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All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Stable Isotope Labeling for Improved Comparative Analysis of RNA Digests by Mass Spectrometry

Even with the advent of high throughput methods to detect modified ribonucleic acids (RNAs), mass spectrometry remains a reliable method to detect, characterize, and place post-transcriptional modifications within an RNA sequence. Here we have developed a stable isotope labeling comparative analysis of RNA digests (SIL-CARD) approach, which improves upon the original {sup 18}O/{sup 16}O labeling CARD method. Like the original, SIL-CARD allows sequence or modification information from a previously uncharacterized in vivo RNA sample to be obtained by direct comparison with a reference RNA, the sequence of which is known. This reference is in vitro transcribed using a {sup 13}C/{sup 15}N isotopically enriched nucleoside triphosphate (NTP). The two RNAs are digested with an endonuclease, the specificity of which matches the labeled NTP used for transcription. As proof of concept, several transfer RNAs (tRNAs) were characterized by SIL-CARD, where labeled guanosine triphosphate was used for the reference in vitro transcription. RNase T1 digestion products from the in vitro transcript will be 15 Da higher in mass than the same digestion products from the in vivo tRNA that are unmodified, leading to a doublet in the mass spectrum. Singlets, rather than doublets, arise if a sequence variation or a post-transcriptional modification is present that results in a relative mass shift different from 15 Da. Moreover, the use of the in vitro synthesized tRNA transcript allows for quantitative measurement of RNA abundance. Overall, SIL-CARD simplifies data analysis and enhances quantitative RNA modification mapping by mass spectrometry. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Optimizing metaproteomics database construction: lessons from a study of the vaginal microbiome

Metaproteomics, a method for untargeted, high-throughput identification of proteins in complex samples, provides functional information about microbial communities and can tie functions to specific taxa. Metaproteomics often generates less data than other omics techniques, but analytical workflows can be improved to increase usable data in metaproteomic outputs. Identification of peptides in the metaproteomic analysis is performed by comparing mass spectra of sample peptides to a reference database of protein sequences. Although these protein databases are an integral part of the metaproteomic analysis, few studies have explored how database composition impacts peptide identification. Here, we used cervicovaginal lavage (CVL) samples from a study of bacterial vaginosis (BV) to compare the performance of databases built using six different strategies. We evaluated broad versus sample-matched databases, as well as databases populated with proteins translated from metagenomic sequencing of the same samples versus sequences from public repositories. Smaller sample-matched databases performed significantly better, driven by the statistical constraints on large databases. Additionally, large databases attributed up to 34% of significant bacterial hits to taxa absent from the sample, as determined orthogonally by 16S rRNA gene sequencing. We also tested a set of hybrid databases which included bacterial proteins from NCBI RefSeq and translated bacterial genes from the samples. These hybrid databases had the best overall performance, identifying 1,068 unique human and 1,418 unique bacterial proteins, ~30% more than a database populated with proteins from typical vaginal bacteria and fungi. Our findings can help guide the optimal identification of proteins while maintaining statistical power for reaching biological conclusions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

A hybrid computational strategy to address WGS variant analysis in >5000 samples

Abstract Background The decreasing costs of sequencing are driving the need for cost effective and real time variant calling of whole genome sequencing data. The scale of these projects are far beyond the capacity of typical computing resources available with most research labs. Other infrastructures like the cloud AWS environment and supercomputers also have limitations due to which large scale joint variant calling becomes infeasible, and infrastructure specific variant calling strategies either fail to scale up to large datasets or abandon joint calling strategies. Results We present a high throughput framework including multiple variant callers for single nucleotide variant (SNV) calling, which leverages hybrid computing infrastructure consisting of cloud AWS, supercomputers and local high performance computing infrastructures. We present a novel binning approach for large scale joint variant calling and imputation which can scale up to over 10,000 samples while producing SNV callsets with high sensitivity and specificity. As a proof of principle, we present results of analysis on Cohorts for Heart And Aging Research in Genomic Epidemiology (CHARGE) WGS freeze 3 dataset in which joint calling, imputation and phasing of over 5300 whole genome samples was produced in under 6 weeks using four state-of-the-art callers. The callers used were SNPTools, GATK-HaplotypeCaller, GATK-UnifiedGenotyper and GotCloud. We used Amazon AWS, a 4000-core in-house cluster at Baylor College of Medicine, IBM power PC Blue BioU at Rice and Rhea at Oak Ridge National Laboratory (ORNL) for the computation. AWS was used for joint calling of 180 TB of BAM files, and ORNL and Rice supercomputers were used for the imputation and phasing step. All other steps were carried out on the local compute cluster. The entire operation used 5.2 million core hours and only transferred a total of 6 TB of data across the platforms. Conclusions Even with increasing sizes of whole genome datasets, ensemble joint calling of SNVs for low coverage data can be accomplished in a scalable, cost effective and fast manner by using heterogeneous computing platforms without compromising on the quality of variants.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Tailoring Hierarchical Structure and Rare Earth Affinity of Compositionally Identical Polymers via Sequence Control

