedback systems do not use a recovery process to return to the original set point. New negative feedback processes now keep the organism at the new set point. A set point must have an energy minimum, such that small variations from the minimum create a driving force returning the system to the set point. Energy minima occur at multiple levels, from atoms to organisms. For systems in transition the energy profile may exhibit metastable states between two large minima. Metastable states offer temporal buffering of state changes. In enzymes and ion channels the energy barriers between the external states and internal metastable states and the depth of the metastable state control the rate of the metabolic reaction or ionic current. Complex analytical methods such as catastrophe theory provide insight into state transitions. Catastrophe theory models changes in space, not time, with state transitions occurring whenever the state variable reaches particular values in parameter space. The feedback systems that maintain homeostasis are deterministic far from equilibrium, but become chaotic when transitions are near equilibrium. Not all catastrophic transitions are fatal, but for living systems catastrophes can lead to death in two ways, homeostatic instability or global thermal equilibrium. These two modes of death correspond to having too much ambient energy or too little ambient energy. This leads to the Goldilocks problem, in which ambient energy will be too high, too low or just right. Since life must be a continuum, a system cannot leave the viable energy range without extinction, leading to restrictions in modeling evolution. All living systems will have feedback systems, both negative and positive, that keep them away from either of the life–death transitions. Fractal systems regularly transition between deterministic and chaotic states. Conditions with multiple fractal inputs can have significant variability around a set point using allometric regulation. Narrowing of the fractal distribution has been associated with pathological states and increased risk of death.