Oscillatory Neural Network-Based Ising Machine Using 2D Memristors

Neural networks are increasingly used to solve optimization problems in various fields, including operations research, design automation, and gene sequencing. However, these networks face challenges due to the nondeterministic polynomial time (NP)-hard issue, which results in exponentially increasing computational complexity as the problem size grows. Conventional digital hardware struggles with the von Neumann bottleneck, the slowdown of Moore's law, and the complexity arising from heterogeneous system design. Two-dimensional (2D) memristors offer a potential solution to these hardware challenges, with their in-memory computing, decent scalability, and rich dynamic behaviors. In this study, we explore the use of nonvolatile 2D memristors to emulate synapses in a discrete-time Hopfield neural network, enabling the network to solve continuous optimization problems, like finding the minimum value of a quadratic polynomial, and tackle combinatorial optimization problems like Max-Cut. Additionally, we coupled volatile memristor-based oscillators with nonvolatile memristor synapses to create an oscillatory neural network-based Ising machine, a continuous-time analog dynamic system capable of solving combinatorial optimization problems including Max-Cut and map coloring through phase synchronization. Our findings demonstrate that 2D memristors have the potential to significantly enhance the efficiency, compactness, and homogeneity of integrated Ising machines, which is useful for future advances in neural networks for optimization problems.

Startle: A star homoplasy approach for CRISPR-Cas9 lineage tracing

CRISPR-Cas9-based genome editing combined with single-cell sequencing enables the tracing of the history of cell divisions, or cellular lineage, in tissues and whole organisms. Although standard phylogenetic approaches may be applied to reconstruct cellular lineage trees from this data, the unique features of the CRISPR-Cas9 editing process motivate the development of specialized models that describe the evolution of CRISPR-Cas9-induced mutations. Here, we introduce the "star homoplasy" evolutionary model that constrains a phylogenetic character to mutate at most once along a lineage, capturing the "non-modifiability" property of CRISPR-Cas9 mutations. We derive a combinatorial characterization of star homoplasy phylogenies and use this characterization to develop an algorithm, "Startle", that computes a maximum parsimony star homoplasy phylogeny. We demonstrate that Startle infers more accurate phylogenies on simulated lineage tracing data compared with existing methods and finds parsimonious phylogenies with fewer metastatic migrations on lineage tracing data from mouse metastatic lung adenocarcinoma.

HOGVAX: Exploiting epitope overlaps to maximize population coverage in vaccine design with application to SARS-CoV-2

The efficacy of epitope vaccines depends on the included epitopes as well as the probability that the selected epitopes are presented by the major histocompatibility complex (MHC) proteins of a vaccinated individual. Designing vaccines that effectively immunize a high proportion of the population is challenging because of high MHC polymorphism, diverging MHC-peptide binding affinities, and physical constraints on epitope vaccine constructs. Here, we present HOGVAX, a combinatorial optimization approach for epitope vaccine design. To optimize population coverage within the constraint of limited vaccine construct space, HOGVAX employs a hierarchical overlap graph (HOG) to identify and exploit overlaps between selected peptides and explicitly models the structure of linkage disequilibrium in the MHC. In a SARS-CoV-2 case study, we demonstrate that HOGVAX-designed vaccines contain substantially more epitopes than vaccines built from concatenated peptides and predict vaccine efficacy in over 98% of the population with high numbers of presented peptides in vaccinated individuals.

Shortest Hyperpaths in Directed Hypergraphs for Reaction Pathway Inference

Signaling and metabolic pathways, which consist of chains of reactions that produce target molecules from source compounds, are cornerstones of cellular biology. Properly modeling the reaction networks that represent such pathways requires directed hypergraphs, where each molecule or compound maps to a vertex, and each reaction maps to a hyperedge directed from its set of input reactants to its set of output products. Inferring the most likely series of reactions that produces a given set of targets from a given set of sources, where for each reaction its reactants are produced by prior reactions in the series, corresponds to finding a shortest hyperpath in a directed hypergraph, which is NP-complete. We give the first exact algorithm for general shortest hyperpaths that can find provably optimal solutions for large, real-world, reaction networks. In particular, we derive a novel graph-theoretic characterization of hyperpaths, which we leverage in a new integer linear programming formulation of shortest hyperpaths that for the first time handles cycles, and develop a cutting-plane algorithm that can solve this integer linear program to optimality in practice. Through comprehensive experiments over all of the thousands of instances from the standard Reactome and NCI-PID reaction databases, we demonstrate that our cutting-plane algorithm quickly finds an optimal hyperpath-inferring the most likely pathway-with a median running time of under 10 seconds, and a maximum time of less than 30 minutes, even on instances with thousands of reactions. We also explore for the first time how well hyperpaths infer true pathways, and show that shortest hyperpaths accurately recover known pathways, typically with very high precision and recall. Source code implementing our cutting-plane algorithm for shortest hyperpaths is available free for research use in a new tool called Mmunin.

Quantum annealing-based clustering of single cell RNA-seq data

Cluster analysis is a crucial stage in the analysis and interpretation of single-cell gene expression (scRNA-seq) data. It is an inherently ill-posed problem whose solutions depend heavily on hyper-parameter and algorithmic choice. The popular approach of K-means clustering, for example, depends heavily on the choice of K and the convergence of the expectation-maximization algorithm to local minima of the objective. Exhaustive search of the space for multiple good quality solutions is known to be a complex problem. Here, we show that quantum computing offers a solution to exploring the cost function of clustering by quantum annealing, implemented on a quantum computing facility offered by D-Wave [1]. Out formulation extracts minimum vertex cover of an affinity graph to sub-sample the cell population and quantum annealing to optimise the cost function. A distribution of low-energy solutions can thus be extracted, offering alternate hypotheses about how genes group together in their space of expressions.

TIVC: An Efficient Local Search Algorithm for Minimum Vertex Cover in Large Graphs

The minimum vertex cover (MVC) problem is a canonical NP-hard combinatorial optimization problem aiming to find the smallest set of vertices such that every edge has at least one endpoint in the set. This problem has extensive applications in cybersecurity, scheduling, and monitoring link failures in wireless sensor networks (WSNs). Numerous local search algorithms have been proposed to obtain "good" vertex coverage. However, due to the NP-hard nature, it is challenging to efficiently solve the MVC problem, especially on large graphs. In this paper, we propose an efficient local search algorithm for MVC called TIVC, which is based on two main ideas: a 3-improvements (TI) framework with a tiny perturbation and edge selection strategy. We conducted experiments on real-world large instances of a massive graph benchmark. Compared with three state-of-the-art MVC algorithms, TIVC shows superior performance in accuracy and possesses a remarkable ability to identify significantly smaller vertex covers on many graphs.

Decision trees: from efficient prediction to responsible AI

This article provides a birds-eye view on the role of decision trees in machine learning and data science over roughly four decades. It sketches the evolution of decision tree research over the years, describes the broader context in which the research is situated, and summarizes strengths and weaknesses of decision trees in this context. The main goal of the article is to clarify the broad relevance to machine learning and artificial intelligence, both practical and theoretical, that decision trees still have today.

