Residue Representations Research Articles

PepNet: an interpretable neural network for anti-inflammatory and antimicrobial peptides prediction using a pre-trained protein language model

Identifying anti-inflammatory peptides (AIPs) and antimicrobial peptides (AMPs) is crucial for the discovery of innovative and effective peptide-based therapies targeting inflammation and microbial infections. However, accurate identification of AIPs and AMPs remains a computational challenge mainly due to limited utilization of peptide sequence information. Here, we propose PepNet, an interpretable neural network for predicting both AIPs and AMPs by applying a pre-trained protein language model to fully utilize the peptide sequence information. It first captures the information of residue arrangements and physicochemical properties using a residual dilated convolution block, and then seizes the function-related diverse information by introducing a residual Transformer block to characterize the residue representations generated by a pre-trained protein language model. After training and testing, PepNet demonstrates great superiority over other leading AIP and AMP predictors and shows strong interpretability of its learned peptide representations. A user-friendly web server for PepNet is freely available at http://liulab.top/PepNet/server.

Intra-Inter Graph Representation Learning for Protein-Protein Binding Sites Prediction.

Graph neural networks have drawn increasing attention and achieved remarkable progress recently due to their potential applications for a large amount of irregular data. It is a natural way to represent protein as a graph. In this work, we focus on protein-protein binding sites prediction between the ligand and receptor proteins. Previous work just simply adopts graph convolution to learn residue representations of ligand and receptor proteins, then concatenates them and feeds the concatenated representation into a fully connected layer to make predictions, losing much of the information contained in complexes and failing to obtain an optimal prediction. In this paper, we present Intra-Inter Graph Representation Learning for protein-protein binding sites prediction (IIGRL). Specifically, for intra-graph learning, we maximize the mutual information between local node representation and global graph summary to encourage node representation to embody the global information of protein graph. Then we explore fusing two separate ligand and receptor graphs as a whole graph and learning affinities between their residues/nodes to propagate information to each other, which could effectively capture inter-protein information and further enhance the discrimination of residue pairs. Extensive experiments on multiple benchmarks demonstrate that the proposed IIGRL model outperforms state-of-the-art methods.

Resonances and residue operators for pseudo-Riemannian hyperbolic spaces

For any pseudo-Riemannian hyperbolic space X over R,C,H or O, we show that the resolvent R(z)=(□−zId)−1 of the Laplace–Beltrami operator −□ on X can be extended meromorphically across the spectrum of □ as a family of operators Cc∞(X)→D′(X). Its poles are called resonances and we determine them explicitly in all cases. For each resonance, the image of the corresponding residue operator in D′(X) forms a representation of the isometry group of X, which we identify with a subrepresentation of a degenerate principal series. Our study includes in particular the case of even functions on de Sitter and Anti-de Sitter spaces.For Riemannian symmetric spaces analogous results were obtained by Miatello–Will and Hilgert–Pasquale. The main qualitative differences between the Riemannian and the non-Riemannian setting are that for non-Riemannian spaces the resolvent can have poles of order two, it can have a pole at the branching point of the covering to which R(z) extends, and the residue representations can be infinite-dimensional.

Residue representations - The rank one case

With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, one can associate a residue representation. The purpose of this paper is to study them. The symmetric space is assumed to have rank-one but the irreducible representation τ of K defining the vector bundle is arbitrary. We give an algorithm that aims at determining if these representations are irreducible, finding their Langlands parameters, their Gelfand-Kirillov dimensions and wave front sets. As an example, we apply this algorithm to the Laplacian of the p-forms in the cases of all the classical real rank-one Lie groups.

Machine learning modeling of family wide enzyme-substrate specificity screens.

Biocatalysis is a promising approach to sustainably synthesize pharmaceuticals, complex natural products, and commodity chemicals at scale. However, the adoption of biocatalysis is limited by our ability to select enzymes that will catalyze their natural chemical transformation on non-natural substrates. While machine learning and in silico directed evolution are well-posed for this predictive modeling challenge, efforts to date have primarily aimed to increase activity against a single known substrate, rather than to identify enzymes capable of acting on new substrates of interest. To address this need, we curate 6 different high-quality enzyme family screens from the literature that each measure multiple enzymes against multiple substrates. We compare machine learning-based compound-protein interaction (CPI) modeling approaches from the literature used for predicting drug-target interactions. Surprisingly, comparing these interaction-based models against collections of independent (single task) enzyme-only or substrate-only models reveals that current CPI approaches are incapable of learning interactions between compounds and proteins in the current family level data regime. We further validate this observation by demonstrating that our no-interaction baseline can outperform CPI-based models from the literature used to guide the discovery of kinase inhibitors. Given the high performance of non-interaction based models, we introduce a new structure-based strategy for pooling residue representations across a protein sequence. Altogether, this work motivates a principled path forward in order to build and evaluate meaningful predictive models for biocatalysis and other drug discovery applications.

