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In this episode of **Breaking Math**, hosts **Autumn** and **Gabriel** take a deep dive into the paper *“Towards Equilibrium Molecular Conformation Generation with GFlowNets”* by **Volokova et al.**, published in the **Digital Discovery Journal** by the **Royal Society of Chemistry**. They explore the cutting-edge intersection of **molecular conformations** and **machine learning**, comparing traditional methods like **molecular dynamics** and **cheminformatics** with the innovative approach of **Generative Flow Networks (GFlowNets)** for molecular conformation generation.

The episode covers **empirical results** that showcase the effectiveness of GFlowNets in **computational chemistry**, their **scalability**, and the role of **energy estimators** in advancing fields like **drug discovery**. Tune in to learn how **machine learning** is transforming the way we understand molecular structures and driving breakthroughs in **chemistry** and **pharmaceuticals**.

Keywords: molecular conformations, machine learning, GFlowNets, computational chemistry, drug discovery, molecular dynamics, cheminformatics, energy estimators, empirical results, scalability, math, mathematics, physics, AI

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You can find the paper “Towards equilibrium molecular conformation generation with GFlowNets” by Volokova et al in Digital Discovery Journal by the Royal Society of Chemistry.

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Transcript

00:00:00

Speaker

Welcome to another episode of Breaking Math Podcast, where we unravel the mysteries of science, geometry, and technology. I'm your host, Autumn Feneff, and I'm joined by my co-host, Gabrielle Hash. Today, we're embarking on a fascinating journey into the realm of molecular confirmation and the revolutionary role of machine learning in this field.

00:00:22

Speaker

Our discussion will cover the latest advancements in computational chemistry, delve into innovative methodologies, and explore how they are transforming drug discovery and molecular research. So join me in this episode to unravel the journal's submission towards Equilibrium Molecular Confirmation Generation with GFLONADS by Volokova et al. and Digital Discovery Journal by the Royal Society of Chemistry. To set the stage, let's start with a fundamental concept in chemistry, molecular conformations. Molecules exist in three dimensional space and can adopt various shapes based on the arrangement of their atoms. These shapes or conformations are crucial for understanding molecular behavior and predicting properties. Molecules are not static entities, they are dynamic and can change their shape due to the rotations of around chemical bonds. The likelihood of a of a molecule being in a specific conformation depends on its formation energy and it follows what's known as the Boltzmann distribution.

00:01:21

Speaker

This distribution helps us understand which conformations are more probable at a given temperature. Knowing the most probable or low energy conformations is essential for predicting molecular properties and behaviors, which has significant implications for drug delivery and other applications.

00:01:37

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Now let's dive into traditional methods used to explore these molecular conformations. One of the most accurate approaches is molecular dynamics simulation. This technique involves solving Newtonian equations of motion to simulate the time evolution of a system.

00:01:53

Speaker

By integrating these equations with the forces derived from the system's potential energy, molecular dynamics can provide detailed insights into how molecules move and change over time. However, while molecular dynamics offers high accuracy, it comes with a significant drawback.

00:02:11

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The process involves simulating a vast number of atomic interactions, which can be prohibitively slow, especially for large molecules or when high throughput screening is required. Simplifications to the energy function can reduce computational costs, but at the expense of accuracy.

00:02:31

Speaker

In contrast, cheminformatics methods offer a faster, albeit less detailed, approach to conformer generation. These methods rely on experimental data, chemical rules, and heuristics to generate plausible three-dimensional structures from molecular graphs. Techniques like experimental torsion distance geometry with additional basic knowledge, or ETK-DG, implemented in tools such as RTKIT and commercial software like Omega, are popular for their speed. However, they often lack the precision and generalization needed for complex studies. Enter the era of machine learning. Recent advancements in this field have introduced new methods for generating molecular conformations. Deep learning approaches such as geomole, geodiff, and torsional diffusion have shown promise, especially in handling complex molecular systems. These methods leverage large data sets to train models that can generate molecular conformations more efficiently than traditional methods.

00:03:26

Speaker

Yet, these machine learning approaches have their limitations. Most of them focus on maximizing the likelihood of confirmations within the training dataset, which doesn't always align with the goal of sampling proportionally to the Boltzmann distribution. This is where generative flow networks, or G-flow nets, come into play. G-flow nets were initially introduced for amortized probabilistic interference in high-dimensional discrete spaces.

