Binding Characterization

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

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)

# 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

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