🔬 Surface Plasmon Resonance (SPR) Kinetics

Sensor Chip Preparation — Ligand Immobilization

Every SPR experiment begins on a piece of engineering that looks unremarkable but is not: a glass slide coated with a ~50 nm gold film, itself coated with a soft, hydrated dextran polymer brush a few hundred nanometers thick. Onto that matrix, a target protein — the "ligand" in SPR terminology, regardless of its biological role — is covalently and stably anchored so that a completely different molecule, the analyte, can be flowed over it later and its binding measured in real time.

• ~100 nm: Dextran matrix thickness (CM5 chip, hydrated)
• 2,000–15,000: Typical immobilization level (RU of ligand loaded)
• 70–90%: Amine coupling efficiency (of activated sites react)
• <100–500: Optimal ligand density for kinetics (RU, to avoid mass transport limits)

The gold film and the Kretschmann geometry

SPR instruments illuminate the back side of a thin (~48–50 nm) gold film through a glass prism, at an angle beyond the critical angle for total internal reflection — the Kretschmann configuration. Reflected light intensity is measured across a range of incident angles. At one specific angle, incident photons resonantly couple their momentum into collective oscillations of free electrons at the gold surface — a surface plasmon — and reflected intensity drops sharply to a minimum. That resonance angle depends sensitively on the refractive index within roughly 200–300 nm of the gold surface.

Gold is used almost universally (rather than silver, which gives a sharper resonance) because it is chemically inert and does not oxidize under aqueous buffer conditions during long experiments — a critical requirement for reproducible biosensing over hours of flow.

CM5 dextran chemistry and amine coupling

The workhorse sensor surface, Cytiva's CM5 chip, presents a ~100 nm layer of carboxymethylated dextran covalently attached to the gold via a thiol linker. This three-dimensional hydrogel — not a flat 2-D surface — provides enormous surface area for ligand capture while keeping immobilized molecules hydrated and native-like.

Standard immobilization uses EDC/NHS amine coupling: EDC (1-ethyl-3-(3-dimethylaminopropyl)carbodiimide) activates the matrix's free carboxyl groups, NHS (N-hydroxysuccinimide) converts them into reactive esters, and primary amines (mostly lysine side chains and the N-terminus) on the ligand protein attack those esters to form stable amide bonds — all within a roughly 7-minute injection at low ionic strength and a pH below the ligand's isoelectric point, so the protein is electrostatically pre-concentrated into the matrix before it reacts.

Alternative chemistries exist for cases where amine coupling would damage activity: thiol coupling for engineered cysteines, streptavidin capture of biotinylated ligand, anti-His or anti-Fc capture surfaces for oriented, regenerable capture of tagged proteins or antibodies.

The CM5 matrix presents an estimated several thousand accessible carboxyl groups per 100 nm² of chip area — a flow cell footprint of roughly 1 mm² but with enough three-dimensional matrix volume to immobilize nanogram quantities of ligand while still leaving the evanescent field, decaying within a few hundred nanometers of the gold, able to sense every binding event above it.

Density and orientation — less ligand is often better

Counterintuitively, the best surfaces for kinetic measurements carry very little ligand. At high immobilization density, newly bound analyte cannot diffuse into the matrix fast enough to keep up with the intrinsic binding reaction — the system becomes mass-transport limited, and the observed "on-rate" reflects diffusion through the matrix rather than the true molecular kon. Kinetics-grade surfaces are therefore immobilized to just tens of RU, sacrificing raw signal for kinetic accuracy, and increasing flow rate (often 30–100 µL/min) further minimizes depletion of analyte near the surface.

Random amine coupling also randomizes ligand orientation — some fraction of immobilized molecules will have their binding site facing the matrix rather than the flow, reducing active site availability. Oriented capture strategies (biotin-streptavidin, anti-tag antibodies, Protein A/G for antibody ligands) present every immobilized molecule with a defined, active orientation and are increasingly preferred for kinetic screening.

Baseline & Analyte Injection — Association Phase

With ligand immobilized, the instrument begins recording the sensorgram — response units (RU) plotted continuously against time. First, buffer alone flows over the chip to establish a flat, stable baseline. Then the injection valve switches to analyte solution: the binding partner of interest, free in solution at a known concentration, sweeps across the immobilized ligand and mass begins to accumulate on the surface.

