What is Life?:How chemistry becomes biology by Addy Pross Page B

likely to fall into a disorganized pile rather than to stack up in an ordered manner. The tendency to disorder is inherent in the Second Law—ordered systems tend toward disorder, and this can be explained in statistical terms. Chemical systems respond to the drive toward disorder in exactly the same way and for exactly the same reasons as do tidy desks. Regardless of energy considerations, a chemical reaction that combines two species into one is
unfavourable
from an entropic point of view since that
increases
the order of the system (i.e. decreases its entropy), while a reaction that breaks up a single molecule into several fragments is
favoured
entropically as it
decreases
the order (increases the entropy) of the system. Accordingly, the free energy of a system incorporates within it an entropic contribution.
Replication and molecular replicators
     
    Catalysts are frequently involved in chemical reactions. In fact, one could confidently say that almost any chemical reaction can becatalysed by some appropriate material. Within biological systems catalysts play a crucial role and are called enzymes. Without the appropriate enzyme(s) most biological reactions would either proceed very slowly, or not at all. Normally the product of a reaction and the catalyst for that reaction are different materials. In the above example of hydrogen and oxygen reacting to give water, the product is water and the catalyst would be some metal or metallic compound. But consider a reaction in which the product and the catalyst are one and the same, i.e., the product acts as a catalyst in its own formation. Such a reaction is termed
autocatalytic
for obvious reasons—the catalyst catalyses its
own
formation, rather than the formation of some other material. At first glance catalysis and autocatalysis may not seem too different. But a simple calculation of the rates at which the two reactions proceed reveals how spectacularly wrong that initial impression is. If one starts each of the two reactions, catalysis and autocatalysis, with just one
single
molecule of catalyst (or autocatalyst), a simple calculation reveals that the time required to make a small amount of material (say 100 grams) by each pathway is dramatically different. For the catalytic reaction the calculated time frame comes out in
billions of years.
For the autocatalytic reaction the corresponding calculated time frame works out at a tiny
fraction of a second!
A comparison of two seemingly similar processes doesn’t get more different than that. (It should be stated that the difference between the two numbers was spectacularly large because we started off in each case with just one molecule of reactant, but even with larger quantities of starting material the effect remains dramatic.) Let me jump way ahead for a moment and state that the essence of life will be found to lie in the dramatic difference between the rates of catalytic and autocatalyticreactions. But we have quite a way to go in this discussion before the basis for that statement becomes clear.
    How can that dramatic difference in reaction rate between catalysis and autocatalysis be explained? Simply put—the power of exponentials. The difference comes about because in the autocatalytic reaction, the rate of product formation proceeds
exponentially,
whereas in the catalytic reaction the rate of production proceeds
linearly,
and that difference could not be more profound. If that sounds too mathematical, let’s explain the difference by recounting the classical legend of the Chinese emperor who was saved in battle by a peasant farmer. When the emperor asked the farmer how he could reward him, the farmer took out a standard chess board and asked that he be rewarded with a quantity of rice, and that the required quantity be established by a simple formula—placing a single grain of rice on the first square, two grains on the second square, four on the third, and so on, right through to the 64th square. The request