On Single-Objective Sub-Graph-Based Mutation for Solving the Bi-Objective Minimum Spanning Tree Problem

We contribute to the efficient approximation of the Pareto-set for the classical NP-hard multi-objective minimum spanning tree problem (moMST) adopting evolutionary computation. More precisely, by building upon preliminary work, we analyse the neighborhood structure of Pareto-optimal spanning trees and design several highly biased sub-graph-based mutation operators founded on the gained insights. In a nutshell, these operators replace (un)connected sub-trees of candidate solutions with locally optimal sub-trees. The latter (biased) step is realized by applying Kruskal's single-objective MST algorithm to a weighted sum scalarization of a sub-graph. We prove runtime complexity results for the introduced operators and investigate the desirable Pareto-beneficial property. This property states that mutants cannot be dominated by their parent. Moreover, we perform an extensive experimental benchmark study to showcase the operator's practical suitability. Our results confirm that the subgraph based operators beat baseline algorithms from the literature even with severely restricted computational budget in terms of function evaluations on four different classes of complete graphs with different shapes of the Pareto-front.

Speeding Up the Structural Analysis of Metabolic Network Models Using the Fredman-Khachiyan Algorithm B

The problem of computing the Elementary Flux Modes (EFMs) and Minimal Cut Sets (MCSs) of metabolic network is a fundamental one in metabolic networks. A key insight is that they can be understood as a dual pair of monotone Boolean functions (MBFs). Using this insight, this computation reduces to the question of generating from an oracle a dual pair of MBFs. If one of the two sets (functions) is known, then the other can be computed through a process known as dualization. Fredman and Khachiyan provided two algorithms, which they called simply A and B that can serve as an engine for oracle-based generation or dualization of MBFs. We look at efficiencies available in implementing their algorithm B, which we will refer to as FK-B. Like their algorithm A, FK-B certifies whether two given MBFs in the form of Conjunctive Normal Form and Disjunctive Normal Form are dual or not, and in case of not being dual it returns a conflicting assignment (CA), that is, an assignment that makes one of the given Boolean functions True and the other one False. The FK-B algorithm is a recursive algorithm that searches through the tree of assignments to find a CA. If it does not find any CA, it means that the given Boolean functions are dual. In this article, we propose six techniques applicable to the FK-B and hence to the dualization process. Although these techniques do not reduce the time complexity, they considerably reduce the running time in practice. We evaluate the proposed improvements by applying them to compute the MCSs from the EFMs in the 19 small- and medium-sized models from the BioModels database along with 4 models of biomass synthesis in Escherichia coli that were used in an earlier computational survey Haus et al. (2008).

Organic Memristor-Based Flexible Neural Networks with Bio-Realistic Synaptic Plasticity for Complex Combinatorial Optimization

Hardware neural networks with mechanical flexibility are promising next-generation computing systems for smart wearable electronics. Several studies have been conducted on flexible neural networks for practical applications; however, developing systems with complete synaptic plasticity for combinatorial optimization remains challenging. In this study, the metal-ion injection density is explored as a diffusive parameter of the conductive filament in organic memristors. Additionally, a flexible artificial synapse with bio-realistic synaptic plasticity is developed using organic memristors that have systematically engineered metal-ion injections, for the first time. In the proposed artificial synapse, short-term plasticity (STP), long-term plasticity, and homeostatic plasticity are independently achieved and are analogous to their biological counterparts. The time windows of the STP and homeostatic plasticity are controlled by the ion-injection density and electric-signal conditions, respectively. Moreover, stable capabilities for complex combinatorial optimization in the developed synapse arrays are demonstrated under spike-dependent operations. This effective concept for realizing flexible neuromorphic systems for complex combinatorial optimization is an essential building block for achieving a new paradigm of wearable smart electronics associated with artificial intelligent systems.

Seriation Using Tree-penalized Path Length

Given a sample of n data points and an n by n dissimilarity matrix, data seriation methods produce a linear ordering of the objects, putting similar objects nearby in the ordering. One may visualize the reordered dissimilarity matrix with a heat map and thus understand the structure of the data, while still displaying the full matrix of dissimilarities. Good orderings produce heat maps that are easy to read and allow for clear interpretation. We consider two popular seriation methods, minimizing path length by solving the Traveling Salesman Problem (TSP), and Optimal Leaf Ordering (OLO), which minimizes path length among all orderings consistent with a given tree structure. Learning from the strengths and weaknesses of the two methods, we introduce a new hybrid seriation method, tree-penalized Path Length (tpPL). The objective is a linear combination of path length and the extent of violations of the tree structure, with a parameter that transitions the optimal paths smoothly from TSP to OLO. We present a detailed study over 44 synthetic datasets which are designed to bring out the strengths and weaknesses of the three methods, finding that the hybrid nature of tpPL enables it to overcome the weaknesses of TSP and OLO.

Radionuclide Reduction by Combinatorial Optimization of Microbial Extracellular Electron Transfer with a Physiologically Adapted Regulatory Platform

Microbial extracellular electron transfer (EET) is the basis for many microbial processes involved in element geochemical recycling, bioenergy harvesting, and bioremediation, including the technique for remediating U(VI)-contaminated environments. However, the low EET rate hinders its full potential from being fulfilled. The main challenge for engineering microbial EET is the difficulty in optimizing cell resource allocation for EET investment and basic metabolism and the optimal coordination of the different EET pathways. Here, we report a novel combinatorial optimization strategy with a physiologically adapted regulatory platform. Through exploring the physiologically adapted regulatory elements, a 271.97-fold strength range, autonomous, and dynamic regulatory platform was established for Shewanella oneidensis, a prominent electrochemically active bacterium. Both direct and mediated EET pathways are modularly reconfigured and tuned at various intensities with the regulatory platform, which were further assembled combinatorically. The optimal combinations exhibit up to 16.12-, 4.51-, and 8.40-fold improvements over the control in the maximum current density (1009.2 mA/m²) of microbial electrolysis cells and the voltage output (413.8 mV) and power density (229.1 mW/m²) of microbial fuel cells. In addition, the optimal strains exhibited up to 6.53-fold improvement in the radionuclide U(VI) removal efficiency. This work provides an effective and feasible approach to boost microbial EET performance for environmental applications.

A Universal Antigen-Ranking Method to Design Personalized Vaccines Targeting Neoantigens against Melanoma

Background: The main purpose of this article is to introduce a universal mathematics-aided vaccine design method against malignant melanoma based on neoantigens. The universal method can be adapted to the mutanome of each patient so that a specific candidate vaccine can be tailored for the corresponding patient. Methods: We extracted the 1134 most frequent mutations in melanoma, and we associated each of them to a vector with 10 components estimated with different bioinformatics tools, for which we found an aggregated value according to a set of weights, and then we ordered them in decreasing order of the scores. Results: We prepared a universal table of the most frequent mutations in melanoma ordered in decreasing order of viability to be used as candidate vaccines, so that the selection of a set of appropriate peptides for each particular patient can be easily and quickly implemented according to their specific mutanome and transcription profile. Conclusions: We have shown that the techniques that are commonly used for the design of personalized anti-tumor vaccines against malignant melanoma can be adapted for the design of universal rankings of neoantigens that originate personalized vaccines when the mutanome and transcription profile of specific patients is considered, with the consequent savings in time and money, shortening the design and production time.

