178

14

The Nature of Living Things

charides, and fats) into oligomers that can be imported into the cell. The funda-

mental process of carbohydrate catabolism is glycolysis, which yields an interme-

diate molecule called pyruvate (CSubscript 33HSubscript 44OSubscript 33). Glycolysis is a principal energy source

for prokaryotes and eukaryotes lacking mitochondria (e.g., erythrocytes). Within

mitochondria, pyruvate is further broken down into acetyl coenzyme A (acetylcoA),

which undergoes the final decomposition in the citric acid (or tricarboxylic or Krebs)

cycle, yielding two molecules of ATP (from ADP), one COSubscript 22, and one NADH (from

NADSuperscript plus⁺). Oxygen is then used to regenerate the NADSuperscript plus⁺ and a further molecule of ATP

from ADP, together with a proton that is pumped outside the mitochondrion. The

resulting proton electrochemical potential gradient across the mitochondrial mem-

brane (“protonmotive force”, p.m.f.) drives ATP synthase upon relaxation. This is

called oxidative phosphorylation (respiration). It uses an exogenous electron accep-

tor (oxygen) to generate significant quantities of stored chemical potential (“energy”;

more than 20 molecules of ATP per glucose molecule). Fermentation is an anaerobic

process for further oxidizing pyruvate using an endogenous electron acceptor such

as some other organic compound (lithotrophs use minerals), which yields much less

stored chemical potential per glucose molecule than oxidative phosphorylation, per-

haps only one-twentieth as much, depending on the final products. Photosynthetic

organisms use light to reduce water to oxygen and develop a p.m.f. that is similarly

used to drive ATP synthesis across the thylakoid membrane.

Autotrophs such as plants can use the smallest carbon building block, namely COSubscript 22,

for anabolism, whereas heterotrophs use monomers for building up their catalytic

and structural polymers.

Biological reactions, especially those in vivo within a cell, typically take place in

very confined volumes. This confinement may have a profound effect on the kinetic

mass action law (KMAL). Consider the reaction A + B right arrow Overscript k Subscript normal a Endscripts

ka→C, which Rényi (1953)

has analysed in detail. We have

MathID24^dc

dt ^{= ka[¯a ¯b + /\2(γt)] = kaab ,}

(14.1)

where lower case symbols denote concentrations, bars denote expected numbers, and

gamma Subscript tγt is the number of C molecules created up to timett. The termDelta squared left parenthesis gamma Subscript t Baseline right parenthesis/\²(γt) expresses the

fluctuations in gamma Subscript tγt: ModifyingAbove gamma Subscript t Superscript 2 Baseline With quotation dash equals ModifyingAbove gamma Subscript t Baseline With quotation dash squared plus Delta squared left parenthesis gamma Subscript t Baseline right parenthesisγ²

t ^{= γ}t ^{2 + /\2(γ}t^{). Supposing that gamma Subscript tγ}t ^{approximates to a Poisson}

distribution, then Delta squared left parenthesis gamma Subscript t Baseline right parenthesis/\²(γt) will be of the same order of magnitude as ModifyingAbove gamma Subscript t Baseline With quotation dashγt. The KMAL,

which puts a overbar equals a 0 minus c left parenthesis t right parenthesis¯a = a0 −c(t), and so on, the subscript 0 denoting initial concentration

(at t equals 0t = 0), is the first approximation in which Delta squared left parenthesis gamma Subscript t Baseline right parenthesis/\²(γt) is supposed negligibly small

compared to a overbar¯a and b overbar^¯b, implying that a overbar b overbar equals ModifyingAbove a b With quotation dash¯a ^¯b = ab, whereas, strictly speaking, it is not

since aa and bb are not independent: the disappearance of A at a certain spot (i.e.,

its transformation into C) implies the simultaneous disappearance of B. The neglect

of Delta squared left parenthesis gamma Subscript t Baseline right parenthesis/\²(γt) is justified for molar quantities of starting reagents, ¹¹ but not for reac-

tions in minute subcellular compartments. The number fluctuations (i.e., theDelta squared left parenthesis gamma Subscript t Baseline right parenthesis/\²(γt)

term) will constantly tend to be eliminated by diffusion. This generally dominates

11 Except near the end of the process, whena overbar¯a andb overbar¯b become very small.