Coordinate-Dependent Drift-Diffusion Reveals the Kinetic Intermediate Traps of Top7-Based Proteins

Abstract

The computer-designed Top7 served as a scaffold to produce immunoreactive proteins by grafting of the 2F5 HIV-1 antibody epitope (Top7−2F5) followed by biotinylation (Top7− 2F5−biotin). The resulting nonimmunoglobulin affinity proteins were effective in inducing and detecting the HIV-1 antibody. However, the grafted Top7−2F5 design led to protein aggregation, as opposed to the soluble biotinylated Top7−2F5−biotin. The structure-based model predicted that the thermodynamic cooperativity of Top7 increases after grafting and biotin-labeling, reducing their intermediate state populations. In this work, the folding kinetic traps that might contribute to the aggregation propensity are investigated by the diffusion theory. Since the engineered proteins have similar sequence and structural homology, they served as protein models to study the kinetic intermediate traps that were uncovered by characterizing the position-dependent driftvelocity (v(Q)) and the diffusion (D(Q)) coefficients. These coordinate-dependent coefficients were taken into account to obtain the folding and transition path times over the free energy transition states containing the intermediate kinetic traps. This analysis may be useful to predict the aggregated kinetic traps of scaffold-epitope proteins that might compose novel diagnostic and therapeutic platforms.

Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook

“…Indeed, eq 24 has been employed for estimating lateral diffusivity of water near interfaces, 80 as well as diffusivity along collective variables (CVs) employed in protein folding simulations. 81,82 Interestingly, it was shown by Hinczewski et al 82 that even for collective variable spaces, the estimated diffusivity is acutely sensitive to τ. A common strategy 83−85 in protein folding simulations involves using eq 29 to fit Gaussians into empirical histograms obtained around a certain point but at different times, and use the following expression to estimate diffusivity,…”

“…The ability to estimate diffusivity from computing a local covariance matrix suggests that the probability density function of X τ , a particle’s position at time τ, can be approximated as boldX τ ∼ scriptN ( r 0 + τ μ false( boldr 0 false) , 2 τ D false( boldr 0 false) ) wherein r 0 is the particle’s position at t = 0, and scriptN ( μ , Σ ) is a multivariate Gaussian distribution with mean ν and covariance matrix Σ . Indeed, eq has been employed for estimating lateral diffusivity of water near interfaces, as well as diffusivity along collective variables (CVs) employed in protein folding simulations. , Interestingly, it was shown by Hinczewski et al that even for collective variable spaces, the estimated diffusivity is acutely sensitive to τ. A common strategy − in protein folding simulations involves using eq to fit Gaussians into empirical histograms obtained around a certain point but at different times, and use the following expression to estimate diffusivity, D ( λ 0 ) ≈ σ 2 ( Λ τ 2 ) − σ 2 ( Λ τ 1 ) 2 (…”

“…In turn, the operator is discretized as a matrix using finite differences, and the boundary conditions appear explicitly in the discretization scheme. The discretized operator L(D) is a matrix whose entries depend on the diffusivity profile, which can then be used as an independent variable to minimize the objective function (81).…”