A Quantitative Description for Optical Mass Measurement of Single Biomolecules

Abstract

Label-free detection of single biomolecules in solution has been achieved using a variety of experimental approaches over the past decade. Yet, our understanding of the magnitude of the optical contrast and its relationship with the underlying atomic structure as well as the achievable measurement sensitivity and precision remain poorly defined. Here, we use a Fourier optics approach combined with an atomic structure-based molecular polarizability model to simulate mass photometry experiments from first principles. We find excellent agreement between several key experimentally determined parameters such as optical contrast-to-mass conversion, achievable mass accuracy, and molecular shape and orientation dependence. This allows us to determine detection sensitivity and measurement precision mostly independent of the optical detection approach chosen, resulting in a general framework for light-based single-molecule detection and quantification.

Figure 1

Fundamentals of image formation in a contrast-enhanced back reflection geometry. (a) Schematic of the simulated, widefield, MP setup, including an attenuation mask in the BFP of the objective lens, which selectively reduces light reflected from the glass coverslip. (b,c) Simulated ratiometric contrast for a single 24-mer of the small heat shock protein Hsp16.5 (m = 396 kDa) at an atomically flat glass–water interface. (d) Relative SNR when varying the refractive indices of the substrate and buffer medium. The diagonal indicates refractive index matching, where no reference field is available due to a lack of reflection. (e) Simulated phase retardation map at λ = 445 nm arising from nanoscopic roughness of glass coverslips on the order of ∼2 nm height variations over ∼100 nm (lateral) length scales. (f) Resulting speckle-like image using a 0.1% transmission mask, normalized to the expected reflectivity from a flat glass–water interface (see Section S6). Scalebars = 0.5 μm.

Figure 2

Simulation of protein landing events and resulting mass distributions as a function of mask strength. (a) Two consecutive sets of n_avg frames are averaged before computing the ratiometric image, revealing individual proteins landing at different positions as a function of time (scale bars: 1 μm). (b) Mass histograms for four oligomeric states of a protein simulated as spheres of radius 3.8 nm and refractive index 1.46 (representing BSA) using different mask strengths and local reflectivity correction. In all cases, the power incident on the detector was kept constant. (c) Standard deviation of the fitted distributions (top) and ratiometric contrast (bottom) as a function of protein mass.

Figure 3

Dependence of mass measurement on biomolecular shape and illumination polarization. (a) Experimentally observed mass distributions for dsDNA illuminated with circularly (top) and linearly (bottom) polarized light. (b) Modeling the shape and orientation of a protein, here the dimer of BSA (PDB ID 3V03), by computing the corresponding polarizability tensor. (c) Mass histograms for a simulated landing assay where all BSA monomers (or dimers) land with the same (fixed) orientation (θ_z = 56°; θ_z = 149°), or with random orientations, while being illuminated with linearly polarized light. (d) Relative change of the ratiometric contrast for the BSA dimer for different orientations (changing θ_y and θ_z) relative to the incident polarization. (e) Same simulation as in (c), except for circularly polarized illumination. (f) Kernel density estimation (Gaussian; bandwidth = 2 kDa) of experimentally measured distributions of partially (SUMO-SRSF1; 4 repeats) and fully disordered (Starmaker; 4 repeats) proteins. The vertical dashed lines represent the mass inferred from the measurement (colored) and the expected mass (gray).

Figure 4

Mass scaling with molecular polarizability and image contrast. (a) Average excess polarizability and (b), calculated ratiometric contrast for proteins of mass 10–1000 kDa. Slope of linear fit (red line): 724 Å/kDa (a) and 4.4 × 10^–5/kDa (b). PDB IDs: HasA = 1B2V; Maspin = 1XQJ; Strep. = 4BX6; BSA = 3V03; Cyt-BC1 = 1BE3; Hsp16.5 = 1SHS; Myosin-V = 2DFS; Choroplast F1F0 = 6FKI; GroEL = 1GR5; IBDV = 2GSY.

Figure 5

Current and future limits of optical mass measurement of single biomolecules. (a) Experimental ratiometric images of buffer medium only (scalebar = 1 μm) for different integration times. (b) Achievable SNR when detecting the BSA monomer (m = 66 kDa). (c) Smallest detectable mass m_q=3 at SNR = 3. (d) Mass resolution σ_m. All given as a function of effective exposure time and illuminating power density in the presence of excess noise on the order of 5 kDa. (e–h) Same (simulated) images and dependencies for purely shot noise limited performance. The white dots indicate experimental parameters from ref (3).