Speeding Task Allocation Search for Reconfigurations in Adaptive Distributed Embedded Systems Using Deep Reinforcement Learning

A Critical Adaptive Distributed Embedded System (CADES) is a group of interconnected nodes that must carry out a set of tasks to achieve a common goal, while fulfilling several requirements associated with their critical (e.g., hard real-time requirements) and adaptive nature. In these systems, a key challenge is to solve, in a timely manner, the combinatorial optimization problem involved in finding the best way to allocate the tasks to the available nodes (i.e., the task allocation) taking into account aspects such as the computational costs of the tasks and the computational capacity of the nodes. This problem is not trivial and there is no known polynomial time algorithm to find the optimal solution. Several studies have proposed Deep Reinforcement Learning (DRL) approaches to solve combinatorial optimization problems and, in this work, we explore the application of such approaches to the task allocation problem in CADESs. We first discuss the potential advantages of using a DRL-based approach over several heuristic-based approaches to allocate tasks in CADESs and we then demonstrate how a DRL-based approach can achieve similar results for the best performing heuristic in terms of optimality of the allocation, while requiring less time to generate such allocation.

A Clustering-Enhanced Memetic Algorithm for the Quadratic Minimum Spanning Tree Problem

The quadratic minimum spanning tree problem (QMSTP) is a spanning tree optimization problem that considers the interaction cost between pairs of edges arising from a number of practical scenarios. This problem is NP-hard, and therefore there is not a known polynomial time approach to solve it. To find a close-to-optimal solution to the problem in a reasonable time, we present for the first time a clustering-enhanced memetic algorithm (CMA) that combines four components, i.e., (i) population initialization with clustering mechanism, (ii) a tabu-based nearby exploration phase to search nearby local optima in a restricted area, (iii) a three-parent combination operator to generate promising offspring solutions, and (iv) a mutation operator using Lévy distribution to prevent the population from premature. Computational experiments are carried on 36 benchmark instances from 3 standard sets, and the results show that the proposed algorithm is competitive with the state-of-the-art approaches. In particular, it reports improved upper bounds for the 25 most challenging instances with unproven optimal solutions, while matching the best-known results for all but 2 of the remaining instances. Additional analysis highlights the contribution of the clustering mechanism and combination operator to the performance of the algorithm.

Quantum annealing for industry applications: introduction and review

Quantum annealing (QA) is a heuristic quantum optimization algorithm that can be used to solve combinatorial optimization problems. In recent years, advances in quantum technologies have enabled the development of small- and intermediate-scale quantum processors that implement the QA algorithm for programmable use. Specifically, QA processors produced by D-Wave systems have been studied and tested extensively in both research and industrial settings across different disciplines. In this paper we provide a literature review of the theoretical motivations for QA as a heuristic quantum optimization algorithm, the software and hardware that is required to use such quantum processors, and the state-of-the-art applications and proofs-of-concepts that have been demonstrated using them. The goal of our review is to provide a centralized and condensed source regarding applications of QA technology. We identify the advantages, limitations, and potential of QA for both researchers and practitioners from various fields.

Cost-Efficient Coverage of Wastewater Networks by IoT Monitoring Devices

Wireless sensor networks are fundamental for technologies related to the Internet of Things. This technology has been constantly evolving in recent times. In this paper, we consider the problem of minimising the cost function of covering a sewer network. The cost function includes the acquisition and installation of electronic components such as sensors, batteries, and the devices on which these components are installed. The problem of sensor coverage in the sewer network or a part of it is presented in the form of a mixed-integer programming model. This method guarantees that we obtain an optimal solution to this problem. A model was proposed that can take into account either only partial or complete coverage of the considered sewer network. The CPLEX solver was used to solve this problem. The study was carried out for a practically relevant network under selected scenarios determined by artificial and realistic datasets.

A New Frequency Analysis Operator for Population Improvement in Genetic Algorithms to Solve the Job Shop Scheduling Problem

Job Shop Scheduling is currently one of the most addressed planning and scheduling optimization problems in the field. Due to its complexity, as it belongs to the NP-Hard class of problems, meta-heuristics are one of the most commonly used approaches in its resolution, with Genetic Algorithms being one of the most effective methods in this category. However, it is well known that this meta-heuristic is affected by phenomena that worsen the quality of its population, such as premature convergence and population concentration in regions of local optima. To circumvent these difficulties, we propose, in this work, the use of a guidance operator responsible for modifying ill-adapted individuals using genetic material from well-adapted individuals. We also propose, in this paper, a new method of determining the genetic quality of individuals using genetic frequency analysis. Our method is evaluated over a wide range of modern GAs and considers two case studies defined by well-established JSSP benchmarks in the literature. The results show that the use of the proposed operator assists in managing individuals with poor fitness values, which improves the population quality of the algorithms and, consequently, leads to obtaining better results in the solution of JSSP instances. Finally, the use of the proposed operator in the most elaborate GA-like method in the literature was able to reduce its mean relative error from 1.395% to 0.755%, representing an improvement of 45.88%.

Domain Knowledge-Based Evolutionary Reinforcement Learning for Sensor Placement

Reducing pollutant detection time based on a reasonable sensor combination is desirable. Clean drinking water is essential to life. However, the water supply network (WSN) is a vulnerable target for accidental or intentional contamination due to its extensive geographic coverage, multiple points of access, backflow, infrastructure aging, and designed sabotage. Contaminants entering WSN are one of the most dangerous events that may cause sickness or even death among people. Using sensors to monitor the water quality in real time is one of the most effective ways to minimize negative consequences on public health. However, it is a challenge to deploy a limited number of sensors in a large-scale WSN. In this study, the sensor placement problem (SPP) is modeled as a sequential decision optimization problem, then an evolutionary reinforcement learning (ERL) algorithm based on domain knowledge is proposed to solve SPP. Extensive experiments have been conducted and the results show that our proposed algorithm outperforms meta-heuristic algorithms and deep reinforcement learning (DRL).

