23.6 Intermolecular Interactions

323

underset t right arrow normal infinity of limit upper Q left parenthesis t right parenthesis equals 0 period lim

t→∞^{Q(t) = 0 .}

(23.13)

Problem. Derive the memory function for the system described by the reactions

(23.9). Hint: Use Laplace transforms.

Specificity

From the above considerations it follows that specificity of interaction is mainly

influenced by geometry (due to hard-body exclusion), the pattern of complementary

arrangements of HB-donors and HB-acceptors (for which an excellent example is the

base-pairing in DNA and RNA (Figs. 15.3 and 15.5) and the pattern of complementary

arrangements of dehydrons and apolar residues on the two associating partners). ²⁷

Thus, specificity of interaction (synonymous with “molecular recognition”) is a

kind of pattern recognition (cf. Sect. 13.1), germane to sequence matching. Clearly,

the more features that are included in the matching problem, the more discriminating

the interaction will be.

Nonspecific Interactions

Most biological interactions show no discontinuity of affinity with some parameter

characterizing the identity of one of the binding partners, or their joint identity,

although the relation may be nonlinear. Hence in most cases the difference between

specific and nonspecific interactions is quantitative, not qualitative. Even nucleotides

can pair with the wrong bases, albeit with much smaller affinity. ²⁸ In many cases,

such as the association of transcription factors with promoter sites, weak nonspecific

binding to any DNA sequence allows early association of the protein with the nucleic

acid, whereupon the search for the promoter sequence becomes a random walk in one

dimension rather than three, which enormously accelerates the finding process. ²⁹ It

should be emphasized that nonspecific binding is an essential precursor to specific

binding. The scheme (23.9) applies, in which case the difference in states 1 and 2

might merely be one of orientation.

Coöperative Binding

Consider again reaction (23.6) with A representing a ligand binding to an unoccupied

site on a receptor (B). Suppose that the ligand-receptor complex C has changed prop-

erties that allow it to undergo further, previously inaccessible reactions (e.g., binding

to a DNA promoter sequence). The rôle of A is to switch B from one of its stable

conformational states to another. The approximate equality of the intramolecular,

molecule–solvent and A–B binding energies is an essential feature of such biologi-

cal switching reactions. An equilibrium binding constantupper K 0K0 is defined according to

the law of mass action (23.7). If there are nn independent binding sites per receptor,

conservation of mass dictates that b equals n b 0 minus cb = nb0 −c, where b 0b0 is the total concentration

27 See Ramsden (2000).

28 See, e.g., Kornyshev and Leikin (2001).

29 E.g. Ramsden and Dreier (1996); see Ramsden and Grätzel (1986) for a nonbiological example

of the effect of dimensional reduction from 3 to 2.