• 10–100: Typical flow rate (µL/min through flow cell)
• <0.1: Baseline noise (stable) (RU drift per minute)
• 60–300: Association phase duration (seconds per injection)
• 5–7: Concentration series (points, half-log dilutions around KD)

Anatomy of a sensorgram cycle

A single SPR kinetic cycle has a characteristic shape repeated for every analyte concentration tested: a flat baseline (buffer only, RU≈0 relative to the immobilized surface), a rising association phase once analyte injection begins, a plateau if the injection is long enough to approach equilibrium, a falling dissociation phase once the injection ends and buffer resumes, and finally — if the ligand-analyte interaction does not fully dissociate on its own within a reasonable time — a short regeneration pulse (often low-pH glycine-HCl) that strips remaining bound analyte so the same surface can be reused for the next concentration.

This full cycle, repeated across a concentration series spanning roughly 0.1× to 10× the expected KD, is what feeds the global kinetic fit performed in the final stage of this simulation.

Microfluidics, referencing, and bulk refractive index jumps

Modern SPR instruments run buffer and analyte through a network of parallel flow cells rather than a single channel. Critically, one flow cell is left without immobilized ligand (or immobilized with an irrelevant control protein) as a reference surface. Because switching from running buffer to analyte solution changes the bulk refractive index of the fluid itself — even with zero specific binding — this reference channel captures that non-specific "bulk shift" so it can be subtracted from the active channel, a step called referencing (or double referencing when a buffer-only blank injection is also subtracted).

Without referencing, a bulk refractive index jump of even a few RU at the start of injection can masquerade as ultra-fast association kinetics — one of the most common artifacts in real SPR data.

The 1:1 Langmuir association equation

The simplest and most widely used binding model treats the interaction as reversible, bimolecular, 1:1 stoichiometry between free ligand sites and analyte:

dR/dt = kon × C × (Rmax − R) − koff × R

where R is the response at time t, C is the constant analyte concentration during injection, Rmax is the response at saturation of all ligand sites, kon is the association rate constant (M⁻¹s⁻¹), and koff is the dissociation rate constant (s⁻¹). During constant-concentration injection this integrates to:

R(t) = Req × (1 − e^(−kobs·t)), where kobs = kon·C + koff

The observed rate constant kobs is what is actually measured from the curvature of a single association trace — it depends on concentration. Only by fitting the kobs-vs-concentration relationship across a full dilution series (kobs = kon·C + koff) can kon and koff be separated as independent parameters, which is exactly why a concentration series, not a single injection, is required for kinetics.

Real-Time Mass Detection via Evanescent Wave

The signal displayed as "response units" on a sensorgram is not a direct measurement of bound molecules — it is an optical readout of a physical field that barely reaches beyond the gold surface itself. Understanding the evanescent wave explains both why SPR is so sensitive to surface binding and why it is essentially blind to anything happening in bulk solution.

• ~200–300 nm: Evanescent field penetration depth (exponential decay, e-folding)
• ~10⁻⁶ RIU: Refractive index sensitivity (resolvable index change)
• ~1 RU ≈ 1 pg/mm²: Mass-to-signal conversion (protein surface density)
• ~0.1°: Resonance angle shift, full scale (millidegree resolution)

What the evanescent wave actually senses

When surface plasmon resonance occurs, the electromagnetic field is not confined to the gold film — it extends a short distance into the solution above it as an evanescent wave, whose intensity decays exponentially with distance from the surface, characterized by a penetration depth of roughly 200–300 nm for typical SPR wavelengths (~760–850 nm). Any change in refractive index within that thin shell — most commonly, a protein binding to immobilized ligand and locally increasing solute concentration — shifts the resonance angle at which reflected light intensity drops to its minimum.

Because the field intensity falls off so steeply, SPR is almost perfectly selective for surface-confined events: molecules diffusing in bulk solution far from the chip contribute essentially nothing to the signal, while a single layer of bound protein sitting directly on the matrix dominates it.

