SME
Genetics · Problem type
PCR copies with an efficiency
Use this for “How many copies do 100 templates make after 30 cycles at 90% efficiency?”
Diagram
N
=
N₀
×
(1
+
E)ⁿ
=
100
×
1.9
30
N
=
2.30 ×
10
10
Each cycle copies a share E = 0.9 of the strands; at E = 1 every one, N₀ × 2ⁿ.
This is an example. Type your own values to start a new problem.
N
=
N₀
(1
+
)
Nₘₐₓ
Copies if each cycle doubles
worked out (not typed)
Formulas
N
=
N₀
×
(1 +
E
)
n
2.30 ×
10
10
=
100
×
(1 + 0.9)
30
Nₘₐₓ
=
N₀
×
2
n
1.07 ×
10
11
=
100
×
2
30
Assumptions
•
Each cycle copies a share E of the strands present, so the copies grow by 1 + E a cycle.
•
E = 1 is perfect doubling; a well-designed run copies about 90% to 100% of the strands.
•
E stays the same every cycle, until primers and nucleotides run low and the run levels off.
Step-by-step
WE KNOW
N₀ = 100, n = 30, E = 0.9
FIND
expected copies after n cycles (N), copies if each cycle doubles (Nₘₐₓ)
Step 1 · Find expected copies after n cycles (N)
Use N = N₀ × (1 + E)ⁿ
Each
cycle
multiplies
the
copies
by
1
+
E
,
n
times
over.
N
=
100
×
(1 + 0.9)
30
N
=
100
×
1.9
30
N
=
100
×
(2.3047
×
10
8
)
N
=
2.30 ×
10
10
Step 2 · Find copies if each cycle doubles (Nₘₐₓ)
Use Nₘₐₓ = N₀ × 2ⁿ
At
E
=
1
every
strand
is
copied,
so
the
copies
double
each
cycle.
Nₘₐₓ
=
100
×
2
30
Nₘₐₓ = 100 × 1,073,741,824
Nₘₐₓ
=
1.07 ×
10
11
Check
Put the numbers back in. Both sides should match.
2.30 ×
10
10
=
100
×
(1 + 0.9)
30
✓
1.07 ×
10
11
=
100
×
2
30
✓
Topic check
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