Binding Characterization: SPR and BLI

Computational and experimental planning guide for Surface Plasmon Resonance (SPR) and Biolayer Interferometry (BLI) binding kinetics. Covers assay design, troubleshooting, and data interpretation for designed proteins.

SPR vs. BLI Selection

Feature	SPR	BLI
Throughput	Low–medium	High (96/384-well)
Sensitivity	Higher	Lower
Reference subtraction	Flow cell	Reference well
Sample consumption	More	Less
Regeneration	Critical	More forgiving
Best for	High-quality kinetics	Screening many variants
Instruments	Biacore (Cytiva), ProteOn	Octet (Sartorius)

Assay Design Principles

Ligand vs. Analyte Choice

Ligand (immobilized on chip/tip):
  - Use the molecule you have abundant, stable supply of
  - Typically: target protein (larger, more stable)
  - Avoid: multivalent molecules on surface (avidity artifacts)

Analyte (flows in solution):
  - Typically: designed binder/antibody
  - Monovalent preferred for clean 1:1 kinetics

Immobilization Strategies (SPR)

Method	Use When
Amine coupling (NHS/EDC)	Any protein, permanent
Streptavidin capture	Biotinylated ligand, reversible
His-tag capture	His-tagged ligand, regenerable
Protein A/G	Antibody Fc capture

# Target immobilization levels (Biacore)
# RMax = Rligand × (MW_analyte / MW_ligand) × stoichiometry
# Target: RMax = 50–200 RU for kinetics (avoid mass transport)

def calc_immobilization_target(
    mw_ligand: float,    # kDa
    mw_analyte: float,   # kDa
    target_rmax: float = 100,   # RU
    stoichiometry: float = 1.0
) -> float:
    """Calculate required ligand immobilization level (RU)."""
    return target_rmax * (mw_ligand / mw_analyte) / stoichiometry

Kinetic Experiment Design

# Analyte concentration series for kinetics
# Span at least 10x above and below Kd
# Use 6–8 concentrations in 2–3x dilution series

def design_concentration_series(
    estimated_kd: float,   # M, rough estimate
    n_points: int = 7,
    dilution_factor: float = 3.0
) -> list:
    """Design analyte concentration series spanning Kd."""
    import numpy as np
    # Center series around Kd
    top = estimated_kd * 30
    bottom = estimated_kd / 30
    concs = [top / (dilution_factor**i) for i in range(n_points)]
    return concs

# Example: estimated Kd = 10 nM
concs = design_concentration_series(10e-9)
# → [300nM, 100nM, 33nM, 11nM, 3.7nM, 1.2nM, 0.4nM]

Data Analysis

import numpy as np
from scipy.optimize import curve_fit

def fit_1to1_kinetics(time: np.ndarray, response: np.ndarray,
                      conc: float) -> dict:
    """
    Fit simple 1:1 Langmuir binding model to SPR/BLI data.
    Returns ka, kd, Rmax.
    """
    def binding_model(t, ka, kd, rmax):
        kobs = ka * conc + kd
        return rmax * (ka * conc / kobs) * (1 - np.exp(-kobs * t))

    popt, pcov = curve_fit(
        binding_model, time, response,
        p0=[1e5, 1e-3, 100],
        bounds=([0, 0, 0], [1e8, 1, 1000])
    )
    ka, kd, rmax = popt
    kd_eq = kd / ka  # Equilibrium Kd = kd/ka

    return {
        "ka": ka,          # M⁻¹s⁻¹ (association rate)
        "kd": kd,          # s⁻¹ (dissociation rate)
        "Kd": kd_eq,       # M (equilibrium dissociation constant)
        "Rmax": rmax,      # RU
        "t_half_dissoc": np.log(2) / kd  # seconds
    }

Troubleshooting

Problem	Cause	Fix
No binding signal	Wrong orientation/inactivation	Switch ligand/analyte; check activity
Biphasic association	Heterogeneous ligand or two-state	Use fresh surface; check protein homogeneity
Incomplete dissociation	Very slow kd or non-specific	Extend dissociation time; add 0.05% Tween-20
Bulk refractive index shift	Buffer mismatch	Match buffer exactly; increase reference subtraction
High non-specific binding	Charge interactions	Add 0.5 M NaCl; block with BSA/ethanolamine
Hook effect	Too high analyte conc	Reduce top concentration 10x
Mass transport limitation	Too much ligand	Reduce immobilization level; increase flow rate
Poor regeneration	Harsh conditions	Test HCl 10mM; glycine pH 2.0; NaOH 10mM

Interpreting Results

def interpret_binding(ka: float, kd: float, kd_eq: float) -> dict:
    """Classify binding kinetics."""
    return {
        "Kd_nM": kd_eq * 1e9,
        "affinity_class": (
            "picomolar" if kd_eq < 1e-10 else
            "nanomolar" if kd_eq < 1e-7 else
            "micromolar" if kd_eq < 1e-4 else
            "weak/non-specific"
        ),
        "kinetic_class": (
            "fast_on_fast_off" if ka > 1e6 and kd > 1e-2 else
            "fast_on_slow_off" if ka > 1e6 and kd < 1e-3 else
            "slow_on_slow_off" if ka < 1e5 else "moderate"
        ),
        "t_half_hours": (np.log(2) / kd) / 3600,
        "diffusion_limited": ka > 1e7,  # Possible mass transport if True
    }

Typical Results for Designed Proteins

Design method	Typical Kd range	Notes
RFdiffusion + MPNN (first round)	10–100 µM	Needs optimization
BoltzGen (first round)	1–10 µM	Better starting point
After affinity maturation	1–100 nM	Target for therapeutic proteins
Antibodies (CDR design)	0.1–10 nM	Mature