The evanescent field decays exponentially with an e-folding depth of only a few hundred nanometers — SPR is effectively blind to anything happening farther from the gold film than roughly the length of a small virus, which is precisely what makes it so sensitive to surface-confined binding rather than bulk solution noise.

From resonance angle to response units

Practically, the instrument does not track a single angle — it continuously scans reflected light intensity across a narrow range of incident angles (often via a fixed wedge of light and a CCD or photodiode array, so the whole angular spectrum is captured simultaneously without any moving parts) and locates the position of the intensity minimum in real time, many times per second.

That angular position is converted into an arbitrary but standardized unit, the response unit (RU): 1,000 RU corresponds to an angle shift of about 0.1° and, for a typical protein, to a surface mass increase of roughly 1 nanogram per square millimeter — meaning 1 RU is approximately 1 picogram of protein per square millimeter of chip surface, an extraordinarily small mass change to resolve optically.

Why label-free beats ELISA and fluorescence for kinetics

ELISA and fluorescence-based binding assays require labeling one binding partner (an enzyme conjugate, a fluorophore, a radioisotope) and typically only report an endpoint signal after washing — a single snapshot, not a real-time trajectory. SPR requires no label at all: the signal is intrinsic to the mass of the unmodified molecules themselves, so there is no risk that a label sterically blocks the binding site or alters binding affinity, and the entire association and dissociation trajectory is captured continuously.

This continuous, label-free readout is what makes kon and koff separately measurable in the first place — endpoint assays like ELISA can report an apparent affinity (an IC50 or EC50) but cannot resolve the two rate constants that combine to produce it, and are blind to the kinetic asymmetries (e.g. fast-on/fast-off vs. slow-on/slow-off at the same affinity) that often matter most for drug behavior in vivo.

Equilibrium & Dissociation Phase

If an analyte injection runs long enough, association slows and the sensorgram flattens into a plateau — the point at which the rate of new binding exactly balances the rate of existing complexes falling apart. Ending the injection and switching back to buffer alone then reveals the reverse half of the story: how quickly, and how completely, bound analyte lets go of its ligand.

• 10⁻¹–10⁻⁶ s⁻¹: Typical koff range (across drug-like interactions)
• 300–600 s: Dissociation phase monitored (or longer for slow off-rates)
• seconds–days: Residence time (1/koff) range (depending on koff)
• Glycine-HCl: Regeneration solution (typical) (pH 1.5–2.5, strips bound analyte)

Equilibrium and the steady-state response

At equilibrium, dR/dt = 0 in the Langmuir equation, which rearranges to:

Req = Rmax × C / (C + KD)

This is the same hyperbolic saturation relationship that describes enzyme kinetics (Michaelis-Menten) and receptor pharmacology (Scatchard/Hill binding) — when analyte concentration C equals KD, exactly half of the ligand sites are occupied (Req = Rmax/2). Plotting Req against C for a full concentration series and fitting this isotherm gives an independent, purely equilibrium-based estimate of KD that can be cross-checked against the kinetic kon/koff ratio — good agreement between the two is a standard sanity check for data quality.

Dissociation kinetics and surface regeneration

Once analyte injection stops and buffer resumes, C effectively drops to zero and the Langmuir equation reduces to pure first-order decay:

dR/dt = −koff × R → R(t) = R0 × e^(−koff·(t−t0))

Plotting ln(R) against time during this phase gives a straight line whose slope is −koff directly — the cleanest and most model-independent measurement in the entire experiment, since it does not depend on knowing the analyte concentration at all.

If koff is very small, dissociation may not go to completion within a practical monitoring window, and a brief regeneration pulse — commonly low-pH glycine-HCl (pH 1.5–2.5), sometimes high salt or mild detergent — is injected to strip any remaining bound analyte and reset the surface to its post-immobilization baseline, so dozens of concentration cycles can be run on a single chip.

Residence time — the drug design parameter hiding inside koff

The reciprocal of koff, 1/koff, has units of time and is called the residence time — literally, the average lifetime of the bound complex. Because in vivo drug concentration falls as a compound is cleared from the body, a drug that dissociates slowly from its target can remain bound and pharmacologically active long after free plasma concentration has dropped, decoupling efficacy from pharmacokinetics in a way that binding affinity (KD) alone cannot predict.

