Biomedical Engineering Reference
In-Depth Information
Figure 2.1a-1 The exponential amplification of the gene in PCR. From Vierstraete (1999).
there are two single strands of DNA, called T1 and T2, for
template 1 and template 2, respectively. Once the tem-
perature is cooled to 54
C (signifying the starting of the
annealing stage), we expect that primer 1 (P1) will anneal
with T1 to form a hybrid (H1) and we also expect that P2
and T2 will anneal to form a hybrid (H2). These two re-
actions can be represented by the chemical equations:
Hence, four reactions can occur simultaneously during
the primer annealing stage. These reactions can be
modeled using either thermodynamic (steady state) or
kinetic (transient) equations.
The steady-state thermodynamic model tracks the
total concentration of all products performing active
roles during the annealing stage of PCR, a mass balance is
performed on reactions (2.1a.1) to (2.1a.4). This pro-
cedure results in the following four equations:
P1
þ
T14H1
(2.1a.1)
P2
þ
T24H2
(2.1a.2)
½
P1
T
¼½
P1
þ½
H1
þ½
D
½
P2
T
¼½
P2
þ½
H2
þ½
D
½
T1
T
¼½
T1
þ½
H1
þ½
HT
½
T2
T
¼½
T2
þ½
H2
þ½
HT
Unfortunately, other reactions can occur during the
annealing stage of PCR. The template strands, T1 and
T2, are complementary and can re-anneal upon contact,
forming a template hybrid (HT) as represented by the
following reaction:
(2.1a.5)
where [X]
T
is a parameter denoting the total concen-
tration of product X.
To complete the thermodynamic model, we need to
introduce four more parameters into the system
T1
þ
T24HT
(2.1a.3)
the
equilibrium constants of each reaction. We define K
H1
,
K
H2
,K
HT
, and K
D
to be the equilibrium constants of
(2.1a.1) to (2.1a.4), respectively. Since the equilibrium
d
Finally, depending on primer design, primer-dimers (D)
can form as well:
P1
þ
P24D
(2.1a.4)