A parametrically constrained optimization method for fitting sedimentation velocity experiments


  • Sedimentation velocity (SV) experiments aim to understand the sedimentation (s) and diffusion (D) transport of solutes in a sample. However, traditional methods can struggle with modeling macromolecular mixtures that display heterogeneity in size and anisotropy. Particularly in polymerizing systems, there's a crucial relationship between a growing polymer chain's molar mass and its anisotropy that must be captured.
  • Multi-dimensional grid methods, such as the high-resolution grid of the 2DSA, often encompass more solutes than can be distinctly resolved. This over-determined grid can lead to solution degeneracy, resulting in potential ambiguities in the resolution.


  • PCSA is presented as an advanced method to fit SV experiments by employing the full boundary Lamm equation solutions.
  • Unlike other grid methods, PCSA ensures that a unique molar mass is tied to a specific anisotropy measurement, sidestepping general issues of degeneracy.
  • To fit empirical data, a Lamm equation solution is simulated for each sedimentation and diffusion coefficient pairing. Using a non-negatively constrained least squares (NNLS) algorithm, a linear amalgamation of all these simulated solutions is crafted to match the empirical data.
  • The PCSA method applies constraints that discretize the sedimentation and diffusion coefficients following an arbitrary function. The function's space is determined by specific user-set limits.
  • For accuracy, the constraint's functional form must depict the distribution attributes of the solutes in the modeled system.
  • The PCSA method uses constraints that discretize the sedimentation and diffusion coefficients along an arbitrary function. This function can span over a space defined by specific limits set by the user.


  • The PCSA method offers a more refined approach to understanding sedimentation velocity experiments, especially in contexts with significant heterogeneity.
  • By allowing users to experiment with various functional forms, the best function to describe solute distribution can be identified. Consequently, each point on the function's curve leads to a unique sedimentation coefficient and frictional ratio pair.
  • The associated diffusion coefficient for these pairs can then be calculated, resulting in a more precise understanding of the system under observation.
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Comparability Studies
Material Science (metal nanoparticles, synthetic polymers, drug compounds)

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