#102
SPR Sensitivity and Detection Limit
When selecting a Surface Plasmon Resonance (SPR) instrument, an obvious question to ask
is: What is the sensitivity of the instrument? This seemingly simple question does not have astraightforward answer. The confusion is partially due to the fact there is simply no perfect way
to define the sensitivity, and partially due to the the inaccurate use of this term by someVendors. This technical note describes some of the most commonly used terms for defining
SPR sensitivity. The goal is to provide SPR users a guideline to determine if a particulardefinition is useful for his/her application, and to compare different instruments in a meaningfulway.
Angular Sensitivity: The most popular SPR detection scheme uses the so-called Kretchmannconfiguration and measures the angle of incident light at which the surface plasmon resonancetakes place (see Figure). The shift of the resonance angle provides a sensitive measurementof a molecular binding event onto the sensor surface or a change in the index refraction of thefluid medium near the sensor surface. For this reason, the minimum detectable angular shift,in unit of degree, may be used to describe the sensitivity. However, an SPR instrument withthe best angular sensitivity does not always mean that it has the best sensitivity in terms ofdetecting molecular binding, as referred to as surface sensitivity.

Figure. Left: A typical SPR setup. An incident light is directed onto a SPR sensor chip via a prism, and thereflected beam is detected via a photodetector or imager. At an appropriate angle (resonance angle), the incident
light excites the surface plasmons in the sensor chip (metal film) and the intensity of the reflected light drops to aminimum. The electromagnetic field created by the SPR penetrates into the fluidic medium and probes molecularbinding processes taking place on the surface and index of refraction changes in the fluidic medium. Right:
Reflectivity vs. incident angle plot shows a sharp drop in the reflection intensity due to SPR, also referred to as
the SPR “dip”. The angular position of the dip is often measured and used to define SPR sensitivity.

Dependence upon Prism Material:
It is worth noting that the resonance angle depends not only on molecular binding and theindex of refraction of the fluid medium, but also on the index of refraction of the prism, thedielectric constant of the metal film as well as on the wavelength of light used to excite thesurface plasmons. So when comparing the sensitivities of different instruments in terms ofdegree angles, one should be aware of the prism material, the metal film as well as thewavelength of light.
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Example 1: If the prism is made of BK7 (n=1.515) glass and the wavelength of incident
light is 635 nm, then the angular shift due to a protein binding layer (n= 1.5) of 3 nm ona gold sensor chip is 0.75 deg. If keeping everything the same, except replacing theBK7 glass prism with a SF10 glass (n=1.723) prism, then the same protein binding layer
leads to an angular shift of 0.35 deg (a weaker response). So if two instruments report
the same angular shift, the one using BK7 prism is actually more sensitive in terms ofmeasuring molecular binding.
Dependence upon Wavelength:
The penetration length of the evanesce field created by SPR into the fluid medium increases
with the wavelength. Longer wavelengths (e.g., near infrared) have the “seeming” advantage
of being able to probe further beyond the sensor surface, however this results in a significant
loss of surface sensitivity.
Example 2: Two SPR instruments both use BK7 glass prisms, gold sensor chips, andhave similar angular sensitivity, but one uses 635 nm light and the other uses 890 nm
light. For a protein binding layer of 3 nm, the first instrument produces 0.75 deg angularshift, but the second instrument leads to only 0.2 deg angular shift (a much weakerresponse). So for two instruments having similar angular shifts, the one using 635 nm
light is actually more sensitive in terms of measuring molecular binding. Although longer
wavelengths allow for slightly deeper detection into the solution bulk, this results in asignificantly lower sensitivity for measuring molecular binding on the sensor surface.
Example 3: Two SPR instruments claim to have similar sensitivities since they havematching values for angular sensitivity. However, one instrument uses a BK7 glass
prism and 635 nm light, while the other instrument uses a SF10 glass prism and 890 nm
light. For a protein binding layer of 3 nm, the first instrument produces 0.75 deg angularshift. Not surprisingly though, the second instrument results in a much weaker
response of 0.15 deg angular shift. So for two instruments having similar angularsensitivity, the one using 635 nm light and BK7 glass is actually 5 times more sensitivein terms of measuring molecular binding.
Relative Index of Refraction Unit: Another quantity often used to describe SPR sensitivity is
the relative change in the index of refraction of the fluid medium, known as RIU. Unlike angularshift, the unit of RIU is more relevant to applications that demand an accurate measurement ofthe index of refraction of a bulk fluid. As a result, RIU may not be the most convenient unit forapplications that aim to study molecular binding events. A relationship between RIU andangular shift in degrees is possible if one knows the exact instrumental conditions (e.g.,wavelength of incident light and material of prism glass). And just like with angular shift, a SPR
instrument that has the best sensitivity in terms of RIU does not always mean that it has thebest sensitivity in terms of detecting molecular binding.
Example 4: If an SPR instrument uses a BK7 glass prism, gold sensor chip, and 635
nm incident light, then a 0.010 RIU change in aqueous buffer solution results in ~1.55
deg angular shift. However, this conversion between RIU and angular shift is notuniversal, as it depends upon the instrumental conditions (e.g., wavelength of incident
light and prism material). By increasing the wavelength to 890 nm but keeping all theother experimental parameters the same, then a new relation is observed in which a0.010 RIU change in aqueous buffer solution results in a smaller ~0.99 deg angular shift.
Additionally, if both the wavelength is increased to 890 nm and the prism glass changed
to SF10 then a 0.010 RIU change in aqueous buffer solution results in ~0.61 deg
angular shift. Thus the comparison of sensitivity between units of degree angular shiftand RIU requires careful consideration of instrumental conditions.
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Example 5: How do the following SPR instruments compare? The first instrument hasa BK7 glass prism with 635 nm light and sensitivity of 0.1 mDeg. A second instrument
has a SF10 glass prism with 890 nm light and sensitivity of 1 µRIU. From Example 4,
we learned that 0.010 RIU corresponds to 0.61 deg for this configuration. Using thisrelationship 1 µRIU corresponds to a 0.06 mDeg sensitivity. Does this mean that thesecond instrument is more sensitive than the first? No, remember that angularsensitivities alone do not tell the complete story. We must determine the surface
binding sensitivity to make the fairest comparison. From Example 3, we learned thatthe configuration of the second instrument is 5 times less sensitive than theconfiguration of the first instrument.
Thus, a 0.06 mDeg sensitivity, actuallycorresponds to an equivalent surface binding sensitivity of 0.3 mDeg. As a result, thefirst instrument is experimentally more sensitive than the second.
Surface coverage: If one is interested in using SPR to detect molecular binding taking place
on a sensor surface, then the surface coverage in terms of mass, e.g., pg/mm2, is anappropriate way to define sensitivity. The unit, RU (termed Resonance Unit or Response Unit)
is defined as 1 RU = 1 pg/mm2, and is also often used to determine surface coverage.
However, this description cannot be ubiquitously used. For instance, SPR really measures theoptical polarizability and size and density of molecules bound to the surface, which are related
to but different from an SPR measurement in terms of mass per unit surface area. The
polarizability depends on the wavelength of light, especially if the wavelength is close to theoptical absorption band of the molecule (e.g. chromophores, UV-vis labels, etc.). Since mostproteins have similar polarizabilities, the SPR signal may be considered approximately
proportional to the coverage of molecules bound to the sensor surface, and pg/mm2 is a usefulway to quantify SPR sensitivity.
Example 6: A monolayer of cytochrom c leads to an angular shift of ~0.5 Deg. The
corresponding mass coverage is ~3000 pg/mm2. For an angular sensitivity of 0.1 mDeg,
the corresponding mass sensitivity is 0.6 pg/mm2 or 0.6 RU.
Molar concentration: Some vendors provide sensitivity in terms of lowest detectable molar
concentration. This is a convenient and attractive measure of SPR instrument sensitivity.
However, the reality is that a highly sensitive instrument cannot faithfully guarantee thedetection of an extremely low analyte concentration. This is because sensitivity and detectionlevel are two different (although related) analytical “figures of merit” [1] which are often
mistakenly mixed. The lowest detectable molar concentration depends upon several significant
experimental factors such as the molecular weight, optical property, and binding affinity of theanalyte as well as the surface coverage of the capture molecules. Background noise also plays
a key role in determining the lowest detection level (more about this later). Molecules withlarge molecular weight and polarizability are easier to detect than those with small molecularweight and polarizability. A high affinity and surface coverage of the capture molecules also
facilitate the detection of analyte molecules per given concentration. Additional factors
influencing the lowest detectable molar concentration include sensor chip preparation (e.g., thethickness of the modifier layer and its refractive index), temperature, and buffer solution
performance. Moreover, numerous experimental strategies exist which can amplify SPR
binding responses (e.g., labels, competitive binding assays, enzymatic reactions, etc.). As aresult, SPR sensitivity in terms of lowest detectable molar concentration can be misleading,and very unforgiving to beginning SPR users.

