A parametrically constrained optimization method for fitting sedimentation velocity experiments
Challenge
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.
Solution
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.
Conclusion
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.
