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DOE OSTI2014

Structural and Functional Consequences of Circular Permutation on the Active Site of Old Yellow Enzyme

Circular permutation of the NADPH-dependent oxidoreductase Old Yellow Enzyme from Saccharomyces pastorianus (OYE1) can significantly enhance the enzyme’s catalytic performance. Termini relocation into four regions of the protein (sectors I–IV) near the active site has proven effective in altering enzyme function. To better understand the structural consequences and rationalize the observed functional gains in these OYE1 variants, we selected representatives from sectors I–III for further characterization by biophysical methods and X-ray crystallography. These investigations not only show trends in enzyme stability and quaternary structure as a function of termini location but also provide a possible explanation for the catalytic gains in our top-performing OYE variant (new N-terminus at residue 303; sector III). Crystallographic analysis indicates that termini relocation into sector III affects the loop β6 region (amino acid positions: 290–310) of OYE1, which forms a lid over the active site. Peptide backbone cleavage greatly enhances local flexibility, effectively converting the loop into a tether and consequently increasing the environmental exposure of the active site. Interestingly, such an active site remodeling does not negatively impact the enzyme’s activity and stereoselectivity; neither does it perturb the conformation of other key active site residues with the exception of Y375. These observations were confirmed in truncation experiments, deleting all residues of the loop β6 region in our OYE variant. Intrigued by the finding that circular permutation leaves most of the key catalytic residues unchanged, we also tested OYE permutants for possible additive or synergistic effects of amino acid substitutions. Distinct functional changes in these OYE variants were detected upon mutations at W116, known in native OYE1 to cause inversion of diastereoselectivity for (S)-carvone reduction. In conclusion, our findings demonstrate the contribution of loop β6 toward determining the stereoselectivity of OYE1, an important insight for future OYE engineering efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Semi-supervised permutation invariant particle-level anomaly detection

The development of analysis methods to distinguish potential beyond the Standard Model phenomena in a model-agnostic way can significantly enhance the discovery reach in collider experiments. However, the typical machine learning (ML) algorithms employed for this task require fixed length and ordered inputs that break the natural permutation invariance in collision events. To address this, a semi-supervised anomaly detection tool is presented that takes a variable number of particle-level inputs and leverages a signal model to encode this information into a permutation invariant, event-level representation via supervised training with a Particle Flow Network (PFN). Data events are then encoded into this representation and given as input to an autoencoder for unsupervised ANomaly deTEction on particLe flOw latent sPacE (ANTELOPE), classifying anomalous events based on a low-level and permutation invariant input modeling. Performance of the ANTELOPE architecture is evaluated on simulated samples of hadronic processes in a high energy collider experiment, showing good capability to distinguish disparate models of new physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chemical systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atmospheric chemistry, and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the number of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. Here, the parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphysical unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems

A rigorous, general, and simple method to fit global and permutation invariant potential energy surfaces (PESs) using neural networks (NNs) is discussed. This so-called permutation invariant polynomial neural network (PIP-NN) method imposes permutation symmetry by using in its input a set of symmetry functions based on PIPs. For systems with more than three atoms, it is shown that the number of symmetry functions in the input vector needs to be larger than the number of internal coordinates in order to include both the primary and secondary invariant polynomials. This PIP-NN method is successfully demonstrated in three atom-triatomic reactive systems, resulting in full-dimensional global PESs with average errors on the order of meV. These PESs are used in full-dimensional quantum dynamical calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Potential energy surface fitting by a statistically localized, permutationally invariant, local interpolating moving least squares method for the many-body potential: Method and application to N{sub 4}

Fitting potential energy surfaces to analytic forms is an important first step for efficient molecular dynamics simulations. Here, we present an improved version of the local interpolating moving least squares method (L-IMLS) for such fitting. Our method has three key improvements. First, pairwise interactions are modeled separately from many-body interactions. Second, permutational invariance is incorporated in the basis functions, using permutationally invariant polynomials in Morse variables, and in the weight functions. Third, computational cost is reduced by statistical localization, in which we statistically correlate the cutoff radius with data point density. We motivate our discussion in this paper with a review of global and local least-squares-based fitting methods in one dimension. Then, we develop our method in six dimensions, and we note that it allows the analytic evaluation of gradients, a feature that is important for molecular dynamics. The approach, which we call statistically localized, permutationally invariant, local interpolating moving least squares fitting of the many-body potential (SL-PI-L-IMLS-MP, or, more simply, L-IMLS-G2), is used to fit a potential energy surface to an electronic structure dataset for N{sub 4}. We discuss its performance on the dataset and give directions for further research, including applications to trajectory calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Unifying the rotational and permutation symmetry of nuclear spin states: Schur-Weyl duality in molecular physics