Solving Generalized Polyomino Puzzles Using the Ising Model

In the polyomino puzzle, the aim is to fill a finite space using several polyomino pieces with no overlaps or blanks. Because it is an NP-complete combinatorial optimization problem, various probabilistic and approximated approaches have been applied to find solutions. Several previous studies embedded the polyomino puzzle in a QUBO problem, where the original objective function and constraints are transformed into the Hamiltonian function of the simulated Ising model. A solution to the puzzle is obtained by searching for a ground state of Hamiltonian by simulating the dynamics of the multiple-spin system. However, previous methods could solve only tiny polyomino puzzles considering a few combinations because their Hamiltonian designs were not efficient. We propose an improved Hamiltonian design that introduces new constraints and guiding terms to weakly encourage favorable spins and pairs in the early stages of computation. The proposed model solves the pentomino puzzle represented by approximately 2000 spins with >90% probability. Additionally, we extended the method to a generalized problem where each polyomino piece could be used zero or more times and solved it with approximately 100% probability. The proposed method also appeared to be effective for the 3D polycube puzzle, which is similar to applications in fragment-based drug discovery.

ScalpelSig Designs Targeted Genomic Panels from Data to Detect Activity of Mutational Signatures

Over the past decade, a promising line of cancer research has utilized machine learning to mine statistical patterns of mutations in cancer genomes for information. Recent work shows that these statistical patterns, commonly referred to as "mutational signatures," have diverse therapeutic potential as biomarkers for cancer therapies. However, translating this potential into reality is hindered by limited access to sequencing in the clinic. Almost all methods for mutational signature analysis (MSA) rely on whole genome or whole exome sequencing data, while sequencing in the clinic is typically limited to small gene panels. To improve clinical access to MSA, we considered the question of whether targeted panels could be designed for the purpose of mutational signature detection. Here we present ScalpelSig, to our knowledge the first algorithm that automatically designs genomic panels optimized for detection of a given mutational signature. The algorithm learns from data to identify genome regions that are particularly indicative of signature activity. Using a cohort of breast cancer genomes as training data, we show that ScalpelSig panels substantially improve accuracy of signature detection compared to baselines. We find that some ScalpelSig panels even approach the performance of whole exome sequencing, which observes over 10 × as much genomic material. We test our algorithm under a variety of conditions, showing that its performance generalizes to another dataset of breast cancers, to smaller panel sizes, and to lesser amounts of training data.

Metabolic engineering of Escherichia coli for efficient osmotic stress-free production of compatible solute hydroxyectoine

Compatible solutes are key for the ability of halophilic bacteria to resist high osmotic stress. They have received wide attention from researchers for their excellent osmotic protection properties. Hydroxyectoine is a particularly important compatible solute, but its production by microbes faces several challenges, including low titer/yield, the presence of the byproduct ectoine, and the requirement of high salinity. Here, we aimed to metabolically engineer Escherichia coli to efficiently produce hydroxyectoine in the absence of osmotic stress without accumulating the byproduct ectoine. First, combinatorial optimization of the expression strength of key genes in the ectoine synthesis module and hydroxyectoine synthesis module was conducted. After optimization of the expression of these genes, 12.12 g/L hydroxyectoine and 0.24 g/L ectoine were obtained at 36 h in shake-flask fermentation with the addition of the co-substrate α-ketoglutarate. Further optimization of the addition of α-ketoglutarate achieved the sole production of hydroxyectoine (i.e., no ectoine accumulation), indicating that the supply of α-ketoglutarate is critically important for sole hydroxyectoine production. Finally, quorum sensing-based auto-regulation of intracellular α-ketoglutarate pool was implemented as an alternative to α-ketoglutarate addition by coupling the expression of sucA with the esaI/esaR circuit, which led to 14.93 g/L hydroxyectoine with a unit cell yield of 1.678 g/g and no ectoine accumulation in the absence of osmotic stress. This is the highest reported titer of sole hydroxyectoine production under salinity-free fermentation to date.

Bi-Level Coordinated Merging of Connected and Automated Vehicles at Roundabouts

Traditional uncoordinated traffic flows in a roundabout can lead to severe traffic congestion, travel delay, and the increased fuel consumption of vehicles. An interesting way to mitigate this would be through cooperative control of connected and automated vehicles (CAVs). In this paper, we propose a novel solution, which is a roundabout control system (RCS), for CAVs to attain smooth and safe traffic flows. The RCS is essentially a bi-level framework, consisting of higher and lower levels of control, where in the higher level, vehicles in the entry lane approaching the roundabout will be made to form clusters based on traffic flow volume, and in the lower level, the vehicles’ optimal sequences and roundabout merging times are calculated by solving a combinatorial optimization problem using a receding horizon control (RHC) approach. The proposed RCS aims to minimize the total time taken for all approaching vehicles to enter the roundabout, whilst minimally affecting the movement of circulating vehicles. Our developed strategy ensures fast optimization, and can be implemented in real-time. Using microscopic simulations, we demonstrate the effectiveness of the RCS, and compare it to the current traditional roundabout system (TRS) for various traffic flow scenarios. From the results, we can conclude that the proposed RCS produces significant improvement in traffic flow performance, in particular for the average velocity, average fuel consumption, and average travel time in the roundabout.

Studying the History of Tumor Evolution from Single-Cell Sequencing Data by Exploring the Space of Binary Matrices

Single-cell sequencing (SCS) data have great potential in reconstructing the evolutionary history of tumors. Rapid advances in SCS technology in the past decade were followed by the design of various computational methods for inferring trees of tumor evolution. Some of the earliest methods were based on the direct search in the space of trees with the goal of finding the maximum likelihood tree. However, it can be shown that instead of searching directly in the tree space, we can perform a search in the space of binary matrices and obtain maximum likelihood tree directly from the maximum likelihood matrix. The potential of the latter tree search strategy has recently been recognized by different research groups and several related methods were published in the past 2 years. Here we provide a review of the theoretical background of these methods and a detailed discussion, which are largely missing in the available publications, of the correlation between the two tree search strategies. We also discuss each of the existing methods based on the search in the space of binary matrices and summarize the best-known single-cell DNA sequencing data sets, which can be used in the future for assessing performance on real data of newly developed methods.

Genome-Scale Screening and Combinatorial Optimization of Gene Overexpression Targets to Improve Cadmium Tolerance in Saccharomyces cerevisiae

Heavy metal contamination is an environmental issue on a global scale. Particularly, cadmium poses substantial threats to crop and human health. Saccharomyces cerevisiae is one of the model organisms to study cadmium toxicity and was recently engineered as a cadmium hyperaccumulator. Therefore, it is desirable to overcome the cadmium sensitivity of S. cerevisiae via genetic engineering for bioremediation applications. Here we performed genome-scale overexpression screening for gene targets conferring cadmium resistance in CEN.PK2-1c, an industrial S. cerevisiae strain. Seven targets were identified, including CAD1 and CUP1 that are known to improve cadmium tolerance, as well as CRS5, NRG1, PPH21, BMH1, and QCR6 that are less studied. In the wild-type strain, cadmium exposure activated gene transcription of CAD1, CRS5, CUP1, and NRG1 and repressed PPH21, as revealed by real-time quantitative PCR analyses. Furthermore, yeast strains that contained two overexpression mutations out of the seven gene targets were constructed. Synergistic improvement in cadmium tolerance was observed with episomal co-expression of CRS5 and CUP1. In the presence of 200 μM cadmium, the most resistant strain overexpressing both CAD1 and NRG1 exhibited a 3.6-fold improvement in biomass accumulation relative to wild type. This work provided a new approach to discover and optimize genetic engineering targets for increasing cadmium resistance in yeast.