00:03:55

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Recently, they have been adapted to work with continuous or hybrid spaces, making them highly relevant for molecular conformation generation. The core idea behind G-flow nets is to sample from an unnormalized probability density, which is represented as a reward function over the sample space. Here's a more detailed breakdown of how G-flow nets work. The process begins with a starting state.

00:04:21

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and generates a sequence of updates to transition through various states until a final state or confirmation is reached. This trajectory is governed by a trainable forward policy which defines the probability of moving from one state to the next. Once a trajectory is complete, a reward function that evaluates the final state guiding the training process. G-Flow nets also incorporates a backward policy, which models the probability of transitioning back to a previous state. This addition provides greater flexibility and allows G-Flow nets to model a richer family of distributions over the sample space. For molecular conformation generation, G-flonets focus on sampling torsion angles, which are critical for defining a molecule's shape. The torsion angle is represented as a hypertorus, and G-flonets generate trajectories through the space to explore various conformations. The reward function used is based on the molecular conformation's potential energy, and which helps G-flonets produce div diverse, low-energy conformations.

00:05:21

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To define the reward function, G-flow nets use the potential energy of the molecular conformation, calculated from the sampled torsion angles. This energy is computed using an approximation of quantum mechanical density function theory, DFT.

00:05:39

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Differential energy estimators such as GFN2, XTB, and GFNFF offer varying trade-offs between accuracy and computational cost, impacting the performance of the GPhone app.

00:05:59

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Let's delve into some empirical results that highlight the effectiveness of G-flow nets. in and In initial experiments, G-flow nets were tested on molecules with just two torsion angles, such as alanine dipeptide, ibuprofen, and catorolac. This setup allowed for a detailed analysis of how well G-flow nets could sample from the target distribution and compare their performance against traditional methods like Markov chain monocarlo or MCMC.

00:06:23

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The findings revealed that G-flow nets could accurately reproduce energy surfaces, often outperforming MCMC in some cases. The low dimensional experiments provided valuable insights into how G-flow nets handle sampling and energy estimation, setting the stage for scaling up more complex systems. Moving on to higher dimensional settings, G-flow nets were tested with molecules featuring up to 12 torsion angles. For this part of the study, molecules from GM drugs, G-E-O-M drugs data set, were used. This data includes drug-like molecules with varying numbers of torsion angles and serves as a benchmark for evaluating conformer generation methods.

00:07:07

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And these experiments, GFLONEDs, were compared to several baselines, including MCMC, RDKit, ETK-DG, and a recent approach combining ETK-DG with clustering. These results showed that GFLONEDs could generate confirmations closely matching ground truth data and performed well in sampling from the Boltzmann distribution.

00:07:34

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This indicates that G-flow nets are capable of handling complex high-dimensional molecular systems effectively. Another critical aspect of the ah this research is the choice of energy estimator. Different methods from highly accurate GFN2 XTB to faster but less precise approaches like GFNFF and Torch ANI were evaluated for their impact on performance. The results highlighted that G-Flow NATs, particularly when using the GFN2 XTB estimator, provided high-quality samples and demonstrated strong scalability to higher dimensions. so

00:08:09

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The scalability of G-flow nets was further examined by and ah by analyzing the correlation between the estimated probability of sampling a conformation and its energy. This analysis showed that while correlation declined with increasing torsion angles, it remained relatively high, indicating that G-flow nets continue to sample according to the Boltzmann distribution even in high dimensional spaces.

00:08:30

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To summarize, G4NS represent a significant advancement in the field of molecular conformation generation. Their ability to sample according to the Boltzmann distribution and handle complex high dimensional spaces effectively makes them a powerful tool in computational chemistry and drug discovery.

00:08:50

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By integrating machine learning with molecular dynamics, GFLOW nets offer a scalable and accurate approach to exploring molecular conformations, paving the way for more effective and efficient research in this domain.

00:09:05

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And that wraps up today's deep dive into molecular confirmations and machine learning innovations. We hope you enjoyed this exploration into how G-Flow nets and other cutting-edge techniques are revolutionizing the field. Don't forget to subscribe to Breaking Math Podcast for more insights in the latest scientific and technological advancements. I'm Gabrielle Hesh. And I'm Autumn Feneff. And I look forward to our next episode. Until then, stay curious and keep exploring.