Geometric learning of knot topology

Sleiman, Joseph Lahoud; Conforto, Filippo; Fosado, Yair Augusto Gutierrez; Michieletto, Davide

doi:10.1039/d3sm01199b

Cited by 4 publications

(9 citation statements)

References 46 publications

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“…Other open knot classification schemes exist but do not satisfy all requirements. Sleiman et al [26] showed a neural network trained on writhe representations of knots can track a knot's topology as it unties, but it cannot be identified with known invariants and lacks smooth interpolation.…”

Section: • For Closed Chains It Should Reproduce Values Of Establishe...mentioning

confidence: 99%

“…We simulate polymer knots using a model used to simulate topologically complex polymers in previous works [13,26]. We use a parameterization that models DNA at the low ionic strengths used in fluorescence experiments, in which the persistence length is ten times the effective width of the molecule [38], and the contour length is ten to twenty persistence lengths.…”

Section: Langevin Dynamics Simulationmentioning

confidence: 99%

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Revisiting the second Vassiliev (In)variant for polymer knots

Klotz,

Estabrooks

2024

J. Phys. A: Math. Theor.

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Knots in open strands such as ropes, fibers, and polymers, cannot typically be described in the language of knot theory, which characterizes only closed curves in space. Simulations of open knotted polymer chains, often parameterized to DNA, typically perform a closure operation and calculate the Alexander polynomial to assign a knot topology. This is limited in scenarios where the topology is less well-defined, for example when the chain is in the process of untying or is strongly confined. Here, we use a discretized version of the Second Vassiliev Invariant for open chains to analyze Langevin Dynamics simulations of untying and strongly confined polymer chains. We demonstrate that the Vassiliev parameter can accurately and efficiently characterize the knotted state of polymers, providing additional information not captured by a single-closure Alexander calculation. We discuss its relative strengths and weaknesses compared to standard techniques, and argue that it is a useful and powerful tool for analyzing polymer knot simulations.

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Section: • For Closed Chains It Should Reproduce Values Of Establishe...mentioning

confidence: 99%

Section: Langevin Dynamics Simulationmentioning

confidence: 99%

Revisiting the second Vassiliev (In)variant for polymer knots

Klotz,

Estabrooks

2024

J. Phys. A: Math. Theor.

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“…From the other perspective, deep learning models have demonstrated exceptional abilities in recognizing and classifying patterns. − By training these models on extensive data sets containing random curve , and protein-like chains with known knot types, it becomes feasible to create reliable algorithms for automating the identification and classification of knots within these intricate structures. Braghetto et al and Sleiman et al demonstrate the effectiveness of long short-term memory (LSTM) based on neural network (NN) in accurately discerning knot types in highly geometrically complex entangled structures. Moreover, Sleiman et al have in fact shown indirectly that these methods can work for open curves since their approach is able to locate the knotted portion.…”

Section: Introductionmentioning

confidence: 99%

“…Braghetto et al and Sleiman et al demonstrate the effectiveness of long short-term memory (LSTM) based on neural network (NN) in accurately discerning knot types in highly geometrically complex entangled structures. Moreover, Sleiman et al have in fact shown indirectly that these methods can work for open curves since their approach is able to locate the knotted portion.…”

Section: Introductionmentioning

confidence: 99%

“…Even the faster Alexander polynomial, which has a time complexity of O ( n 3 ), where n is the number of crossings in a given projection, is still inefficient for proteins that possess complex geometric representations. Employing ML techniques for knot recognition provides other opportunities. − If it were possible to build such an ML that detects knots on proteins, for example, one could use ML models to filter doubtful cases, e.g., by fixing a very high probability threshold to pick unknots, exclude them, and analyze through polynomials only the presumably knotted configurations.…”

Section: Introductionmentioning

confidence: 99%

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Knots and θ-Curves Identification in Polymeric Chains and Native Proteins Using Neural Networks

Bruno da Silva,

Gabrovšek,

Korpacz

et al. 2024

Macromolecules

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Entanglement in proteins is a fascinating structural motif that is neither easy to detect via traditional methods nor fully understood. Recent advancements in AI-driven models have predicted that millions of proteins could potentially have a nontrivial topology. Herein, we have shown that long short-term memory (LSTM)-based neural networks (NN) architecture can be applied to detect, classify, and predict entanglement not only in closed polymeric chains but also in polymers and protein-like structures with open knots, actual protein configurations, and also θ-curves motifs. The analysis revealed that the LSTM model can predict classes (up to the 61 knot) accurately for closed knots and open polymeric chains, resembling real proteins. In the case of open knots formed by protein-like structures, the model displays robust prediction capabilities with an accuracy of 99%. Moreover, the LSTM model with proper features, tested on hundreds of thousands of knotted and unknotted protein structures with different architectures predicted by AlphaFold 2, can distinguish between the trivial and nontrivial topology of the native state of the protein with an accuracy of 93%.

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Machine Learning in Soft Matter: From Simulations to Experiments

Zhang,

Gong,

Jiang

2024

Adv Funct Materials

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Soft matter with diverse functionalities that are easily designable has fascinated tremendous research interests in the past several decades. Nevertheless, the inherent confluence of time and length scale ubiquitous in soft matter immensely complicates the elucidation of the structure–property relationship and thereby severely impedes the function exploration of soft materials. Recently, the emergent machine learning (ML) techniques open new paradigms in property prediction and molecular design of functional materials, due to their extraordinarily distinguished performance in the aspect of trend identity and pattern extraction from data, and objective optimization by accelerating the guided search in high‐dimensional spaces. This review exclusively focuses on the current state‐of‐the‐art progress in the development of ML techniques applied in the realms of soft matter, ranging from coarse‐grained simulations to theoretical prediction on the structural formation and macroscopic properties, as well as the optimization and algorithm‐aided design in experiments. Finally, an outlook on the challenges and opportunities for this rapidly evolving field is discussed.

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Geometric learning of knot topology

Abstract: Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish...

Cited by 4 publications

References 46 publications

Revisiting the second Vassiliev (In)variant for polymer knots

Revisiting the second Vassiliev (In)variant for polymer knots

Knots and θ-Curves Identification in Polymeric Chains and Native Proteins Using Neural Networks

Machine Learning in Soft Matter: From Simulations to Experiments

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