An integration of deep learning with feature embedding for protein-protein interaction prediction.

Protein–protein interactions are closely relevant to protein function and drug discovery. Hence, accurately identifying protein–protein interactions will help us to understand the underlying molecular mechanisms and significantly facilitate the drug discovery. However, the majority of existing computational methods for protein–protein interactions prediction are focused on the feature extraction and combination of features and there have been limited gains from the state-of-the-art models. In this work, a new residue representation method named Res2vec is designed for protein sequence representation. Residue representations obtained by Res2vec describe more precisely residue-residue interactions from raw sequence and supply more effective inputs for the downstream deep learning model. Combining effective feature embedding with powerful deep learning techniques, our method provides a general computational pipeline to infer protein–protein interactions, even when protein structure knowledge is entirely unknown. The proposed method DeepFE-PPI is evaluated on the S. Cerevisiae and human datasets. The experimental results show that DeepFE-PPI achieves 94.78% (accuracy), 92.99% (recall), 96.45% (precision), 89.62% (Matthew’s correlation coefficient, MCC) and 98.71% (accuracy), 98.54% (recall), 98.77% (precision), 97.43% (MCC), respectively. In addition, we also evaluate the performance of DeepFE-PPI on five independent species datasets and all the results are superior to the existing methods. The comparisons show that DeepFE-PPI is capable of predicting protein–protein interactions by a novel residue representation method and a deep learning classification framework in an acceptable level of accuracy. The codes along with instructions to reproduce this work are available from https://github.com/xal2019/DeepFE-PPI.

A Scaling-Assisted Signed Integer Comparator for the Balanced Five-Moduli Set RNS $\{2^{n}-1, 2^{n}, 2^{n}+ 1, 2^{n+1}- 1, 2^{n-1}- 1\}$

Signed integer comparison occurs prevalently in process control, sorting, address decoding, and conditional branching. Existing algorithms for magnitude comparison in RNS are based either on parity check or partial reverse conversion. With separately designed RNS sign detectors, they can also be used to compare residue representations of signed integers. In this paper, a radically different approach to this problem is proposed for the five-moduli set $\{2^{n}- 1, 2^{n}, 2^{n}+ 1, 2^{n+1}- 1, 2^{n-1}-1\}$ . The signs of the operands in comparison, as well as their difference are detected after scaling by a factor of ( $2^{2n}- 1$ )( $2^{n-1}- 1$ ). The resulting finite series in the composite modulus channel is further factored into parallel carry-saved additions in the existing mod $2^{n}$ and mod $2^{n+1}- 1$ modulus channels, thus reducing the sizes of modulo adders from $5n$ bits to $n$ and $n + 1$ bits. Upon detecting the signs of the operands and their difference, the relation is inference with a small fraction of logic gates. Our synthesis results in 65-nm CMOS technology show that the proposed design is 36.9% smaller, 7.6% faster, and 45.5% more energy efficient than the best Chinese remainder theorem-II-based magnitude comparator and at least 12.9% smaller, 7.3% faster, and 20.8% more energy efficient than the best reverse-conversion-based implementation of signed integer comparator for the same five-moduli set.

New Algorithm for Signed Integer Comparison in $\{2^{n+k},2^{n}-1,2^{n}+1,2^{n\pm 1}-1\}$ and Its Efficient Hardware Implementation

