Developing accurate and efficient coarse-grained representations of proteins
is crucial for understanding their folding, function, and interactions over
extended timescales. Our methodology involves simulating proteins with
molecular dynamics and utilizing the resulting trajectories to train a neural
network potential through differentiable trajectory reweighting. Remarkably,
this method requires only the native conformation of proteins, eliminating the
need for labeled data derived from extensive simulations or memory-intensive
end-to-end differentiable simulations. Once trained, the model can be employed
to run parallel molecular dynamics simulations and sample folding events for
proteins both within and beyond the training distribution, showcasing its
extrapolation capabilities. By applying Markov State Models, native-like
conformations of the simulated proteins can be predicted from the
coarse-grained simulations. Owing to its theoretical transferability and
ability to use solely experimental static structures as training data, we
anticipate that this approach will prove advantageous for developing new
protein force fields and further advancing the study of protein dynamics,
folding, and interactions.

使用分子动力学仿真和可微重要性抽样训练神经网络势能，可以开发出准确和高效的蛋白质粗粒化表示方法，在预测蛋白质动力学、折叠和相互作用等方面具有重要应用价值。

基于自上而下的机器学习法推导蛋白质粗粒度力场

Top-down machine learning of coarse-grained protein force-fields

Extracting insight from the enormous quantity of data generated from
molecular simulations requires the identification of a small number of
collective variables whose corresponding low-dimensional free-energy landscape
retains the essential features of the underlying system. Data-driven techniques
provide a systematic route to constructing this landscape, without the need for
extensive a priori intuition into the relevant driving forces. In particular,
autoencoders are powerful tools for dimensionality reduction, as they naturally
force an information bottleneck and, thereby, a low-dimensional embedding of
the essential features. While variational autoencoders ensure continuity of the
embedding by assuming a unimodal Gaussian prior, this is at odds with the
multi-basin free-energy landscapes that typically arise from the identification
of meaningful collective variables. In this work, we incorporate this physical
intuition into the prior by employing a Gaussian mixture variational
autoencoder (GMVAE), which encourages the separation of metastable states
within the embedding. The GMVAE performs dimensionality reduction and
clustering within a single unified framework, and is capable of identifying the
inherent dimensionality of the input data, in terms of the number of Gaussians
required to categorize the data. We illustrate our approach on two toy models,
alanine dipeptide, and a challenging disordered peptide ensemble, demonstrating
the enhanced clustering effect of the GMVAE prior compared to standard VAEs.
The resulting embeddings appear to be promising representations for
constructing Markov state models, highlighting the transferability of the
dimensionality reduction from static equilibrium properties to dynamics.

本研究论文介绍了使用 Gaussian mixture variational autoencoder（GMVAE）进行分子模拟数据的降维和聚类，以及其在构建 Markov 状态模型方面的潜在应用。

使用高斯混合变分自编码器从分子模拟中生成可解释的嵌入

Interpretable Embeddings From Molecular Simulations Using Gaussian  Mixture Variational Autoencoders

Markov state models (MSMs) and Master equation models are popular approaches
to approximate molecular kinetics, equilibria, metastable states, and reaction
coordinates in terms of a state space discretization usually obtained by
clustering. Recently, a powerful generalization of MSMs has been introduced,
the variational approach (VA) of molecular kinetics and its special case the
time-lagged independent component analysis (TICA), which allow us to
approximate slow collective variables and molecular kinetics by linear
combinations of smooth basis functions or order parameters. While it is known
how to estimate MSMs from trajectories whose starting points are not sampled
from an equilibrium ensemble, this has not yet been the case for TICA and the
VA. Previous estimates from short trajectories, have been strongly biased and
thus not variationally optimal. Here, we employ Koopman operator theory and
ideas from dynamic mode decomposition (DMD) to extend the VA and TICA to
non-equilibrium data. The main insight is that the VA and TICA provide a
coefficient matrix that we call Koopman model, as it approximates the
underlying dynamical (Koopman) operator in conjunction with the basis set used.
This Koopman model can be used to compute a stationary vector to reweight the
data to equilibrium. From such a Koopman-reweighted sample, equilibrium
expectation values and variationally optimal reversible Koopman models can be
constructed even with short simulations. The Koopman model can be used to
propagate densities, and its eigenvalue decomposition provide estimates of
relaxation timescales and slow collective variables for dimension reduction.
Koopman models are generalizations of Markov state models, TICA and the linear
VA and allow molecular kinetics to be described without a cluster
discretization.

本文提出了一种使用 Koopman 算子理论和动态模式分解（DMD）来扩展分子动力学中第一个变分方法（VA）和延迟时间独立分量分析（TICA）的方法，通过 Koopman 模型来近似描绘分子的动力学规律。