Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential

Amid
collective-variable (CV)-based importance-sampling algorithms,
a hybrid of the extended adaptive biasing force and the well-tempered
metadynamics algorithms (WTM-eABF) has proven particularly cost-effective
for exploring the rugged free-energy landscapes that underlie biological
processes. However, as an inherently CV-based algorithm, this hybrid
scheme does not explicitly accelerate sampling in the space orthogonal
to the chosen CVs, thereby limiting its efficiency and accuracy, most
notably in those cases where the slow degrees of freedom of the process
at hand are not accounted for in the model transition coordinate.
Here, inspired by Gaussian-accelerated molecular dynamics (GaMD),
we introduce the same CV-independent harmonic boost potential into
WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm
leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified
potential and recovers the unbiased free-energy landscape through
thermodynamic integration followed by proper reweighting. As illustrated
in our numerical tests, GaWTM-eABF effectively overcomes the free-energy
barriers in orthogonal space and correctly recovers the unbiased potential
of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF
to two biologically relevant processes, namely, the reversible folding
of (i) deca-alanine and (ii) chignolin, our results indicate that
GaWTM-eABF reduces the uncertainty in the PMF calculation and converges
appreciably faster than WTM-eABF. Obviating the need of multiple-copy
strategies, GaWTM-eABF is a robust, computationally efficient algorithm
to surmount the free-energy barriers in orthogonal space and maps
with utmost fidelity the free-energy landscape along selections of
CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be
easily extended to other biasing-force algorithms.

在基于集体变量（collective-variable, CV）的重要性采样算法中，扩展自适应偏置力与回火元动力学的混合算法（WTM-eABF）已被证实计算效率尤为突出，可用于探索支撑生物过程的粗糙自由能景观。然而，作为一种本质上依赖CV的算法，该混合方案无法显式加速所选CV正交空间内的采样过程，进而限制了其效率与精度，尤其当目标过程的慢自由度未在模型过渡坐标中得到覆盖时，这一局限尤为显著。受高斯加速分子动力学（Gaussian-accelerated molecular dynamics, GaMD）的启发，我们将相同的与CV无关的简谐增强势引入WTM-eABF，得到了一种名为GaWTM-eABF的混合算法。该算法依托WTM-eABF，结合经GaMD平滑后的势场对过渡坐标进行探索，并通过热力学积分与恰当的重加权步骤还原无偏自由能景观。如我们的数值测试结果所示，GaWTM-eABF可有效突破正交空间内的自由能垒，并准确还原无偏平均力势（potential of mean force, PMF）。进一步地，我们将GaWTM-eABF与WTM-eABF分别应用于两类生物相关过程——即（i）十丙氨酸的可逆折叠与（ii）奇诺林（chignolin）的可逆折叠，结果表明GaWTM-eABF可降低PMF计算中的不确定性，且收敛速度显著优于WTM-eABF。GaWTM-eABF无需采用多副本策略，是一种鲁棒性强、计算高效的算法，可有效克服正交空间内的自由能垒，并以极高保真度沿所选CV维度绘制自由能景观。此外，我们将WTM-eABF与GaMD相结合的策略可轻松拓展至其他偏置力类算法。