Macromolecule sequence, structure, and function are inherently intertwined. While well-established relationships exist in proteins, they are more challenging to define for synthetic polymer nanoparticles due to their molecular weight, sequence, and conformational dispersities. Furthermore, to explore the impact of sequence on nanoparticle structure, we synthesized a set of 16 compositionally identical, sequence-controlled polymers with distinct monomer patterning of dimethyl acrylamide and a bioinspired, structure-driving di(phenylalanine) acrylamide (FF). Sequence control was achieved through multiblock polymerizations, yielding unique ensembles of polymer sequences which were simulated by kinetic Monte Carlo simulations. Systematic analysis of the global (tertiary- and quaternary-like) structure in this amphiphilic copolymer series revealed the effect of multiple sequence descriptors: the number of domains, the hydropathy of terminal domains, and the patchiness (density) of FF within a domain, each of which impacted both chain collapse and the distribution of single- and multichain assemblies. Furthermore, both the conformational freedom of chain segments and local-scale, β-sheet-like interactions were sensitive to the patchiness of FF. To connect sequence, structure, and target function, we evaluated an additional series of nine sequence-controlled copolymers as sequestrants for rare earth elements (REEs) by incorporating a functional acrylic acid monomer into select polymer scaffolds. We identified key sequence variables that influence the binding affinity, capacity, and selectivity of the polymers for REEs. Collectively, these results highlight the potential of and boundaries of sequence control via multiblock polymerizations to drive primary sequence ensembles hierarchical structures, and ultimately the functionality of compositionally identical polymeric materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Molecular phylogenetic analysis of the Paguristes tortugae Schmitt, 1933 complex and selected other Paguroidea (Crustacea: Decapoda: Anomura)

Morphological characters, as presently applied to describe members of the Paguristes tortugae Schmitt, 1933 species complex, appear to be of limited value in inferring phylogenetic relationships within the genus, and may have similarly misinformed understanding of relationships between members of this complex and those presently assigned to the related genera Areopaguristes Rahayu & McLaughlin, 2010 and Pseudopaguristes McLaughlin, 2002. Previously undocumented observations of similarities and differences in color patterns among populations additionally suggest genetic divergences within some species, or alternatively seem to support phylogenetic groupings of some species. In the present study, a Maximum Likelihood (ML) phylogenetic analysis was undertaken based on the H3, 12S mtDNA, and 16S mtDNA sequences of 148 individuals, primarily representatives of paguroid species from the western Atlantic. This molecular analysis supported a polyphyletic Diogenidae Ortmann, 1892, although incomplete taxonomic sampling among the genera of Diogenidae limits the utility of this finding for resolving family level relationships. Several hypotheses regarding the evolutionary relationships among hermit crab genera were refuted by the Kishino-Hasegawa (KH). ShimodairaHasegawa (SH) and Approximately Unbiased (AU) tree topology tests, among them the hypothesis that Areopaguristes is monophyletic. A lack of support for the monophyly of Areopaguristes calls into question the phylogenetic validity of gill number for the differentiation of Paguristes, Areopaguristes, and Pseudopaguristes. The study was inconclusive with regard to the relationships among these three genera, but previously unknown diversity within both Paguristes and Areopaguristes was demonstrated. Existence of an undescribed species confounded under the name Paguristes tortugae Schmitt, 1933 was supported by genetics, morphology, and coloration. A second undescribed species with remarkable similarity to Areopaguristes hummi Wass, 1955 was discovered based on genetics and coloration.