Iterated local search with partition crossover for computational protein design

Structure-based computational protein design (CPD) refers to the problem of finding a sequence of amino acids which folds into a specific desired protein structure, and possibly fulfills some targeted biochemical properties. Recent studies point out the particularly rugged CPD energy landscape, suggesting that local search optimization methods should be designed and tuned to easily escape local minima attraction basins. In this article, we analyze the performance and search dynamics of an iterated local search (ILS) algorithm enhanced with partition crossover. Our algorithm, PILS, quickly finds local minima and escapes their basins of attraction by solution perturbation. Additionally, the partition crossover operator exploits the structure of the residue interaction graph in order to efficiently mix solutions and find new unexplored basins. Our results on a benchmark of 30 proteins of various topology and size show that PILS consistently finds lower energy solutions compared to Rosetta fixbb and a classic ILS, and that the corresponding sequences are mostly closer to the native.

Graph Neural Networks for Maximum Constraint Satisfaction

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for all binary constraint satisfaction problems. Training is unsupervised, and it is sufficient to train on relatively small instances; the resulting networks perform well on much larger instances (at least 10-times larger). We experimentally evaluate our approach for a variety of problems, including Maximum Cut and Maximum Independent Set. Despite being generic, we show that our approach matches or surpasses most greedy and semi-definite programming based algorithms and sometimes even outperforms state-of-the-art heuristics for the specific problems.

A Hybrid Genetic-Hierarchical Algorithm for the Quadratic Assignment Problem

In this paper, we present a hybrid genetic-hierarchical algorithm for the solution of the quadratic assignment problem. The main distinguishing aspect of the proposed algorithm is that this is an innovative hybrid genetic algorithm with the original, hierarchical architecture. In particular, the genetic algorithm is combined with the so-called hierarchical (self-similar) iterated tabu search algorithm, which serves as a powerful local optimizer (local improvement algorithm) of the offspring solutions produced by the crossover operator of the genetic algorithm. The results of the conducted computational experiments demonstrate the promising performance and competitiveness of the proposed algorithm.

Predicted Cellular Immunity Population Coverage Gaps for SARS-CoV-2 Subunit Vaccines and Their Augmentation by Compact Peptide Sets

Subunit vaccines induce immunity to a pathogen by presenting a component of the pathogen and thus inherently limit the representation of pathogen peptides for cellular immunity-based memory. We find that severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) subunit peptides may not be robustly displayed by the major histocompatibility complex (MHC) molecules in certain individuals. We introduce an augmentation strategy for subunit vaccines that adds a small number of SARS-CoV-2 peptides to a vaccine to improve the population coverage of pathogen peptide display. Our population coverage estimates integrate clinical data on peptide immunogenicity in convalescent COVID-19 patients and machine learning predictions. We evaluate the population coverage of 9 different subunits of SARS-CoV-2, including 5 functional domains and 4 full proteins, and augment each of them to fill a predicted coverage gap.

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Clinical data and machine learning predict SARS-CoV-2 peptide-HLA immunogenicity

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Human population coverage gaps of COVID-19 subunit vaccines are predicted

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Subunit augmentation improves vaccine population coverage for cellular immunity

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Subunit-free peptide vaccines are predicted to have high population coverage

A Modified Genetic Algorithm with Local Search Strategies and Multi-Crossover Operator for Job Shop Scheduling Problem

It is not uncommon for today’s problems to fall within the scope of the well-known class of NP-Hard problems. These problems generally do not have an analytical solution, and it is necessary to use meta-heuristics to solve them. The Job Shop Scheduling Problem (JSSP) is one of these problems, and for its solution, techniques based on Genetic Algorithm (GA) form the most common approach used in the literature. However, GAs are easily compromised by premature convergence and can be trapped in a local optima. To address these issues, researchers have been developing new methodologies based on local search schemes and improvements to standard mutation and crossover operators. In this work, we propose a new GA within this line of research. In detail, we generalize the concept of a massive local search operator; we improved the use of a local search strategy in the traditional mutation operator; and we developed a new multi-crossover operator. In this way, all operators of the proposed algorithm have local search functionality beyond their original inspirations and characteristics. Our method is evaluated in three different case studies, comprising 58 instances of literature, which prove the effectiveness of our approach compared to traditional JSSP solution methods.

An Adaptive Optimization Spiking Neural P System for Binary Problems

Optimization Spiking Neural P System (OSNPS) is the first membrane computing model to directly derive an approximate solution of combinatorial problems with a specific reference to the 0/1 knapsack problem. OSNPS is composed of a family of parallel Spiking Neural P Systems (SNPS) that generate candidate solutions of the binary combinatorial problem and a Guider algorithm that adjusts the spiking probabilities of the neurons of the P systems. Although OSNPS is a pioneering structure in membrane computing optimization, its performance is competitive with that of modern and sophisticated metaheuristics for the knapsack problem only in low dimensional cases. In order to overcome the limitations of OSNPS, this paper proposes a novel Dynamic Guider algorithm which employs an adaptive learning and a diversity-based adaptation to control its moving operators. The resulting novel membrane computing model for optimization is here named Adaptive Optimization Spiking Neural P System (AOSNPS). Numerical result shows that the proposed approach is effective to solve the 0/1 knapsack problems and outperforms multiple various algorithms proposed in the literature to solve the same class of problems even for a large number of items (high dimensionality). Furthermore, case studies show that a AOSNPS is effective in fault sections estimation of power systems in different types of fault cases: including a single fault, multiple faults and multiple faults with incomplete and uncertain information in the IEEE 39 bus system and IEEE 118 bus system.

Computationally Optimized SARS-CoV-2 MHC Class I and II Vaccine Formulations Predicted to Target Human Haplotype Distributions

We present a combinatorial machine learning method to evaluate and optimize peptide vaccine formulations for SARS-CoV-2. Our approach optimizes the presentation likelihood of a diverse set of vaccine peptides conditioned on a target human-population HLA haplotype distribution and expected epitope drift. Our proposed SARS-CoV-2 MHC class I vaccine formulations provide 93.21% predicted population coverage with at least five vaccine peptide-HLA average hits per person (≥ 1 peptide: 99.91%) with all vaccine peptides perfectly conserved across 4,690 geographically sampled SARS-CoV-2 genomes. Our proposed MHC class II vaccine formulations provide 97.21% predicted coverage with at least five vaccine peptide-HLA average hits per person with all peptides having an observed mutation probability of ≤ 0.001. We provide an open-source implementation of our design methods (OptiVax), vaccine evaluation tool (EvalVax), as well as the data used in our design efforts here: https://github.com/gifford-lab/optivax.