In modern physics and chemistry concerned with many-body systems, one of the mainstays is identical-particle-permutation symmetry. In particular, both the intra-molecular dynamics of a single molecule and the inter-molecular dynamics associated, for example, with reactive molecular collisions are strongly affected by selection rules originating in nuclear-permutation symmetry operations being applied to the total internal wavefunctions, including nuclear spin, of the molecules involved. We propose here a general tool to determine coherently the permutation symmetry and the rotational symmetry (associated with the group of arbitrary rotations of the entire molecule in space) of molecular wavefunctions, in particular the nuclear-spin functions. Thus far, these two symmetries were believed to be mutually independent and it has even been argued that under certain circumstances, it is impossible to establish a one-to-one correspondence between them. However, using the Schur-Weyl duality theorem we show that the two types of symmetry are inherently coupled. In addition, we use the ingenious representation-theory technique of Young tableaus to represent the molecular nuclear-spin degrees of freedom in terms of well-defined mathematical objects. This simplifies the symmetry classification of the nuclear wavefunction even for large molecules. Also, the application to reactive collisions is very straightforward and provides a much simplified approach to obtaining selection rules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Five-point functions and the permutation group 𝑆 5

Five-point functions and five-body wave functions play an important role in many areas of nuclear and particle physics, e.g., in 2 →3 scattering processes, in the five-gluon vertex, or in the study of pentaquarks. In this work we consider the permutation group 𝑆 5 to facilitate the description of such objects. We work out the multiplets transforming under irreducible representations of 𝑆 5 and provide compact formulas allowing one to cast the permutations of an object 𝑓 12345 into combinations with definite permutation symmetry. We also give the explicit expressions for the irreducible multiplet products. We consider several practical applications as examples: We arrange the four-momenta and Lorentz invariants of a five-point function into the multiplet structure, we work out the color tensors of the five-gluon vertex in the multiplet notation, and we discuss applications for five-body wave functions like those of pentaquarks.

Bethe-Salpeter equation↗

DOE OSTI2024

High-dimensional and permutation invariant anomaly detection

Methods for anomaly detection of new physics processes are often limited to low-dimensional spaces due to the difficulty of learning high-dimensional probability densities. Particularly at the constituent level, incorporating desirable properties such as permutation invariance and variable-length inputs becomes difficult within popular density estimation methods. In this work, we introduce a permutation-invariant density estimator for particle physics data based on diffusion models, specifically designed to handle variable-length inputs. We demonstrate the efficacy of our methodology by utilizing the learned density as a permutation-invariant anomaly detection score, effectively identifying jets with low likelihood under the background-only hypothesis. To validate our density estimation method, we investigate the ratio of learned densities and compare to those obtained by a supervised classification algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1989

A family of permutations for concurrent factorization of block tridiagonal matrices

The inherent strong seriality of closely coupled systems is circumvented by defining a family of permutations for reordering equation sets whose matrix of coefficients is Hermitian block tridiagonal. The authors show how these permutations can be used to achieve relatively high concurrency in the Cholesky factorization of banded systems at the expense of introducing limited extra computations due to fill-in terms in the factors. Directed graphs are developed for the concurrent factorization of the transformed matrix of coefficients by the Cholesky algorithm. Expressions for speedup and efficiency are derived in terms of parameters of the permutation, set of equations, and machine architecture.

Utku, Senol↗

DOE OSTI2019

CRISPR-Cas9 Circular Permutants as Programmable Scaffolds for Genome Modification

The ability to engineer natural proteins is pivotal to a future, pragmatic biology. CRISPR proteins have revolutionized genome modification, yet the CRISPR-Cas9 scaffold is not ideal for fusions or activation by cellular triggers. Here in this paper, we show that a topological rearrangement of Cas9 using circular permutation provides an advanced platform for RNA-guided genome modification and protection. Through systematic interrogation, we find that protein termini can be positioned adjacent to bound DNA, offering a straightforward mechanism for strategically fusing functional domains. Additionally, circular permutation enabled protease-sensing Cas9s (ProCas9s), a unique class of single-molecule effectors possessing programmable inputs and outputs. ProCas9s can sense a wide range of proteases, and we demonstrate that ProCas9 can orchestrate a cellular response to pathogen-associated protease activity. Together, these results provide a toolkit of safer and more efficient genome-modifying enzymes and molecular recorders for the advancement of precision genome engineering in research, agriculture, and biomedicine.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Developing a circularly permuted variant of Renilla luciferase as a bioluminescent sensor for measuring Caspase-9 activity in the cell-free and cell-based systems