12S↗
DOE OSTI2019

Sequenceserver: A Modern Graphical User Interface for Custom BLAST Databases

Comparing newly obtained and previously known nucleotide and amino-acid sequences underpins modern biological research. BLAST is a well-established tool for such comparisons but is challenging to use on new data sets. We combined a user-centric design philosophy with sustainable software development approaches to create Sequenceserver, a tool for running BLAST and visually inspecting BLAST results for biological interpretation. Sequenceserver uses simple algorithms to prevent potential analysis errors and provides flexible text-based and visual outputs to support researcher productivity. Our software can be rapidly installed for use by individuals or on shared servers.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Identifying RNA contacts from SHAPE-MaP by partial correlation analysis

In a recent paper Siegfried et al. published a new sequence-based structural RNA assay that utilizes mutational profiling to detect base pairing (MaP). Output from MaP provides information about both pairing (via reactivities) and contact (via correlations). Reactivities can be coupled to partition function folding models for structural inference, while correlations can reveal pairs of sites that may be in structural proximity. The possibility for inference of 3D contacts via MaP suggests a novel approach to structural prediction for RNA analogous to covariance structural prediction for proteins. We explore this approach and show that partial correlation analysis outperforms na\"ive correlation analysis. Our results should be applicable to a wide range of high-throughput sequencing based RNA structural assays that are under development.

Tambe, Akshay↗
DOE OSTI2023

Simulation-Based Recovery Action Analysis Using the EMRALD Dynamic Risk Assessment Tool

A recovery action is defined as the action that prevents deviant conditions from producing unwanted effects. It generally indicates a kind of countermeasure performed in response to a failure of human action. The recovery actions especially play an important role in complex systems like nuclear power plants (NPPs), which consist of highly sophisticated controllers to ensure that desired performance and safety must be achieved and maintained. This is because a combination of human error and its recovery failure may be able to cause a catastrophic effect on a system. Analyzing recovery actions has been a critical part of HRA, which is a technique to evaluate human errors and provide human error probabilities (HEPs) for application in probabilistic safety assessment (PSA). If recovery actions are not adequately analyzed and applied to PSA models, the PSA results may be under-estimated or be not able to reasonably account for the failure of human actions in the context of PSA. For this reason, some regulatory documents such as ASME/ANS RA-Sb-2013 by the American Society for Mechanical Engineers and the American Nuclear Society and NUREG-1792 by U.S. Nuclear Regulatory Commission have emphasized the importance of recovery analysis within the HRA. A couple of existing HRA methods, such as the Technique for Human Error-Rate Prediction (THERP), the Cause-Based Decision Tree (CBDT), and the Korean Standard HRA (K-HRA), have respectively suggested their own approaches to the HRA recovery analysis. However, there are a couple of limitations to treating recovery actions using only the current HRA methods available. The biggest limitation is that the existing recovery analysis does not explicitly consider a variety of recovery action types and recovery sequences as they occur in actual NPPs. To handle the limitations of existing recovery analysis, this study proposes a simulation-based recovery analysis method using the Event Modeling Risk Assessment Using Linked Diagram (EMRALD) software. The EMRALD software is a dynamic simulation tool for PSA. It supports realistic and dynamic modeling of human actions as they would be performed at NPPs. It is also favorable to simultaneously model the specific moment at which an action is performed, the time it takes to perform the action, and the failure probability of that action. In this paper, a detailed methodology for modeling recovery actions in the simulation platform is proposed with a couple of examples. Then, outputs from the simulation are discussed as reviewing if this novel approach can complement the challenges of existing recovery analyses.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Biomass yields, reproductive fertility, compositional analysis, and genetic diversity of newly developed triploid giant miscanthus hybrids

