Foundations

Reading Sensorgrams by Eye

The skill that prevents more bad papers than any fitting software ever will.

22 min read 4 sections 11 sources cited (5 verified)

Everything is an exponential#

A first-order process approaches its endpoint exponentially. Both phases of a 1:1 sensorgram are first-order processes. So both phases are exponentials, and any deviation from an exponential is telling you that your interaction is not 1:1 — or that something other than binding is happening.

This is the single most useful reading skill in SPR, and it requires no software. An exponential has three properties you can check by eye. It is steepest at the start. Its curvature is smooth and monotonic. And crucially, an exponential approaching a plateau reaches 63% of the way in one time constant, 86% in two, 95% in three. (O’Shannessy et al., 1993) If your association phase is still rising linearly at the end of a three-minute injection, it is not an exponential that has nearly plateaued; it is something else.

R(t) = R_eq · ( 1 − e^{−k_obs t} ) with k_obs = k_a·C + k_d

(4.1)

where

R(t)response at time t during injection

R_eqthe plateau this concentration would reach

k_obsobserved exponential rate constant, s⁻¹

Canalyte concentration in the bulk

Both rate constants appear in k_obs. This is why the association phase alone cannot separate them from a single concentration — and why plotting k_obs against C across a series, which gives a line of slope k_a and intercept k_d, is a valuable check that does not depend on your fitting software.

R(t) = R₀ · e^{−k_d t} t_½ = ln2 / k_d

(4.2)

where

R₀response at the moment injection stopped

t_½complex half-life — the time for half the complexes to dissociate

The dissociation phase is a pure single exponential for a 1:1 interaction, because nothing re-associates. Every departure from that — a fast component followed by a slow tail, a plateau that never reaches baseline — is diagnostic information (O’Shannessy & Winzor, 1996).

Interactive 1:1 sensorgram. Hold K_D fixed and trade k_a against k_d: the plateaus do not move, but the shapes are unrecognisably different.

The landmarks on a curve#

Baseline. Should be flat. A slope here contaminates everything downstream.
Injection start. A small vertical step is normal (bulk shift). A large one means your buffers do not match (Myszka, 1999).
Association. Curved, steepest at the start, flattening towards R_eq.
Steady state. The plateau where association and dissociation balance. Reaching it is not required for kinetic fitting, but is required for equilibrium analysis.
Injection end. A step down, mirroring the step up. If the two steps are not equal and opposite, something bound irreversibly or the surface changed.
Dissociation. Exponential decay towards baseline.
Regeneration. A large excursion of no analytical value, followed by a return to the original baseline. If it does not return to the original baseline, the surface has changed (Karlsson et al., 1994).

The same simulator, framed around the phase structure. Shorten the dissociation window and watch how little information about k_d survives.

Steady-state affinity. Set the top concentration below K_D, then switch to the linear axis, and see how convincing a fabricated K_D can look.

A diagnostic gallery#

Most curve pathologies have a characteristic shape. Learning to name them from the shape alone is faster and more reliable than discovering them from a bad fit.

Six curve shapes and their usual causes. The first is what you want; the rest are what you usually get.

Mass transport limitation

Association looks almost straight rather than exponential, because the rate is set by delivery rather than chemistry. Dissociation starts fast, then drags, because released analyte rebinds before it can be washed out of the matrix. The definitive test is to lower the ligand density: a genuine k_a does not change, a transport-distorted one rises (Myszka et al., 1998; Schuck & Minton, 1996). kinetics and mass transport treats this in full.

Bivalent analyte / avidity

The dissociation is biphasic — a fast component and a stubborn slow tail — and the tail gets slower as ligand density rises. This is the standard behaviour of an IgG over an antigen surface, and it is the most common reason antibody off-rates in the literature are tighter than the true intrinsic values (Nieba et al., 1996). Use a Fab, or invert the format and capture the antibody so the antigen is the monovalent analyte.

Drift

A steady slope through the entire cycle including the baseline. Usually incomplete equilibration or a temperature ramp; occasionally ligand slowly leaching from the surface, in which case it appears only on the active channel (Nieba et al., 1997).

Spikes and jumps

Sharp excursions at injection boundaries are valve and pressure transients. They are reproducible, appear on reference channels, and should simply be excluded from the fitted region. What they must not do is tempt you into excluding other, inconvenient parts of the curve on the same pretext.

Decaying surface

Each cycle reaches a lower maximum than the last. Plot maximum response against cycle number — a linear decline means regeneration is stripping ligand along with analyte. Soften the regeneration or move to a capture format where a fresh ligand layer is built each cycle (Karlsson et al., 2006).

What good curves require you to have decided in advance#

By this point the design rules stop being arbitrary and start being consequences.