Sign detection and magnitude comparison are two difficult operations in Residue Number System (RNS). Existing algorithms mainly tackle either problem independently. Magnitude comparison in RNS is typically solved by parity check or transcoding the residues into weighted representation. Comparison of signed integers in residue domain is supplemented by separately designed RNS sign detector. In this paper, a radically different quantization approach for comparing signed integers in the four-moduli supersets, $S_{1}\equiv\{2^{n+k},2^{n}-1,2^{n}+1,2^{n+1}-1\}$ and $S_{2}\equiv\{2^{n+k},2^{n}-1,2^{n}+1,2^{n-1}-1\}$ , is proposed. The dynamic range of the target moduli set is quantized into equal divisions, and the ranks of the divisions resided by the integers in comparison are identified and compared from their residue representations. The sign of a residue representation can be directly extracted from the most significant bit of its rank, or with simple logic function if it resides in the middle rank. Comparing with the best existing signed magnitude comparator applicable to these two moduli sets, our synthesis results on 65 nm CMOS technology show that the proposed design is at least 22.48% smaller, 19.08% faster and 27.66% more energy-efficient for $S_{1}$ and 18.75% smaller, 16.41% faster and 23.30% more energy-efficient for $S_{2}$ .

Multifunction Residue Architectures for Cryptography

A design methodology for incorporating Residue Number System (RNS) and Polynomial Residue Number System (PRNS) in Montgomery modular multiplication in GF(p) or GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ) respectively, as well as a VLSI architecture of a dual-field residue arithmetic Montgomery multiplier are presented in this paper. An analysis of input/output conversions to/from residue representation, along with the proposed residue Montgomery multiplication algorithm, reveals common multiply-accumulate data paths both between the converters and between the two residue representations. A versatile architecture is derived that supports all operations of Montgomery multiplication in GF(p) and GF(2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> ), input/output conversions, Mixed Radix Conversion (MRC) for integers and polynomials, dual-field modular exponentiation and inversion in the same hardware. Detailed comparisons with state-of-the-art implementations prove the potential of residue arithmetic exploitation in dual-field modular multiplication.

Exploring Residue Component Contributions to Dynamical Network Models of Allostery

Allosteric regulation in biological systems is of considerable interest given the vast number of proteins that exhibit such behavior. Network models obtained from molecular dynamics simulations have been shown to be powerful tools for the analysis of allostery. In this work, different coarse-grain residue representations (nodes) are used together with a dynamical network model to investigate models of allosteric regulation. This model assumes that allosteric signals are dependent on positional correlations of protein substituents, as determined through molecular dynamics simulations, and uses correlated motion to generate a signaling weight between two given nodes. We examine four types of network models using different node representations in Cartesian coordinates: the (i) residue alpha-carbons, (ii) sidechain center of mass, (iii) backbone center of mass, and the entire (iv) residue center of mass. All correlations are filtered by a dynamic contact map that defines the allowable interactions between nodes based on physical proximity. We apply the four models to imidazole glycerol phosphate synthase (IGPS), which provides a well-studied experimental framework in which allosteric communication is known to persist across disparate protein domains (e.g. a protein dimer interface). IGPS is modeled as a network of nodes and weighted edges. Optimal allosteric pathways are traced using the Floyd Warshall algorithm for weighted networks, and community analysis (a form of hierarchical clustering) is performed using the Girvan-Newman algorithm. Our results show that dynamical information encoded in the residue center of mass must be included in order to detect residues that are experimentally known to play a role in allosteric communication for IGPS. More broadly, this new method may be useful for predicting pathways of allosteric communication for any biomolecular system in atomic detail.

A molecular model for Illinois No. 6 Argonne Premium coal: Moving toward capturing the continuum structure

A large-scale molecular model for Illinois No. 6 Argonne Premium coal is generated based on an automated construction approach in an effort to move toward capturing the continuum structure. The model contains 50,789atoms within 728 molecules and is the largest, most complex coal representation constructed to-date. The aromatic ring size distribution was based on multiple high-resolution transmission electron microscope (HRTEM) lattice fringe micrographs and was duplicated with automated construction protocols (Fringe3D) in molecular modeling space. Additional structural data was obtained from the abundant literature assessing this Argonne Premium coal. Organic oxygen, nitrogen, and sulfur functionalities were incorporated primarily into the polyaromatic structures according to X-ray photoelectron spectroscopy and X-ray adsorption near-edge structure spectroscopy data. Aliphatic carbons were in the form of cross-links (bridges and loops) and pendant alkyl groups based on the combination of laser desorption ionization mass spectrometry (LDIMS), ruthenium ion catalyzed oxidation, elemental analysis, and NMR data in good agreement with the literature. Bound and bulk water was also included. Construction of the coal molecules was performed by use of Perl scripts developed in Materials Studio to eliminate personal bias and improve the accuracy and the scale of the structure generated. The large-scale model captured a broad and continuous molecular weight distribution in accordance with LDIMS data here ranging from 100 to 2850Da, enabling inclusion of structural diversity to capture a portion of the continuum structure. A theoretical pyridine extraction yield, determined by a group contribution approach, was in agreement with the experimental value. The extract and residue representations were generated from the large-scale Illinois coal model and showed consistency with NMR, elemental analysis and LDIMS trends. The distribution of heteroatomic classes and double bond equivalents was also well-defined experimentally based on electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry. These data further constrain the molecular weight of extractable material and was consistent with limited pyridine extractability and model heteroatom classes. Future work will be well served by staying within the limits established by the approach and increasing the structural diversity (sampling frequency through increased scale) to better capture the complex nature of coal structural diversity, i.e., the continuum.