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Example 7: A sensor chip is functionalized with 5 x 10-16 mol/mm2 anti-PNA (peanutagglutinin), PNA molecular weight is about 100 kDa, and PNA-anit PNA equilibrium
dissociation constant, K, is about 20 nM. For a SPR instrument with sensitivity of 0.1
mDeg, or corresponding mass sensitivity of ~0.6 pg/mm2, the minimum detectableconcentration will be: ~0.5 nM at equilibrium. Clearly, if factors such as surface
coverage and equilibrium dissociation constant were different, then the minimum
detectable concentration would also change. Thus, the evaluation of sensitivity in termsof analyte concentration should be carefully considered, keeping in mind that chip andexperimental conditions play critical roles
Determination of detection levels: The definition of “lowest detectable level” is often not
clearly spelled out. The lowest detection level is largely governed by the background noise.
Some choose the peak-to-peak value of the noise in the SPR signal, while others use rootmean-square or standard deviation. In analytical chemistry, an often used definition ofdetection limit is three times the standard deviation of the background (blank) noise. Second,
the noise of a measured physical quantity usually occurs at various time scales, so SPR
sensitivity should be given together with the time scale of the measurement. Filters, such as
time averaging and smoothening of data, can remove certain noises and improve thesensitivity and detection level. This practice tends to slow down the response time. So one
must also make sure the response time is fast enough for an application when choosing aninstrument. Third, the noise level may be influenced by electronic amplification (or gain control).
A higher gain may improve signal to noise ratio, but this usually affects the dynamic range(detection range) of the instrument. Finally, when comparing with imaging SPR or other pixelbased detectors, the sensitivity depends on how many pixels the SPR signal is averaged overand for how long. More pixels and more time lead to better sensitivity, but it may sacrificespatial resolution and response time.
Referenece.
[1] Skoog, D. A.; Holler, F. J.; Crouch, S. R. Principles of Instrumental Analysis, 6th ed.;Thomson Higher Education, Belmont, CA, 2007.

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