Table of Contents
Life and persistence
Function and Metabolism
The Thought Experiment
Life as a dynamic system
What is catalysis?
What are solitons?
Solitons in biology
Scale invariance in biology
Structure, energy, unity and resonance
Application of catalysis 1
Application of catalysis 2
Life as catalysis
Ontology of consciousness
Fractal catalysis and autopoiesis 1
Fractal catalysis and autopoiesis 2
Scale invariance in biology
The possibility of scale invariant processes in biology is supported by the work of Brown, Enquist and West (1997, 1999). They have investigated scaling laws in biological structures and processes. Below we see a continuous relationship between the log of the body mass and the log of the rate of metabolism from the scale of the enzyme to the elephant.
In addition to the metabolic rate/mass law illustrated above, they have found simple universal scaling laws that can be used to predict the structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, and insect tracheal tubes (West et al 1997). Below is a commonly cited example of a fractal in biology - the fern leaf:
In addition to the above examples more subtle instances of scale invariance in biology may be cited. Oscillating catalyzed reactions may give rise to characteristic travelling waves (generally agreed to be solitons) of different concentrations of reagents and products. Similar travelling waves may also be produced in bacterial cultures. Also, patterns of travelling waves have been found by analyzing the spatial/temporal dynamics of measles epidemics (Grenfell et al 2001), field vole populations (Lambin et al 1998) and even in the dynamics of herd grazing (Gueron and Liron 1989). These travelling waves, observed in a wide variety of differing biological contexts (Odell 1980), are indicative of non-linear dynamics and suggest that living processes may share similar physical properties at many different levels of scale.
More direct support of the scale invariant catalytic model may be found by comparing two ostensibly different biological processes - protein folding and muscle function. A solitonic mechanism has been proposed as the principle agent in the process of protein folding and conformational changes (Capri & Ben-Jacob, 1999). On the surface, this process does not appear to be catalytic in nature - there is no enzyme involved. However, it has already been argued that the principle agent of catalysis is not the enzyme per se, but a vibrational mode of the enzyme - the soliton.
Let us consider what happens in the case of a catalysed chemical reaction. Before the catalyst is added and the reaction has not yet occurred the solution is out of equilibrium. However, it is clear that the solution is stable. This may be described as a meta-stable state. The action of the catalyst is to effect a transition from a meta-stable state to the ground state via a chemical reaction. Likewise, in the case of an unfolded protein, in as far as the protein is stable it is described as being in a meta-stable state. Again, the action of the soliton is to effect a transition from a meta-stable state to the ground state via, in this case, a conformational change. What is suggested here is that the soliton may be described as catalytic in that it effects transitions to more favourable thermodynamic states. Whether this is achieved as a result of a chemical reaction or a conformational change is simply a matter of contingency.
Given that the soliton is the principle agent of catalysis let us re-examine the Davydov model of muscle function in the light of this.
No chemical reaction or conformational change in the body defies the laws of thermodynamics. From this it follows that whatever changes take place in the body they are always to thermodynamically favorable states. The fact that muscles can both relax and contract would seem to imply that this is not the case. However, we must remember that the most favorable state (or ground state) is dependent upon local thermodynamic conditions. Changes in the local chemical and structural environment of actin and myosin molecules within the cell may alter the local thermodynamics such that what was previously the ground state configuration may suddenly become a met-stable state (with no alteration of configuration) and thus be out of equilibrium. If the soliton is the principle agent of muscle function, then the action of the Davydov soliton, whether during relaxation or contraction, is to effect a transition from a meta-stable configuration of actin relative to myosin to the ground state configuration. It should be pointed out that the Davydov model of muscle function is not widely accepted. However, the broad thrust of this argument does not depend on the Davydov model alone. Increasingly, solitons are being implicated in a wide range of biological processes which in itself represents evidence of the importance of the soliton in biology and points to the possibility of a scale invariant catalytic theme.