Switching Circuit Optimization for Matrix Gradient Coils

Matrix gradient coils with up to 84 coil elements were recently introduced for magnetic resonance imaging. Ideally, each element is driven by a dedicated amplifier, which may be technically and financially infeasible. Instead, several elements can be connected in series (called a “cluster”) and driven by a single amplifier. In previous works, a set of clusters, called a “configuration,” was sought to approximate a target field shape. Because a magnetic resonance pulse sequence requires several distinct field shapes, a mechanism to switch between configurations is needed. This can be achieved by a hypothetical switching circuit connecting all terminals of all elements with each other and with the amplifiers. For a predefined set of configurations, a switching circuit can be designed to require only a limited amount of switches. Here we introduce an algorithm to minimize the number of switches without affecting the ability of the configurations to accurately create the desired fields. The problem is modeled using graph theory and split into 2 sequential combinatorial optimization problems that are solved using simulated annealing. For the investigated cases, the results show that compared to unoptimized switching circuits, the reduction of switches in optimized circuits ranges from 8% to up to 44% (average of 31%). This substantial reduction is achieved without impeding circuit functionality. This study shows how technical effort associated with implementation and operation of a matrix gradient coil is related to different hardware setups and how to reduce this effort.

Combinatorial Detection of Conserved Alteration Patterns for Identifying Cancer Subnetworks

BACKGROUND

Advances in large-scale tumor sequencing have led to an understanding that there are combinations of genomic and transcriptomic alterations specific to tumor types, shared across many patients. Unfortunately, computational identification of functionally meaningful and recurrent alteration patterns within gene/protein interaction networks has proven to be challenging.

FINDINGS

We introduce a novel combinatorial method, cd-CAP (combinatorial detection of conserved alteration patterns), for simultaneous detection of connected subnetworks of an interaction network where genes exhibit conserved alteration patterns across tumor samples. Our method differentiates distinct alteration types associated with each gene (rather than relying on binary information of a gene being altered or not) and simultaneously detects multiple alteration profile conserved subnetworks.

CONCLUSIONS

In a number of The Cancer Genome Atlas datasets, cd-CAP identified large biologically significant subnetworks with conserved alteration patterns, shared across many tumor samples.

HNCcorr: A Novel Combinatorial Approach for Cell Identification in Calcium-Imaging Movies

Calcium imaging is a key method in neuroscience for investigating patterns of neuronal activity in vivo. Still, existing algorithms to detect and extract activity signals from calcium-imaging movies have major shortcomings. We introduce the HNCcorr algorithm for cell identification in calcium-imaging datasets that addresses these shortcomings. HNCcorr relies on the combinatorial clustering problem HNC (Hochbaum's Normalized Cut), which is similar to the Normalized Cut problem of Shi and Malik, a well known problem in image segmentation. HNC identifies cells as coherent clusters of pixels that are highly distinct from the remaining pixels. HNCcorr guarantees a globally optimal solution to the underlying optimization problem as well as minimal dependence on initialization techniques. HNCcorr also uses a new method, called "similarity squared", for measuring similarity between pixels in calcium-imaging movies. The effectiveness of HNCcorr is demonstrated by its top performance on the Neurofinder cell identification benchmark. We believe HNCcorr is an important addition to the toolbox for analysis of calcium-imaging movies.

coli

Resveratrol, a plant-derived polyphenolic compound with various health activities, is widely used in nutraceutical and food additives. Herein, combinatorial optimization of resveratrol biosynthetic pathway and intracellular environment of E. coli was carried out. By screening pathway genes from various species and exploring their expression pattern, we initially constructed resveratrol-producing strains. Further targeting at availability of malonyl-CoA through expressing ACC of Corynebacterium glutamicum and antisense inhibiting native fabD significantly increased resveratrol biosynthesis. Transport engineering for resveratrol secretion and molecular chaperones helping for folding heterologous enzymes were employed to improve the intracellular environments in remarkable degrees. By introducing PcTAL of Phanerochaete chrysosporium and tuning expression model of PcTAL, At4CL, and VvSTS, an engineered E. coli produced 57.77 mg/L of resveratrol from l-tyrosine. After integrating the above strategies, resveratrol titer reached to 238.71 mg/L from l-tyrosine. The combinatorial optimization in this study provides a promising strategy to produce valuable natural products in heterologous expression systems.

Synthesis-Structure-Activity Relationships in Co3O4 Catalyzed CO Oxidation

In this work, a statistical design and analysis platform was used to develop cobalt oxide based oxidation catalysts prepared via one pot metal salt reduction. An emphasis was placed upon understanding the effects of synthesis conditions, such as heating regimen and Co²⁺ concentration on the metal salt reduction mechanism, the resultant nanomaterial properties (i.e., size, crystal structure, and crystal faceting), and the catalytic activity in CO oxidation. This was accomplished by carrying out XRD, TEM, and FTIR studies on synthesis intermediates and products. Additionally, high-throughput experimentation was employed to study the performance of Co₃O₄ oxidation catalysts over a wide range of reaction conditions using a 16-channel fixed bed reactor equipped with a parallel infrared imaging system. Specifically, Co₃O₄ nanomaterials of varying properties were evaluated for their performance as CO oxidation catalysts. Figure-of-merits including light-off temperatures and activation energies were measured and mapped back to the catalyst properties and synthesis conditions. Statistical analysis methods were used to elucidate significant property-activity relationships as well as the design rules relevant in the synthesis of active catalysts. It was found that the degree of grain boundary consolidation and anisotropic growth in fcc and hcp CoO intermediates significantly influenced the catalytic activity. By utilizing the discovered synthesis-structure-activity relationships, CO oxidation light off temperatures were decreased to <90°C.

Dynamic Hierarchical Energy-Efficient Method Based on Combinatorial Optimization for Wireless Sensor Networks

Routing protocols based on topology control are significantly important for improving network longevity in wireless sensor networks (WSNs). Traditionally, some WSN routing protocols distribute uneven network traffic load to sensor nodes, which is not optimal for improving network longevity. Differently to conventional WSN routing protocols, we propose a dynamic hierarchical protocol based on combinatorial optimization (DHCO) to balance energy consumption of sensor nodes and to improve WSN longevity. For each sensor node, the DHCO algorithm obtains the optimal route by establishing a feasible routing set instead of selecting the cluster head or the next hop node. The process of obtaining the optimal route can be formulated as a combinatorial optimization problem. Specifically, the DHCO algorithm is carried out by the following procedures. It employs a hierarchy-based connection mechanism to construct a hierarchical network structure in which each sensor node is assigned to a special hierarchical subset; it utilizes the combinatorial optimization theory to establish the feasible routing set for each sensor node, and takes advantage of the maximum–minimum criterion to obtain their optimal routes to the base station. Various results of simulation experiments show effectiveness and superiority of the DHCO algorithm in comparison with state-of-the-art WSN routing algorithms, including low-energy adaptive clustering hierarchy (LEACH), hybrid energy-efficient distributed clustering (HEED), genetic protocol-based self-organizing network clustering (GASONeC), and double cost function-based routing (DCFR) algorithms.

