Page 124 - Nanotechnology an introduction

backbone (linked via the “peptide” bond) with variable side chains—short aliphatic groups, small aromatic groups, carboxylate, amine, hydroxyl,
etc. functionalities. Template-directed synthesis with a very high yield is used in nature, with the templates being closely related to genes via the
genetic code (triplets of nucleotide bases encode each amino acid). After synthesis (polymerization), they fold, often spontaneously, to a compact
structure according to a least-action principle (see Section 8.2.11). Typical natural proteins have 50~500 amino acids. Depending on their
sequence, they adopt a definite remembered conformation (proteins acting as devices, rather than having a passive structural role, have two or
more stable conformations) and can carry out varied functions, ranging from essentially structural or scavenging to enzymes and motors. Some
proteins (called glycoproteins) are branched with oligosaccharides attached to certain residues.
Nucleic Acids (NA)
These are polymerized from nucleotides (the monomers) each constituted from a sugar, a phosphate group, and a “base” derived from a purine or
pyrimidine (aromatic heterocycle). The sugar and phosphate are polymerized by eliminating water to form a linear backbone, with the bases
playing the role of the residues in PP. There are 4 natural bases, abbreviated A, C, G, T (in deoxyribonucleic acid, DNA) and A, C, G, U (in
ribonucleic acid, RNA). The bases pair preferentially: A with T (or U), via 2 hydrogen bonds, and C with G via 3 hydrogen bonds (complementary
base pairing, CBP). Template-directed synthesis with a very high yield is used in nature to create the polymers. The templates are the genes
(DNA), and operate according to the principle of CBP. During polymerization RNA spontaneously folds to a definite compact structure according to
a least-action principle (see Section 8.2.11), in which base-pairing via hydrogen bonding is equivalent to the potential energy, and loop and hairpin
formation is equivalent to the kinetic energy. DNA forms the famous double helix in which genetic information is stably stored in living cells and
many viruses.

Polysaccharides (PS) and Oligosaccharides (OS)
These are linear or branched polymers of diverse sugar (cyclic oligoalcohol) monomers, linked via water elimination (“condensation”) at any of the
several hydroxyl groups. The problem of predicting their structure is not yet solved. Polymerization is not templated (i.e., not under direct genetic
control) and there is variability (to a degree that is only poorly characterized) in sequence and length of the polysaccharides found fulfilling the same
function in comparable organisms.
11.2. Some General Characteristics of Biological Molecules
The energy contained in a given system can be divided into two categories: (i) the multitude of microscopic or thermal motions sufficiently
characterized by the temperature; and (ii) the (usually small number of) macroscopic, highly correlated motions, whose existence turns the
construction into a machine (a device). The total energy contained in the microscopic degrees of freedom may be far larger than those in the
macroscopic ones, but nevertheless the microscopic energy can usually be successfully neglected in the analysis of a construction (in informational
terms, the macrostates are remembered but the microstates are not).
Biological molecules are constructions. Hence a statistical approach, in which the motions of an immense number of individual particles are
subsumed into a few macroscopic parameters such as temperature and pressure, is inadequate. A construction uses only an insignificant fraction
of the Gibbs canonical ensemble and hence is essentially out of equilibrium. This is different from thermodynamic nonequilibrium—it arises
because the system is being investigated at timescales much shorter than those required for true statistical equilbrium. Such systems exhibit
“broken ergodicity”, as epitomized by a cup of coffee in a closed room to which cream is added and then stirred. The cream and coffee equilibrate
within a few seconds (during which vast amounts of microinformation are generated within the whorled patterns); the cup attains room temperature
within tens of minutes; and days may be required for the water in the cup to saturate the air in the room.
Broken ergodicity may be regarded as a generalization of broken symmetry, which leads to a new thermodynamic quantity, the order parameter ξ
whose value is zero in the symmetrical phase. ξ may be thought of as conferring a kind of generalized rigidity on a system, allowing an external
force applied at one point to be transferred to another. Some protein molecules demonstrate this very clearly: flash photolysis of oxygenated
hemoglobin (causing the oxygen molecule to dissociate from the iron core of the porphyrin (the heme) to which it is bound) causes motion of the
iron core of the heme, which results in (much larger) movement at the distant intersubunit contacts, leading ultimately to an overall change in the
protein conformation involving hundreds of atoms.
11.3. The Mechanism of Biological Machines
Active proteins (i.e., all proteins apart from those fulfilling a purely passive structural or space-filling role) have two or more stable conformations.
Unfortunately there is very little information about these multiple conformations available. Useful as X-ray diffraction is for determining the structure
of proteins, it has the disadvantage of usually fixing the protein in just one of these conformations in the crystal that is used to diffract the X-rays. If a
fraction of the proteins does happen to be present in one of the other stable conformations, this is usually regarded as “disorder” and any
information about it is lost during structural refinement of the diffraction data. However, these multiple conformations are the key to the general
mechanism of biological machines, originally formulated by L.A. Blumenfeld to explain enzymatic catalysis [23].
The prototypical example is an enzyme E catalyzing (say) the decomposition of a molecule A−B (called the substrate of the enzyme in the
biochemical literature) into products A + B. In this case, work has to be done to break the chemical bond A−B; the principle can equally well be
applied to any action where work is done, such as pulling on a spring (as in muscle). The binding and release of oxygen to and from hemoglobin
also works on this principle.
The enzyme consists of an active site and the rest of the protein, which may be considered to be much bigger than the active site (Figure 11.1). The
“rest” has two stable conformations, E and Ẽ. The mechanism proceeds in four stages:

1. A complex is formed between the substrate and the enzyme, A−B + E → (A−B)E*. A−B binds to the active site, releasing free energy and
resulting in a local conformational change, which creates a strain between the active site and the rest of the protein. Local fast vibrational
relaxation takes place on the picosecond timescale, but the active site is no longer in equilibrium with the rest of the molecule and the resulting
strain modifies the energy surface on which the enzymatic reaction takes place. The asterisk denotes that the protein is overall in a strained,
nonequilibrium state. Strain creation requires energy, but its magnitude must of course be less than the energy of binding.
2. The complex slowly relaxes to a new conformation Ẽ, releasing the energy to drive the energy-requiring breaking of the A−B bond: (A−B)E* →
AẼB. This is the elementary act of the enzymatic reaction. This conformational relaxation involves making and breaking a multiplicity of weak