Transferable kriging machine learning models for the multipolar electrostatics of helical deca-alanine

2016

J Comput Chem

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Continuing the development of the FFLUX, a multipolar polarizable force field driven by machine learning, we present a modern approach to atom-typing and building transferable models for predicting atomic properties in proteins. Amino acid atomic charges in a peptide chain respond to the substitution of a neighboring residue and this response can be categorized in a manner similar to atom-typing. Using a machine learning method called kriging, we are able to build predictive models for an atom that is defined, not only by its local environment, but also by its neighboring residues, for a minimal additional computational cost. We found that prediction errors were up to 11 times lower when using a model specific to the correct group of neighboring residues, with a mean prediction of $0.0015 au. This finding suggests that atoms in a force field should be defined by more than just their immediate atomic neighbors. When comparing an atom in a single alanine to an analogous atom in a deca-alanine helix, the mean difference in charge is 0.026 au. Meanwhile, the same difference between a trialanine and a deca-alanine helix is only 0.012 au. When compared to deca-alanine models, the transferable models are up to 20 times faster to train, and require significantly less ab initio calculation, providing a practical route to modeling large biological systems.

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Toward amino acid typing for proteins in FFLUX

Fletcher¹,

2016

J Comput Chem

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“…More precisely, FFLUX needs to be trained by a sufficient number of relevant geometries such that it can interpolate a property of a given atom of interest between the data learnt. The selected [12] machine learning method is Kriging [13], which has been tested successfully on a variety of systems, including ethanol [14], (peptide-capped) alanine [15], the microhydrated sodium ion [15], N-methylacetamide (NMA) and histidine [16], the four aromatic (peptidecapped) amino acids [17], all naturally occurring amino acids [18], helical deca-alanines [19,20], water clusters [21], cholesterol [22] and carbohydrates [23]. This collective work shows an existing proof-of-concept that kriging models generate sufficiently accurate atomic property models, and they do this directly from the coordinates of the surrounding atoms.…”

Section: Introductionmentioning

confidence: 99%

Accurate prediction of the energetics of weakly bound complexes using the machine learning method kriging

Maxwell

2017

Struct Chem

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Here, we extend the system energy prediction approach used in the force field FFLUX (Maxwell et al. Theor Chem Acc 135:195, 2016) to complexes bound by weak intermolecular interactions. The investigation features the first application of the approach to bound complex systems, additionally challenged by investigating complexes held together only weakly, through either a predominant dispersion contribution, or through mixed dispersion and hydrogen-bonding. Our approach uses the interacting quantum atoms (IQA) energy partitioning scheme to obtain the intra-atomic, E inter energies are mapped to the positions of the nuclear coordinates through the machine learning method kriging to build atomic energy models. A model's quality is established through its ability to accurately predict the atomic and molecular energies of atoms in an external test set. Mean absolute error percentages (MAE%) of 1.5, 1.5, 1.6, 1.0, 2.6 and 1.7% are obtained in recovering the molecular energy for ammonia…benzene, water…benzene, HCN…benzene, methane…benzene, stackedbenzene (C 2h ) dimer and T-benzene (C 2v ) dimer complexes, respectively.

“…As the strength of interaction between two atoms usually decreases as a function of increasing distance, their results 15 are intuitive, and that method can be viewed as similar to the application of the cutoff radius commonly applied in molecular dynamics simulations, beyond which interactions are considered negligible. Thus, the reliance of machine learning models in general, and kriging in particular, on a fixed number of inputs (i.e., surrounding atoms) instead of a flexible number of inputs determined by interaction distance, must be seen as a limitation of their application to chemical systems.…”

Section: Introductionmentioning

confidence: 99%

“…At the core of FFLUX is the machine learning method "kriging" or "Gaussian Process Regression," 12 which has repeatedly demonstrated its versatility, accurately predicting atomic and molecular properties for amino acids, 13 carbohydrates, 14 oligopeptides, 15 and water clusters. 16 Developed from a geostatistical background, 17 and applied to computer experiments by Sacks et al, 18 then Jones, 19,20 kriging is an interpolating predictor that relates a set of outputs to a corresponding set of inputs in order to predict a given property of interest.…”

Section: Introductionmentioning

confidence: 99%

Kriging atomic properties with a variable number of inputs

Davie

Pasquale

The Journal of Chemical Physics

2016

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A new force field called FFLUX uses the machine learning technique kriging to capture the link between the properties (energies and multipole moments) of topological atoms (i.e., output) and the coordinates of the surrounding atoms (i.e., input). Here we present a novel, general method of applying kriging to chemical systems that do not possess a fixed number of (geometrical) inputs. Unlike traditional kriging methods, which require an input system to be of fixed dimensionality, the method presented here can be readily applied to molecular simulation, where an interaction cutoff radius is commonly used and the number of atoms or molecules within the cutoff radius is not constant. The method described here is general and can be applied to any machine learning technique that normally operates under a fixed number of inputs. In particular, the method described here is also useful for interpolating methods other than kriging, which may suffer from difficulties stemming from identical sets of inputs corresponding to different outputs or input biasing. As a demonstration, the new method is used to predict 54 energetic and electrostatic properties of the central water molecule of a set of 5000, 4 Å radius water clusters, with a variable number of water molecules. The results are validated against equivalent models from a set of clusters composed of a fixed number of water molecules (set to ten, i.e., decamers) and against models created by using a naïve method of treating the variable number of inputs problem presented. Results show that the 4 Å water cluster models, utilising the method presented here, return similar or better kriging models than the decamer clusters for all properties considered and perform much better than the truncated models. C 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license