Highlights: • A luciferase based biosensor for measuring caspase-9 activity has been constructed using circular permutation strategy. • The designed biosensor detects the caspase-9 activity in a cell-free coupled assay system. • The designed biosensor can be implemented as a cell-based biosensor to detect cellular caspase-9 activity and apoptosis. Biosensors and whole cell biosensors consisting of biological molecules and living cells can sense a special stimulus on a living system and convert it to a measurable signal. A major group of them are the bioluminescent sensors derived from luciferases. This type of biosensors has a broad application in molecular biology and imaging systems. In this project, a luciferase-based biosensor for detecting and measuring caspase-9 activity is designed and constructed using the circular permutation strategy. The spectroscopic method results reveal changes in the biosensor structure. Additionally, its activity is examined in a cell-free coupled assay system. Afterward, the biosensor is utilized for measuring the cellular caspase-9 activity upon apoptosis induction in a cancer cell line. In following the gene of biosensor is sub-cloned into a eukaryotic vector and transfected to HEK293T cell line and then its activity is measured upon apoptosis induction in the presence and absence of a caspase-9 inhibitor. The obtained results show that the designed biosensor detects the caspase-9 activity in the cell-free and cell-based systems.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Quantum and quasi-classical dynamics of the OH + CO → H + CO{sub 2} reaction on a new permutationally invariant neural network potential energy surface

A permutationally invariant global potential energy surface for the HOCO system is reported by fitting a larger number of high-level ab initio points using the newly proposed permutation invariant polynomial-neural network method. The small fitting error (∼5 meV) indicates a faithful representation of the potential energy surface over a large configuration space. Full-dimensional quantum and quasi-classical trajectory studies of the title reaction were performed on this potential energy surface. While the results suggest that the differences between this and an earlier neural network fits are small, discrepancies with state-to-state experimental data remain significant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Permutation-invariant distance between atomic configurations

We present a permutation-invariant distance between atomic configurations, defined through a functional representation of atomic positions. This distance enables us to directly compare different atomic environments with an arbitrary number of particles, without going through a space of reduced dimensionality (i.e., fingerprints) as an intermediate step. Moreover, this distance is naturally invariant through permutations of atoms, avoiding the time consuming associated minimization required by other common criteria (like the root mean square distance). Finally, the invariance through global rotations is accounted for by a minimization procedure in the space of rotations solved by Monte Carlo simulated annealing. A formal framework is also introduced, showing that the distance we propose verifies the property of a metric on the space of atomic configurations. Two examples of applications are proposed. The first one consists in evaluating faithfulness of some fingerprints (or descriptors), i.e., their capacity to represent the structural information of a configuration. The second application concerns structural analysis, where our distance proves to be efficient in discriminating different local structures and even classifying their degree of similarity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Permutation invariant polynomial neural network based diabatic ansatz for the ( E + A ) × ( e + a ) Jahn–Teller and Pseudo-Jahn–Teller systems

In this work, the permutation invariant polynomial neural network (PIP-NN) approach is employed to construct a quasi-diabatic Hamiltonian for system with non-Abelian symmetries. It provides a flexible and compact NN-based diabatic ansatz from the related approach of Williams, Eisfeld, and co-workers. The example of $H^3_+$ is studied, which is an (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller system. The PIP-NN diabatic ansatz is based on the symmetric polynomial expansion of Viel and Eisfeld, the coefficients of which are expressed with neural network functions that take permutation-invariant polynomials as input. This PIP-NN-based diabatic ansatz not only preserves the correct symmetry but also provides functional flexibility to accurately reproduce ab initio electronic structure data, thus resulting in excellent fits. Further, the adiabatic energies, energy gradients, and derivative couplings are well reproduced. A good description of the local topology of the conical intersection seam is also achieved. Therefore, this diabatic ansatz completes the PIP-NN based representation of DPEM with correct symmetries and will enable us to diabatize even more complicated systems with complex symmetries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Random permutations fix a worst case for cyclic coordinate descent

Abstract Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through the components of $x$ in order; randomized (RCD), in which the component to update is selected randomly and independently at each iteration; and random-permutations cyclic (RPCD), which differs from CCD only in that a random permutation is applied to the variables at the start of each cycle. Known convergence guarantees are weaker for CCD and RPCD than for RCD, though in most practical cases, computational performance is similar among all these variants. There is a certain type of quadratic function for which CCD is significantly slower than for RCD; a recent paper by Sun & Ye (2016, Worst-case complexity of cyclic coordinate descent: $O(n^2)$ gap with randomized version. Technical Report. Stanford, CA: Department of Management Science and Engineering, Stanford University. arXiv:1604.07130) has explored the poor behavior of CCD on functions of this type. The RPCD approach performs well on these functions, even better than RCD in a certain regime. This paper explains the good behavior of RPCD with a tight analysis.

Lee, Ching-pei↗

DOE OSTI2017

Application of permutation entropy method in the analysis of chaotic, noisy, and chaotic noisy series

We have considered a permutation entropy method for analyzing chaotic, noisy, and chaotic noisy series. We have introduced the concept of permutation entropy from a survey of some features of information entropy (Shannon entropy), described the algorithm for its calculation, and indicated the advantages of this approach in the analysis of time series; the application of this method in the analysis of various model systems and experimental data has also been demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement

We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1984

Permutation codes for the Laplacian source

Permutation codes for the Laplacian source are developed. The performance of these codes is evaluated and compared with other quantizers and the rate-distortion function. It is shown that there is a bit-rate region in which the permutation codes outperform certain single-sample quantizers.

Townes, S. A.↗