Electrostatic control of occupancy and valence selectivity in a charged nanometer‐sized cylindrical pore

AbstractSimple analytical calculations of the electrostatic energy for systems composed of positive charges confined to the axis of a negatively charged cylindrical pore are used to explore the role of electrostatic forces in the problems of ion permeation, ion occupancy and valence selectivity in biological ion channels. Considering the effect of finite length of the charged pore as an alternative to fixed charged residue representations, we show that ion occupancy and ion configurations in the pore are governed by two parameters: (i) the magnitude of the uniform surface charge density of the pore and (ii) the pore (diameter‐to‐length) aspect ratio through the interplay between favorable interaction of the mobile ions with the pore interior and unfavorable interaction among the ions themselves. The pore with an overall surface charge of ‐2e (representing a potassium channel) is found to favor occupancy by three K+ ions over two K+ ions at low aspect ratio but not at high. The pore with surface charge ‐4e (representing a calcium channel) favors occupancy by two lateral Ca2+ ions and one central Na+ ion over two symmetrically positioned Ca2+ ions at a low aspect ratio, but this preference is reversed at a higher aspect ratio. These results allow us to speculate that Ca2+ block of sodium current in the calcium channel is due to lower electrostatic energy for the Na+ ‐ Ca2+ ‐ Na+ configuration than for the Na+ ‐ Na+ ‐ Na+ configuration, and that the yet lower energy of the Ca2+ ‐ Ca2+ configuration would facilitate Ca2+ relief of Ca2+ block.

Protein cutoff scanning: A comparative analysis of cutoff dependent and cutoff free methods for prospecting contacts in proteins

In this study, we carried out a comparative analysis between two classical methodologies to prospect residue contacts in proteins: the traditional cutoff dependent (CD) approach and cutoff free Delaunay tessellation (DT). In addition, two alternative coarse-grained forms to represent residues were tested: using alpha carbon (CA) and side chain geometric center (GC). A database was built, comprising three top classes: all alpha, all beta, and alpha/beta. We found that the cutoff value at about 7.0 A emerges as an important distance parameter. Up to 7.0 A, CD and DT properties are unified, which implies that at this distance all contacts are complete and legitimate (not occluded). We also have shown that DT has an intrinsic missing edges problem when mapping the first layer of neighbors. In proteins, it may produce systematic errors affecting mainly the contact network in beta chains with CA. The almost-Delaunay (AD) approach has been proposed to solve this DT problem. We found that even AD may not be an advantageous solution. As a consequence, in the strict range up to 7.0 A, the CD approach revealed to be a simpler, more complete, and reliable technique than DT or AD. Finally, we have shown that coarse-grained residue representations may introduce bias in the analysis of neighbors in cutoffs up to 6.8 A, with CA favoring alpha proteins and GC favoring beta proteins. This provides an additional argument pointing to the value of 7.0 A as an important lower bound cutoff to be used in contact analysis of proteins.

Use of surface area computations to describe atom-atom interactions.

Accessible surface (ASA) and atomic contact (ACA) areas are powerful tools for protein structure analysis. However, their use for analysis purposes could be extended if a relationship between them and protein stability could be found. At present, this is the case only for ASAs, which have been used to assess the contribution of the hydrophobic effect to protein stability. In the present work we study whether there is a relationship between atomic contact areas and the free energy associated to atom-atom interactions. We utilise a model in which the contribution of atomic interactions to protein stability is expressed as a linear function of the accessible surface area buried between atom pairs. We assess the validity of this hypothesis, using a set of 124 lysozyme mutants (Matthews, 1995, Adv Protein Chem, 249-278) for which both the X-ray structure and the experimental stability are known. We tested this assumption for residue representations with increasing numbers of atom types. Our results indicate that for simple residue representations, with only 4 to 5 atom types, there is not a clear linear relationship between stability and buried accessible area. However, this relationship is observed for representations with 6 to 9 atom types, where gross heterogeneities in the atom type definition are eliminated. Finally, we also study a version of the linear model in which the atom- atom interactions are represented utilising a simple function for the buried accessible area, which may be useful for protein structure prediction studies.

