Bioinformatics An Introduction 4th Edition (Jeremy Ramsden)

322

Regulatory Networks

“Hydrophobic effects” or “forces” are also a manifestation of hydrogen bonding

in the presence of water, which can effectively compete for intermolecular H-bonds.

The wrapping of dehydrons by appropriate apolar residues is a key contributor to

protein–protein afﬁnity.

It may be useful to think of the interactions between macromolecules in a cell

as analogous to those between people at a party. It is clear that everyone is subject

to hard-body exclusion. Likewise, one may feel a weak (nonspeciﬁc) attraction for

everyone—misanthropes would presumably not have bothered to come. This is sufﬁ-

cient to allow one to ﬂeetingly spend time exchanging a few words with a good many

people, among whom there will be a few with strong mutual interest and a longer

conversation will ensue. Once such mutual attraction is apparent, the conversation

may deepen further, and so on. This is very like the temporal awareness shown by

interacting macromolecules capable of existing in multiple states.

Time-Dependent Rate “Constants”

Even a two-state molecule can display temporal awareness. Consider the reaction

between a receptor R that can exist in either of two states and a ligand L:

StartLayout 1st Row upper R Subscript 1 Baseline plus upper L underset k Subscript normal d 1 Baseline of right harpoon over left harpoon Overscript k Subscript normal a Baseline Endscripts upper R Subscript 1 Baseline upper L comma 2nd Row Blank 3rd Row upper R Subscript 1 Baseline upper L underset k Subscript normal d 2 Baseline of right harpoon over left harpoon Overscript k Subscript normal s Baseline Endscripts upper R Subscript 2 Baseline upper L semicolon EndLayoutR1 + L

ka⇌

kd1

R1L ,

(23.9)

R1L

ks⇌

kd2

R2L ;

(23.10)

the interpretation of this would be that after initial binding, the receptor changes its

conformation into that of state 2, in which the ligand is much more tightly bound. The

probability of R and L remaining together can be described by a memory function,

in which the amount nu left parenthesis t right parenthesisν(t) of associated protein is represented by the integral

nu left parenthesis t right parenthesis equals k Subscript normal a Baseline integral Subscript 0 Superscript t Baseline phi left parenthesis t 1 right parenthesis upper Q left parenthesis t comma t 1 right parenthesis d t 1 commaν(t) = ka

{ t

φ(t1)Q(t, t1) dt1 ,

(23.11)

where phiφ is the fraction of unoccupied binding sites. The memory kernel upper QQ denotes

the fraction of A bound at epoch t 1t1 that remains adsorbed at epoch tt. Often, upper QQ

simply depends on the difference t minus t 1t −t1. If dissociation is a simple ﬁrst-order (Pois-

son) process, as is the case if the associated partners each only have a single state,

then upper Q left parenthesis t right parenthesis equals exp left parenthesis minus k Subscript normal d Baseline t right parenthesisQ(t) = exp(−kdt) and there is no memory, but in general the dissociation rate

coefﬁcient is time-dependent and can be obtained from the quotient

k Subscript normal d Baseline left parenthesis t right parenthesis equals StartFraction integral Subscript 0 Superscript t Baseline phi left parenthesis t 1 right parenthesis upper Q prime left parenthesis t comma t 1 right parenthesis d t 1 Over integral Subscript 0 Superscript t Baseline phi left parenthesis t 1 right parenthesis upper Q left parenthesis t comma t 1 right parenthesis d t 1 EndFraction commakd(t) =

{ t

0 ^φ⁽^t¹⁾^Q^,⁽^t^,^t¹⁾^d^t¹

{ t

0 ^φ⁽^t¹⁾^Q⁽^t^,^t¹⁾^d^t¹

(23.12)

whereupper Q primeQ^,is the derivative of the memory function with respect to time. A necessary

condition for the system to reach equilibrium is