Chapter 9 – Emerging Biophysics Techniques 401
for example, to simulate biochemical reactions efficiently. The algorithm is a form of Monte
Carlo simulation. For example, consider two biomolecules A and B that reversibly bind to
form AB, with forward and reverse rates for the process k1 and k−1. So, the total reaction rate
Rtot is given by
(9.2)
R
k
A B
k
AB
tot =
[ ][ ]+
[
]
−
1
1
Here, square brackets indicate concentration values. This simple system here could utilize the
Gillespie algorithm as follows:
1 Initialize the numbers of A and B in the system, the reaction constants, and random
number generator seed.
2 Calculate the time to the next reaction by advancing the current time t of the simu
lation to time t + Δt, where Δt is optimized to be small enough to ensure that the
forward and reverse reaction events in that time interval have a small probability
of occurring (e.g., ~0.3–0.5, similar to that used in molecular MC simulations, see
Chapter 8).
3 Calculate the forward and reverse reaction event deterministic probability values, p1
and p−1, respectively, as
(9.3)
p
k
R
p
k
R
tot
tot
1
1
1
1
=
[ ][ ]
=
[
]
−
−
A B
AB
4 Compare these probabilities against pseudorandom numbers generated in the range
0–1 to decide if the reaction event has occurred or not.
5 Update the system with new values of number of A and B, etc., and iterate back to
step 2.
This can clearly be generalized to far more complex reactions involving multiple different
biomolecule types, provided the rate constants are well defined. There are, as we will see
in the following text, several examples of rate constants that are functions of the reactant
and product molecule concentrations (this implies that there is feedback in the system) in a
nontrivial way. This adds to the computational complexity of the simulation, but these more
complex schemes can still be incorporated into a modified Gillespie algorithm. What is not
embodied in this approach however is any spatial information, since the assumption is clearly
one of a reaction-limited regime (see Chapter 8).
9.3 SYNTHETIC BIOLOGY, BIOMIMICRY, AND BIONANOTECHNOLOGY
Richard Feynman, one of the forefathers of the theory of quantum electrodynamics in the
oretical physics, a genius, and a notorious bongo-drum enthusiast, is also viewed by many
as the prophet who heralded a future era of synthetic biology and bionanotechnology. For
example, he stated something that one might consider to be the entry point into the general
engineering of materials, in one sentence that he thought in the English language conveyed
the most information in the fewest words:
All things are made of atoms.
—Feynman (1963)
KEY BIOLOGICAL
APPLICATIONS:
SYSTEMS BIOPHYSICS
TECHNIQUES
Analysis of complex biological
systems in vivo.