RNS architectures for the implementation of the `diagonal function'

The `diagonal function' is a new tool for performing non-modular operations in the Residue Number System (RNS). It is defined from the RNS to the integers and exploits the geometrical disposal in multi-dimensional discrete spaces of integers in residue representations. This paper presents a new class of RNS architectures for the effective implementation of the `diagonal function'. The architectures are general, since they do not impose constraints on the set of moduli, and flexible, since they can be best suited depending on specific system requirements. The superiority of the new architectures with respect to traditional approaches is shown in terms of waste of hardware and time delay.

Parallel Multiplication in GF(2^k) usingPolynomial Residue Arithmetic

We present a novel method of parallelization of the multiplication operation in \GF(2^k) for an arbitrary value of k and arbitrary irreducible polynomial n(x) generating the field. The parallel algorithm is based on polynomial residue arithmetic, and requires that we find L pairwise relatively prime modulim_i(x) such that the degree of the product polynomialM(x)=m_1(x)m_2(x)\cdots m_L(x) is at least 2k. The parallel algorithm receives the residue representations of the input operands (elements of the field) and produces the result in its residue form, however, it is guaranteed that the degree of this polynomial is less than k and it is properly reduced by the generating polynomial n(x), i.e., it is an element of the field. In order to perform the reductions, we also describe a new table lookup based polynomial reduction method.

A new residue arithmetic error correction scheme

Automatic detection and correction of errors in the residue number system involves the conversion of residue representations to integers and base extension. The residue number system is generally restricted to moduli that are pairwise relatively prime. In this paper we consider error detection and correction using a moduli set with common factors. A method to construct a moduli set that leads to simplified error detection and correction is presented. Error detection can now be performed by computing residues in parallel. Error correction does not involve base extension any more. It is also shown that, removing all restrictions on the moduli set, leads to more complex error detection/correction algorithms.

Base conversion in residue number systems

We are concerned in this paper with the representation of an integer in a (multiple-modulus) residue number system and, in particular, with an algorithm for changing the base vector of the residue number system. Szabo and Tanaka [1, p.47] describe such an algorithm when each modulus of the second base vector is relatively prime to each modulus of the first base vector. However, we show that a much simpler algorithm exists if we allow the moduli of the second base vector to have factors in common with the moduli of the first base vector (even though the moduli of the second base vector are pairwise relatively prime among themselves). Since the algorithm involves the use of "associated" residue and mixed-radix representations for integers, Section 2 contains an elementary survey of the terminology, notation, and theory behind these two types of representation. Section 3 contains the proofs of the basic theorems upon which our algorithm for residue base conversion is based along with a description of the algorithm. It also contains illustrative examples which demonstrate the power of the algorithm. In this paper we lay the foundation for a subsequent paper in which we propose procedures for extending single-precision residue arithmetic to multiple-precision residue arithmetic.

General Division in the Symmetric Residue Number System

In the residue number system, the arithmetic operations of addition, subtraction, and multiplication are executed in the same period of time without the need for interpositional carry. There is a hope for high-speed operation if residue arithmetic is used for digital computation. The division process, which is one of the difficulties of this operation, is developed in the symmetric residue number system. The method described here is iterative in nature and requires the availability of two tables of the symmetric residue representations of a certain kind of integer. An algorithm for general division is derived, and the way of choosing the entries which are used to find a quotient is discussed.

The Residue Number System

A novel number system called the residue number system is developed from the linear congruence viewpoint. The residue number system is of particular interest because the arithmetic operations of addition, subtraction and multiplication may be executed in the same period of time without the need for carry. The main difficulties of the residue code pertain to the determination of the relative magnitude of two residue representations, and to the division process. A discussion of the arithmetic operations and the conversion process required to convert from a residue code to a weighted code is given. It is concluded that in its present state the residue code is probably not suitable for general purpose computation but is suitable for a special class of control problems. Further research in both components and arithmetic is required if a residue code suitable for general purpose computation is to be obtained.