SME
Microbiology · Problem type
Antibody titer from a two-fold dilution row
Use this for “Two-fold dilutions from 1:10 are positive through tube 6. What is the titer?”
Diagram
Each tube is a 1:2 dilution of the one before.
Positive through tube 6: titer = 10 × 2⁵ = 320 (1:320).
This is an example. Type your own values to start a new problem.
T
=
D₁
×
2
−
1
Formulas
T
=
D₁
×
2
k
− 1
320
=
10
×
2
6 − 1
Assumptions
•
Each tube holds half the serum of the one before: 1:10, 1:20, 1:40 and so on.
•
Tubes 1 to k still react (they clump); every tube after them is negative.
•
The titer is the reciprocal of the last positive dilution: 1:320 is a titer of 320.
Step-by-step
WE KNOW
D₁ = 10, k = 6
FIND
titer (T)
Step 1 · Find titer (T)
Use T = D₁ × 2ᵏ⁻¹
Each
tube
after
the
first
doubles
the
dilution:
k
−
1
doublings.
T
=
10
×
2
6 − 1
T
=
10
×
2
5
T
=
10
×
32
T
=
320
Check
Put the numbers back in. Both sides should match.
320
=
10
×
2
6 − 1
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
Immunology and pathogens
Main lesson
Primary and secondary antibody responses
Use this for “The first peak is 100 units on day 12 and the booster’s is 1,500 on day 6. How many times higher, and how many days sooner?”
The adaptive immune response in order
Use this for “Which cells act, and in what order, from antigen presentation to memory?”