Analyte concentration range. Span roughly 0.1–10 × K_D, in a geometric series. Below K_D everywhere and the response is near-linear in concentration, so R_max and K_D become inseparable and the fit will invent a plausible pair.
Injection length. At least 3/k_obs at the lowest concentration if you want steady state, since low concentrations equilibrate most slowly. For kinetics alone, enough curvature is sufficient.
Dissociation length. Long enough to see a real decay. A useful rule: aim to observe at least 5% signal loss, which for a slow off-rate can mean tens of minutes. A 60 s dissociation on a k_d of 10⁻⁴ s⁻¹ loses 0.6% of signal — indistinguishable from drift, and any k_d fitted to it is extrapolation.
Surface density. Target R_max of 20–100 RU for kinetics (Karlsson & Fält, 1997).
Replicates. At least one concentration repeated at the start and end of the run, plus blank injections throughout (Myszka, 1999).

Work backwards from the R_max you want to the immobilisation level you need — before making the surface.

Sources cited on this page

Listed alphabetically. Each badge records whether the bibliographic record was confirmed against Crossref. unverified marks a real, deliberately chosen source whose volume and page numbers we have not yet machine-checked — it is not a comment on the science.

Karlsson et al., 1994R. Karlsson, H. Roos, L. Fägerstam, B. Persson (1994). Kinetic and concentration analysis using BIA technology. Methods 6, 99–110. doi:10.1006/meth.1994.1013 verified
Karlsson & Fält, 1997R. Karlsson, A. Fält (1997). Experimental design for kinetic analysis of protein–protein interactions with surface plasmon resonance biosensors. Journal of Immunological Methods 200, 121–133. doi:10.1016/S0022-1759(96)00195-0 verified
Where the low-density / high-flow-rate / analyte-range design rules come from.
Karlsson et al., 2006R. Karlsson, P. S. Katsamba, H. Nordin, E. Pol, D. G. Myszka (2006). Analyzing a kinetic titration series using affinity biosensors. Analytical Biochemistry 349, 136–147. doi:10.1016/j.ab.2005.09.034 unverified
Single-cycle kinetics: the whole concentration series in one injection sequence, no regeneration.
Myszka et al., 1998D. G. Myszka, X. He, M. Dembo, T. A. Morton, B. Goldstein (1998). Extending the range of rate constants available from BIACORE: interpreting mass transport-influenced binding data. Biophysical Journal 75, 583–594. doi:10.1016/S0006-3495(98)77549-6 verified
Shows transport can be fitted rather than merely avoided, and defines the transport coefficient kₜ.
Myszka, 1999D. G. Myszka (1999). Improving biosensor analysis. Journal of Molecular Recognition 12, 279–284. unverified
Origin of double referencing and blank-injection subtraction as standard practice.
Myszka, 2000D. G. Myszka (2000). Kinetic, equilibrium, and thermodynamic analysis of macromolecular interactions with BIACORE. Methods in Enzymology 323, 325–340. doi:10.1016/S0076-6879(00)23372-7 unverified
Nieba et al., 1996L. Nieba, A. Krebber, A. Plückthun (1996). Competition BIAcore for measuring true affinities: large differences from values determined from binding kinetics. Analytical Biochemistry 234, 155–165. doi:10.1006/abio.1996.0067 unverified
A direct demonstration that surface-measured kinetic constants can diverge substantially from solution affinities, and a solution-competition format that avoids the problem.
Nieba et al., 1997L. Nieba, S. E. Nieba-Axmann, A. Persson, et al. (1997). BIACORE analysis of histidine-tagged proteins using a chelating NTA sensor chip. Analytical Biochemistry 252, 217–228. doi:10.1006/abio.1997.2326 unverified
Characterises His-tag capture on NTA surfaces, including the baseline drift caused by its finite stability.
O’Shannessy et al., 1993D. J. O’Shannessy, M. Brigham-Burke, K. K. Soneson, P. Hensley, I. Brooks (1993). Determination of rate and equilibrium binding constants for macromolecular interactions using surface plasmon resonance: use of nonlinear least squares analysis methods. Analytical Biochemistry 212, 457–468. doi:10.1006/abio.1993.1355 verified
The case for fitting the sensorgram directly rather than linearising it.
O’Shannessy & Winzor, 1996D. J. O’Shannessy, D. J. Winzor (1996). Interpretation of deviations from pseudo-first-order kinetic behavior in the characterization of ligand binding by biosensor technology. Analytical Biochemistry 236, 275–283. doi:10.1006/abio.1996.0167 unverified
Where non-exponential behaviour comes from, and how to tell the causes apart.
Schuck & Minton, 1996P. Schuck, A. P. Minton (1996). Analysis of mass transport-limited binding kinetics in evanescent wave biosensors. Analytical Biochemistry 240, 262–272. doi:10.1006/abio.1996.0356 verified
The two-compartment model in the form most SPR software still implements.