Abstract Miscanthus × giganteus (giant miscanthus), first found as a naturally occurring hybrid, has shown promise as a bioenergy/biomass crop throughout much of the temperate world. This allotriploid (2 n = 3 x = 57) hybrid resulted from a cross between tetraploid Miscanthus sacchariflorus (2 n = 4 x = 76) and diploid Miscanthus sinensis (2 n = 2 x = 38) and is particularly desirable due to its low fertility that minimizes reseeding and potential invasiveness. However, there is limited genetic diversity in commonly grown cultivars of triploid M. × giganteus and breeding and development efforts to improve and domesticate this crop have been minimal. Here, we report on newly developed M. × giganteus hybrids compared with the industry standard M. × giganteus '1993‐1780'. Dry biomass yields of new hybrids ranged from 19.5 to 32.4 Mg/ha/year for the fourth growing season, compared with 21.0 Mg/ha/year for M. × giganteus '1993‐1780'. Plant reproductive fertility remained low for all accessions with overall fertility [(seed set × seed germination)/100] ranging from 0.3% to 4.5% for new hybrids compared to 0.4% for M. × giganteus '1993‐1780'. Culm density and height varied among accessions and were positively correlated with increased biomass. Based on compositional analyses, theoretical ethanol yields ranged from 9, 740 to 16,278 L/ha/year for new hybrids compared to 10,406 L/ha/year for M. × giganteus '1993‐1780'. Relative feed value indices were low overall and ranged between 66.0 and 72.8 for new hybrids compared to M. × giganteus '1993‐1780' with 71.3. The genetic diversity of new hybrids, compared with existing cultivars, was characterized using whole genome sequences. Based on pair‐wise distances, cluster analysis clearly showed increased diversity of new hybrids compared with earlier selections. These results document new triploid hybrids of M. × giganteus with enhanced biomass and theoretical ethanol yields in combination with broader genetic diversity and lowreproductive fertility.

Touchell, Darren H.↗
DOE OSTI2020

Accurate and complete genomes from metagenomes

Genomes are an integral component of the biological information about an organism; thus, the more complete the genome, the more informative it is. Historically, bacterial and archaeal genomes were reconstructed from pure (monoclonal) cultures, and the first reported sequences were manually curated to completion. However, the bottleneck imposed by the requirement for isolates precluded genomic insights for the vast majority of microbial life. Shotgun sequencing of microbial communities, referred to initially as community genomics and subsequently as genome-resolved metagenomics, can circumvent this limitation by obtaining metagenome-assembled genomes (MAGs); but gaps, local assembly errors, chimeras, and contamination by fragments from other genomes limit the value of these genomes. Here, we discuss genome curation to improve and, in some cases, achieve complete (circularized, no gaps) MAGs (CMAGs). To date, few CMAGs have been generated, although notably some are from very complex systems such as soil and sediment. Through analysis of about 7000 published complete bacterial isolate genomes, we verify the value of cumulative GC skew in combination with other metrics to establish bacterial genome sequence accuracy. The analysis of cumulative GC skew identified potential misassemblies in some reference genomes of isolated bacteria and the repeat sequences that likely gave rise to them. We discuss methods that could be implemented in bioinformatic approaches for curation to ensure that metabolic and evolutionary analyses can be based on very high-quality genomes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

KBase Narrative - Supplemental Data for "Mixed waste contamination selects for a mobile genetic element population enriched in multiple heavy metal resistance genes"

Here we provide the complete set of circular elements produced by SCAPP from metagenomic data that may represent mobile genetic elements (MGEs). For the publication, these sequences were de-replicated within the high [U] and low [U] sample sets. Additionally, 98 of the circular elements were removed for downstream analysis due to high suspicion of being (1) chloroplast or mitochondrial sequences or (2) erroneously circularized long repeat regions. The complete list of circular elements used for the analysis along with metadata can be found in Tables S5 and S6.

Goff, Jennifer↗
DOE OSTI2020

Single-Cell Genomics of Novel Actinobacteria With the Wood–Ljungdahl Pathway Discovered in a Serpentinizing System