This has made residence time, not just KD, a first-class optimization target in modern structure-based drug design — medicinal chemists now routinely run SPR dissociation-phase measurements specifically to rank candidate compounds by koff, seeking the slowest off-rate compatible with acceptable on-rate and selectivity.

Because residence time equals 1/koff, a compound with koff = 10⁻⁵ s⁻¹ stays bound to its target for roughly 28 hours on average, while one with koff = 10⁻¹ s⁻¹ lets go in under 10 seconds — a thousand-fold difference in target engagement duration that is completely invisible to a standard endpoint IC50 assay, yet is now considered a primary lever for in vivo efficacy.

Kinetic Fitting — kon, koff, and KD Determination

The final step turns a family of sensorgrams — one full association/dissociation cycle per analyte concentration — into three numbers that summarize the entire interaction: kon, koff, and KD = koff/kon. This is where SPR moves from a real-time picture of binding into quantitative structural pharmacology.

• 10³–10⁷ M⁻¹s⁻¹: Typical kon range (diffusion-limited ceiling ~10⁸)
• 10⁻¹–10⁻⁶ s⁻¹: Typical koff range (seconds to weeks residence)
• pM to mM: KD range measurable (across the same instrument platform)
• sub-pg/mm²: Detection sensitivity (mass change resolvable)

Global fitting across a concentration series

Rather than fitting each concentration's curve independently, modern SPR analysis software (Biacore Insight, Scrubber, TraceDrawer) performs a global fit: a single set of kon, koff, and Rmax parameters is required to simultaneously reproduce every association and dissociation curve in the series, with only the known analyte concentration C varying between curves. Because kobs = kon·C + koff must hold across the whole dilution series, global fitting is far more robust than fitting one curve at a time — it prevents a single noisy injection from distorting the result and directly reports residuals (typically evaluated as reduced chi-square, with values well below 10% of Rmax considered a good fit) as an objective measure of how well the 1:1 model actually describes the data.

Reading kon, koff and knowing when 1:1 breaks down

Once the fit converges, KD = koff / kon falls out directly, with units of molar concentration — the concentration at which half the ligand sites are occupied at equilibrium. A tight, "sticky" interaction has a small KD; that smallness can come from a fast kon, a slow koff, or both, and the two curve shapes look distinctly different: fast-on/fast-off interactions produce sensorgrams that shoot up and drop back down quickly, while slow-on/slow-off interactions of the very same affinity rise and fall gradually — a distinction totally invisible to an endpoint assay that only reports the equilibrium KD.

Deviations from a clean 1:1 fit are common and diagnostic: mass-transport limitation (analyte cannot diffuse to the surface fast enough) makes association look artificially slow and concentration-independent; avidity from a bivalent analyte (e.g. an IgG binding a densely immobilized antigen with both Fab arms) produces apparent kinetics far tighter than the true monovalent interaction; and genuine two-state binding (an initial encounter complex followed by a conformational change) requires a more complex model with four rate constants instead of two.

Where this data is actually used

Commercial SPR platforms — principally Cytiva's Biacore family (T200, 8K, S200) and competing systems from Sartorius (Octet, using the related BLI technology) — run this exact workflow daily across pharma and academic labs for: ranking antibody clones by affinity and residence time during lead selection and affinity maturation; fragment-based drug discovery (FBDD), where SPR's sensitivity to sub-100 µM affinities lets chemists detect and rank weak fragment hits that other assays miss entirely; comparing binding kinetics of a biosimilar antibody against its reference product for regulatory biosimilarity packages; and characterizing viral receptor-binding interactions (e.g. spike protein–ACE2 kinetics), where kon and koff differences between variants correlate directly with transmissibility and immune escape.

Biacore-class instruments can resolve binding affinities spanning nearly twelve orders of magnitude on the same platform and the same 1:1 Langmuir framework — from millimolar fragment hits (KD ~10⁻³ M) in early drug discovery screening to femtomolar antibody-antigen pairs (KD ~10⁻¹⁵ M) at the tightest end of affinity maturation.

Label-free biophysical binding methods compared