Angwani Monika Narayan, Rane Kaustubh
Department of Physics, Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat 382055, India.
Department of Chemical Engineering, Indian Institute of Technology Gandhinagar, Gandhinagar, Gujarat 382055, India.
J Chem Phys. 2025 Jul 7;163(1). doi: 10.1063/5.0271346.
We present a novel application of the Transition Matrix Monte Carlo (TMMC) algorithm to compute the relative free energies of polymers in explicit solvents as a function of a selected order parameter. Our method leverages a pre-generated library of polymer conformations in vacuum, coupled with explicit solvent environments using the Growth Expanded Ensemble (GEE) framework. The integration of TMMC within GEE addresses sampling challenges by introducing bias in Monte Carlo simulations while enabling the computation of unbiased probability distributions and relative free energies. A key advantage of our approach is its flexibility-the polymer conformation library can be generated using any sampling technique, including Molecular Dynamics or Monte Carlo simulations, in implicit or explicit solvents and at different temperatures. The method is adaptable to any collective variable (CV) and can be extended to compute free energies as a function of multiple CVs. Furthermore, its parallelizable structure makes it highly scalable on multi-core central processing units and graphics processing unit architectures. To demonstrate its applicability, we apply it to a fully flexible polymer model consisting of Lennard-Jones particles connected via a harmonic potential, immersed in an explicit solvent of Lennard-Jones particles. The relative free energies are computed as a function of the radius of gyration. Results for three different solvents, obtained by varying the polymer-solvent interaction strength, reveal that the polymer preferentially adopts an extended conformation in good solvents and a collapsed conformation in poor solvents, consistent with theoretical expectations. Our method provides a computationally efficient and scalable framework for free energy calculations, with broad applications in polymer physics and macromolecular thermodynamics.
我们展示了转移矩阵蒙特卡罗（TMMC）算法的一种新应用，用于计算在显式溶剂中聚合物的相对自由能，该自由能是所选序参量的函数。我们的方法利用预先生成的真空中聚合物构象库，并结合使用生长扩展系综（GEE）框架的显式溶剂环境。在GEE中集成TMMC通过在蒙特卡罗模拟中引入偏差来解决采样挑战，同时能够计算无偏概率分布和相对自由能。我们方法的一个关键优势在于其灵活性——聚合物构象库可以使用任何采样技术生成，包括分子动力学或蒙特卡罗模拟，在隐式或显式溶剂中以及在不同温度下。该方法适用于任何集体变量（CV），并且可以扩展以计算作为多个CV函数的自由能。此外，其可并行化结构使其在多核中央处理器和图形处理器架构上具有高度可扩展性。为了证明其适用性，我们将其应用于一个完全柔性的聚合物模型，该模型由通过谐振势连接的 Lennard-Jones 粒子组成，浸没在 Lennard-Jones 粒子的显式溶剂中。相对自由能作为回转半径的函数进行计算。通过改变聚合物 - 溶剂相互作用强度获得的三种不同溶剂的结果表明，聚合物在良溶剂中优先采用伸展构象，在不良溶剂中采用塌缩构象，这与理论预期一致。我们的方法为自由能计算提供了一个计算高效且可扩展的框架，在聚合物物理和大分子热力学中有广泛应用。
