ECE 416 Homework 1
Due: Friday, January 25.
“Sensitivity and Specificity”
I.
Sensitivity
A sensor is being tested for detection of the protein “Tumor
Necrosis Factor α“ (TNFα) in blood. TNFα is a biomarker protein
that can be used to identify the presence of cancerous tumors in
the body.
a. Sensor Preparation
The sensor is prepared by attaching a capture antibody molecule
that attaches to TNFα, called “Anti- TNFα”, to a biosensor
surface. When a TNFα molecule is captured onto the sensor, it
generates changes in the measured electrical resistance of the
device (in units of Ohms (Ω) – don’t worry too much about the
exact detection mechanism for now…)
b. Measuring sensitivity to TNFα
We start by preparing test samples with various concentrations of
TNFα in pure buffered saline solution (to simulate blood), but with
no other interfering molecules present. With the following data:
[TNFα] (ng/mL)
Sensor Reading
(Ω)
.0001
5
.001
4.96
.01
4.8
.1
3.3
1.0
1.6
10
1.06
100
1.05
1000
1
1
Q1: Plot the values of the above dataset. (𝑙𝑜𝑔10 (TNFα) vs )
𝛺
Q2: What is the Sensitivity in each concentration range…?:

.0001 < [TNFα] < .01 (ng/mL)

.1 < [TNFα] < 10 (ng/mL)
 100 ng/mL < [TNFα]
Here, Sensitivity is defined as the ratio of change in sensor output
to change in input concentration, or (|
𝛥𝛺
𝛥𝑙𝑜𝑔10 𝑇𝑁𝐹𝛼 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
|).
The next test of the sensor is to prepare some whole blood samples
(now adding red and white blood cells to our previous solutions). If
we process these new samples the data results as follows:
[TNFα] (ng/mL)
.0001
.001
.01
0.1
1.0
10
100
1000
Sensor Reading
(Ω)
0.7
0.69
0.69
0.68
0.65
0.62
0.61
0.6
Q3: Plot the above data with data from Q1 so it appears on the same
axis, and calculate sensitivity from the same 3 concentration ranges.
Q4: Why does the data look different now? Explain.
 One hypothesis is that the blood cells are ‘fouling’ the sensor by
attaching to the surface, giving a false reading. To test this, we
can put the solutions in a centrifuge to remove the blood cells,
leaving us with a serum solution to perform the next round of
tests. Performing tests on the serum results in the following
measurements:
[TNFα] (ng/mL)
.0001
.001
.01
0.1
1.0
10
100
1000
Sensor Reading
(Ω)
3
2.9
2.86
2.2
1.3
0.9
0.86
0.85
Q5: Plot this data with data from Q1 and Q3 so it appears on the same
axis, and calculate sensitivity from the same 3 concentration ranges.
II.
Selectivity
The Serum we have been using is comprised of ~60% albumin by
weight. Albumin has a molecular weight of 66,500 Da. 1 Dalton (Da)
is equal to 1 g/mol.
Q6: Calculate the concentration of the albumin in serum in units of
ng/mL. Hint: estimate that 1 mL of serum weighs 1 gram.
Q7: Estimate the change in biosensor signal (1/Ω) that can be
attributed to the presence of albumin.
Hint: Assume that 60% of the “non-specific” biosensor signal at
[TNFα] = 1 ng/mL comes from albumin attachment to the antiTNFα antibody.
Q8: Estimate the selectivity of the anti-TNFα antibody for recognizing
the target TNFα while not recognizing other proteins in the serum
(such as albumin).
Selectivity is defined as:
[𝑻𝑵𝑭𝜶]
[𝒂𝒍𝒃𝒖𝒎𝒊𝒏]
= (
𝑻𝑵𝑭𝜶 𝒔𝒊𝒈𝒏𝒂𝒍
)𝒙
𝒂𝒍𝒃𝒖𝒎𝒊𝒏 𝒔𝒊𝒈𝒏𝒂𝒍
𝟏
𝒔𝒆𝒍𝒆𝒄𝒕𝒊𝒗𝒊𝒕𝒚