On Proportions of Fit Individuals in Population of Mutation-Based Evolutionary Algorithm with Tournament Selection

In this article, we consider a fitness-level model of a non-elitist mutation-only evolutionary algorithm (EA) with tournament selection. The model provides upper and lower bounds for the expected proportion of the individuals with fitness above given thresholds. In the case of so-called monotone mutation, the obtained bounds imply that increasing the tournament size improves the EA performance. As corollaries, we obtain an exponentially vanishing tail bound for the Randomized Local Search on unimodal functions and polynomial upper bounds on the runtime of EAs on the 2-SAT problem and on a family of Set Cover problems proposed by E. Balas.

Flexible Fusion Structure-Based Performance Optimization Learning for Multisensor Target Tracking

Compared with the fixed fusion structure, the flexible fusion structure with mixed fusion methods has better adjustment performance for the complex air task network systems, and it can effectively help the system to achieve the goal under the given constraints. Because of the time-varying situation of the task network system induced by moving nodes and non-cooperative target, and limitations such as communication bandwidth and measurement distance, it is necessary to dynamically adjust the system fusion structure including sensors and fusion methods in a given adjustment period. Aiming at this, this paper studies the design of a flexible fusion algorithm by using an optimization learning technology. The purpose is to dynamically determine the sensors’ numbers and the associated sensors to take part in the centralized and distributed fusion processes, respectively, herein termed sensor subsets selection. Firstly, two system performance indexes are introduced. Especially, the survivability index is presented and defined. Secondly, based on the two indexes and considering other conditions such as communication bandwidth and measurement distance, optimization models for both single target tracking and multi-target tracking are established. Correspondingly, solution steps are given for the two optimization models in detail. Simulation examples are demonstrated to validate the proposed algorithms.

Improving Metabolic Pathway Efficiency by Statistical Model-Based Multivariate Regulatory Metabolic Engineering

Metabolic engineering entails target modification of cell metabolism to maximize the production of a specific compound. For empowering combinatorial optimization in strain engineering, tools and algorithms are needed to efficiently sample the multidimensional gene expression space and locate the desirable overproduction phenotype. We addressed this challenge by employing design of experiment (DoE) models to quantitatively correlate gene expression with strain performance. By fractionally sampling the gene expression landscape, we statistically screened the dominant enzyme targets that determine metabolic pathway efficiency. An empirical quadratic regression model was subsequently used to identify the optimal gene expression patterns of the investigated pathway. As a proof of concept, our approach yielded the natural product violacein at 525.4 mg/L in shake flasks, a 3.2-fold increase from the baseline strain. Violacein production was further increased to 1.31 g/L in a controlled benchtop bioreactor. We found that formulating discretized gene expression levels into logarithmic variables (Linlog transformation) was essential for implementing this DoE-based optimization procedure. The reported methodology can aid multivariate combinatorial pathway engineering and may be generalized as a standard procedure for accelerating strain engineering and improving metabolic pathway efficiency.

OptSSeq: High-Throughput Sequencing Readout of Growth Enrichment Defines Optimal Gene Expression Elements for Homoethanologenesis

The optimization of synthetic pathways is a central challenge in metabolic engineering. OptSSeq (Optimization by Selection and Sequencing) is one approach to this challenge. OptSSeq couples selection of optimal enzyme expression levels linked to cell growth rate with high-throughput sequencing to track enrichment of gene expression elements (promoters and ribosome-binding sites) from a combinatorial library. OptSSeq yields information on both optimal and suboptimal enzyme levels, and helps identify constraints that limit maximal product formation. Here we report a proof-of-concept implementation of OptSSeq using homoethanologenesis, a two-step pathway consisting of pyruvate decarboxylase (Pdc) and alcohol dehydrogenase (Adh) that converts pyruvate to ethanol and is naturally optimized in the bacterium Zymomonas mobilis. We used OptSSeq to determine optimal gene expression elements and enzyme levels for Z. mobilis Pdc, AdhA, and AdhB expressed in Escherichia coli. By varying both expression signals and gene order, we identified an optimal solution using only Pdc and AdhB. We resolved current uncertainty about the functions of the Fe²⁺-dependent AdhB and Zn²⁺-dependent AdhA by showing that AdhB is preferred over AdhA for rapid growth in both E. coli and Z. mobilis. Finally, by comparing predictions of growth-linked metabolic flux to enzyme synthesis costs, we established that optimal E. coli homoethanologenesis was achieved by our best pdc-adhB expression cassette and that the remaining constraints lie in the E. coli metabolic network or inefficient Pdc or AdhB function in E. coli. OptSSeq is a general tool for synthetic biology to tune enzyme levels in any pathway whose optimal function can be linked to cell growth or survival.

Alignment of Tractograms As Graph Matching

The white matter pathways of the brain can be reconstructed as 3D polylines, called streamlines, through the analysis of diffusion magnetic resonance imaging (dMRI) data. The whole set of streamlines is called tractogram and represents the structural connectome of the brain. In multiple applications, like group-analysis, segmentation, or atlasing, tractograms of different subjects need to be aligned. Typically, this is done with registration methods, that transform the tractograms in order to increase their similarity. In contrast with transformation-based registration methods, in this work we propose the concept of tractogram correspondence, whose aim is to find which streamline of one tractogram corresponds to which streamline in another tractogram, i.e., a map from one tractogram to another. As a further contribution, we propose to use the relational information of each streamline, i.e., its distances from the other streamlines in its own tractogram, as the building block to define the optimal correspondence. We provide an operational procedure to find the optimal correspondence through a combinatorial optimization problem and we discuss its similarity to the graph matching problem. In this work, we propose to represent tractograms as graphs and we adopt a recent inexact sub-graph matching algorithm to approximate the solution of the tractogram correspondence problem. On tractograms generated from the Human Connectome Project dataset, we report experimental evidence that tractogram correspondence, implemented as graph matching, provides much better alignment than affine registration and comparable if not better results than non-linear registration of volumes.

LUTE (Local Unpruned Tuple Expansion): Accurate Continuously Flexible Protein Design with General Energy Functions and Rigid Rotamer-Like Efficiency

Most protein design algorithms search over discrete conformations and an energy function that is residue-pairwise, that is, a sum of terms that depend on the sequence and conformation of at most two residues. Although modeling of continuous flexibility and of non-residue-pairwise energies significantly increases the accuracy of protein design, previous methods to model these phenomena add a significant asymptotic cost to design calculations. We now remove this cost by modeling continuous flexibility and non-residue-pairwise energies in a form suitable for direct input to highly efficient, discrete combinatorial optimization algorithms such as DEE/A* or branch-width minimization. Our novel algorithm performs a local unpruned tuple expansion (LUTE), which can efficiently represent both continuous flexibility and general, possibly nonpairwise energy functions to an arbitrary level of accuracy using a discrete energy matrix. We show using 47 design calculation test cases that LUTE provides a dramatic speedup in both single-state and multistate continuously flexible designs.

Gene-Family Extension Measures and Correlations

The existence of multiple copies of genes is a well-known phenomenon. A gene family is a set of sufficiently similar genes, formed by gene duplication. In earlier works conducted on a limited number of completely sequenced and annotated genomes it was found that size of gene family and size of genome are positively correlated. Additionally, it was found that several atypical microbes deviated from the observed general trend. In this study, we reexamined these associations on a larger dataset consisting of 1484 prokaryotic genomes and using several ranking approaches. We applied ranking methods in such a way that genomes with lower numbers of gene copies would have lower rank. Until now only simple ranking methods were used; we applied the Kemeny optimal aggregation approach as well. Regression and correlation analysis were utilized in order to accurately quantify and characterize the relationships between measures of paralog indices and genome size. In addition, boxplot analysis was employed as a method for outlier detection. We found that, in general, all paralog indexes positively correlate with an increase of genome size. As expected, different groups of atypical prokaryotic genomes were found for different types of paralog quantities. Mycoplasmataceae and Halobacteria appeared to be among the most interesting candidates for further research of evolution through gene duplication.

Classifying the Progression of Ductal Carcinoma from Single-Cell Sampled Data via Integer Linear Programming: A Case Study

Ductal Carcinoma In Situ (DCIS) is a precursor lesion of Invasive Ductal Carcinoma (IDC) of the breast. Investigating its temporal progression could provide fundamental new insights for the development of better diagnostic tools to predict which cases of DCIS will progress to IDC. We investigate the problem of reconstructing a plausible progression from single-cell sampled data of an individual with synchronous DCIS and IDC. Specifically, by using a number of assumptions derived from the observation of cellular atypia occurring in IDC, we design a possible predictive model using integer linear programming (ILP). Computational experiments carried out on a preexisting data set of 13 patients with simultaneous DCIS and IDC show that the corresponding predicted progression models are classifiable into categories having specific evolutionary characteristics. The approach provides new insights into mechanisms of clonal progression in breast cancers and helps illustrate the power of the ILP approach for similar problems in reconstructing tumor evolution scenarios under complex sets of constraints.

On the Minimum Error Correction Problem for Haplotype Assembly in Diploid and Polyploid Genomes

In diploid genomes, haplotype assembly is the computational problem of reconstructing the two parental copies, called haplotypes, of each chromosome starting from sequencing reads, called fragments, possibly affected by sequencing errors. Minimum error correction (MEC) is a prominent computational problem for haplotype assembly and, given a set of fragments, aims at reconstructing the two haplotypes by applying the minimum number of base corrections. MEC is computationally hard to solve, but some approximation-based or fixed-parameter approaches have been proved capable of obtaining accurate results on real data. In this work, we expand the current characterization of the computational complexity of MEC from the approximation and the fixed-parameter tractability point of view. In particular, we show that MEC is not approximable within a constant factor, whereas it is approximable within a logarithmic factor in the size of the input. Furthermore, we answer open questions on the fixed-parameter tractability for parameters of classical or practical interest: the total number of corrections and the fragment length. In addition, we present a direct 2-approximation algorithm for a variant of the problem that has also been applied in the framework of clustering data. Finally, since polyploid genomes, such as those of plants and fishes, are composed of more than two copies of the chromosomes, we introduce a novel formulation of MEC, namely the k-ploid MEC problem, that extends the traditional problem to deal with polyploid genomes. We show that the novel formulation is still both computationally hard and hard to approximate. Nonetheless, from the parameterized point of view, we prove that the problem is tractable for parameters of practical interest such as the number of haplotypes and the coverage, or the number of haplotypes and the fragment length.

Probing RNA Native Conformational Ensembles with Structural Constraints

Noncoding ribonucleic acids (RNA) play a critical role in a wide variety of cellular processes, ranging from regulating gene expression to post-translational modification and protein synthesis. Their activity is modulated by highly dynamic exchanges between three-dimensional conformational substates, which are difficult to characterize experimentally and computationally. Here, we present an innovative, entirely kinematic computational procedure to efficiently explore the native ensemble of RNA molecules. Our procedure projects degrees of freedom onto a subspace of conformation space defined by distance constraints in the tertiary structure. The dimensionality reduction enables efficient exploration of conformational space. We show that the conformational distributions obtained with our method broadly sample the conformational landscape observed in NMR experiments. Compared to normal mode analysis-based exploration, our procedure diffuses faster through the experimental ensemble while also accessing conformational substates to greater precision. Our results suggest that conformational sampling with a highly reduced but fully atomistic representation of noncoding RNA expresses key features of their dynamic nature.

comets (Constrained Optimization of Multistate Energies by Tree Search): A Provable and Efficient Protein Design Algorithm to Optimize Binding Affinity and Specificity with Respect to Sequence

Practical protein design problems require designing sequences with a combination of affinity, stability, and specificity requirements. Multistate protein design algorithms model multiple structural or binding "states" of a protein to address these requirements. comets provides a new level of versatile, efficient, and provable multistate design. It provably returns the minimum with respect to sequence of any desired linear combination of the energies of multiple protein states, subject to constraints on other linear combinations. Thus, it can target nearly any combination of affinity (to one or multiple ligands), specificity, and stability (for multiple states if needed). Empirical calculations on 52 protein design problems showed comets is far more efficient than the previous state of the art for provable multistate design (exhaustive search over sequences). comets can handle a very wide range of protein flexibility and can enumerate a gap-free list of the best constraint-satisfying sequences in order of objective function value.

Automating unambiguous NOE data usage in NVR for NMR protein structure-based assignments

Nuclear Magnetic Resonance (NMR) Spectroscopy is an important technique that allows determining protein structure in solution. An important problem in protein structure determination using NMR spectroscopy is the mapping of peaks to corresponding amino acids, also known as the assignment problem. Structure-Based Assignment (SBA) is an approach to solve this problem using a template structure that is homologous to the target. Our previously developed approach Nuclear Vector Replacement-Binary Integer Programming (NVR-BIP) computed the optimal solution for small proteins, but was unable to solve the assignments of large proteins. NVR-Ant Colony Optimization (ACO) extended the applicability of the NVR approach for such proteins. One of the input data utilized in these approaches is the Nuclear Overhauser Effect (NOE) data. NOE is an interaction observed between two protons if the protons are located close in space. These protons could be amide protons, protons attached to the alpha-carbon atom in the backbone of the protein, or side chain protons. NVR only uses backbone protons. In this paper, we reformulate the NVR-BIP model to distinguish the type of proton in NOE data and use the corresponding proton coordinates in the extended formulation. In addition, the threshold value over interproton distances is set in a standard manner for all proteins by extracting the NOE upper bound distance information from the data. We also convert NOE intensities into distance thresholds. Our new approach thus handles the NOE data correctly and without manually determined parameters. We accordingly adapt NVR-ACO solution methodology to these changes. Computational results show that our approaches obtain optimal solutions for small proteins. For the large proteins our ant colony optimization-based approach obtains promising results.