Serpentinite-hosted systems represent modern-day analogs of early Earth environments. In these systems, water-rock interactions generate highly alkaline and reducing fluids that can contain hydrogen, methane, and low-molecular-weight hydrocarbons-potent reductants capable of fueling microbial metabolism. In this study, we investigated the microbiota of Hakuba Happo hot springs (~50°C; pH~10.5–11), located in Nagano (Japan), which are impacted by the serpentinization process. Analysis of the 16S rRNA gene amplicon sequences revealed that the bacterial community comprises Nitrospirae (47%), “Parcubacteria” (19%), Deinococcus-Thermus (16%), and Actinobacteria (9%), among others. Notably, only 57 amplicon sequence variants (ASV) were detected, and fifteen of these accounted for 90% of the amplicons. Among the abundant ASVs, an early-branching, uncultivated actinobacterial clade identified as RBG-16-55-12 in the SILVA database was detected. Ten single-cell genomes (average pairwise nucleotide identity: 0.98–1.00; estimated completeness: 33–93%; estimated genome size: ~2.3 Mb) that affiliated with this clade were obtained. Taxonomic classification using single copy genes indicates that the genomes belong to the actinobacterial class-level clade UBA1414 in the Genome Taxonomy Database. Based on metabolic pathway predictions, these actinobacteria are anaerobes, capable of glycolysis, dissimilatory nitrate reduction and CO 2 fixation via the Wood–Ljungdahl (WL) pathway. Several other genomes within UBA1414 and two related class-level clades also encode the WL pathway, which has not yet been reported for the Actinobacteria phylum. For the Hakuba actinobacterium, the energy metabolism related to the WL pathway is likely supported by a combination of the Rnf complex, group 3b and 3d [NiFe]-hydrogenases, [FeFe]-hydrogenases, and V-type (H + /Na + pump) ATPase. The genomes also harbor a form IV ribulose 1,5-bisphosphate carboxylase/oxygenase (RubisCO) complex, also known as a RubisCO-like protein, and contain signatures of interactions with viruses, including clustered regularly interspaced short palindromic repeat (CRISPR) regions and several phage integrases. This is the first report and detailed genome analysis of a bacterium within the Actinobacteria phylum capable of utilizing the WL pathway. The Hakuba actinobacterium is a member of the clade UBA1414/RBG-16-55-12, formerly within the group “OPB41.” We propose to name this bacterium ‘Candidatus Hakubanella thermoalkaliphilus.'

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Portable Rabies Virus Sequencing in Canine Rabies Endemic Countries Using the Oxford Nanopore MinION

As countries with endemic canine rabies progress towards elimination by 2030, it will become necessary to employ techniques to help plan, monitor, and confirm canine rabies elimination. Sequencing can provide critical information to inform control and vaccination strategies by identifying genetically distinct virus variants that may have different host reservoir species or geographic distributions. However, many rabies testing laboratories lack the resources or expertise for sequencing, especially in remote or rural areas where human rabies deaths are highest. We developed a low-cost, high throughput rabies virus sequencing method using the Oxford Nanopore MinION portable sequencer. A total of 259 sequences were generated from diverse rabies virus isolates in public health laboratories lacking rabies virus sequencing capacity in Guatemala, India, Kenya, and Vietnam. Phylogenetic analysis provided valuable insight into rabies virus diversity and distribution in these countries and identified a new rabies virus lineage in Kenya, the first published canine rabies virus sequence from Guatemala, evidence of rabies spread across an international border in Vietnam, and importation of a rabid dog into a state working to become rabies-free in India. Taken together, our evaluation highlights the MinION’s potential for low-cost, high volume sequencing of pathogens in locations with limited resources.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Unraveling the functional dark matter through global metagenomics

Metagenomes encode an enormous diversity of proteins, reflecting a multiplicity of functions and activities1,2. Exploration of this vast sequence space has been limited to a comparative analysis against reference microbial genomes and protein families derived from those genomes. Here, to examine the scale of yet untapped functional diversity beyond what is currently possible through the lens of reference genomes, we develop a computational approach to generate reference-free protein families from the sequence space in metagenomes. We analyse 26,931 metagenomes and identify 1.17 billion protein sequences longer than 35 amino acids with no similarity to any sequences from 102,491 reference genomes or the Pfam database3. Using massively parallel graph-based clustering, we group these proteins into 106,198 novel sequence clusters with more than 100 members, doubling the number of protein families obtained from the reference genomes clustered using the same approach. We annotate these families on the basis of their taxonomic, habitat, geographical and gene neighbourhood distributions and, where sufficient sequence diversity is available, predict protein three-dimensional models, revealing novel structures. Overall, our results uncover an enormously diverse functional space, highlighting the importance of further exploring the microbial functional dark matter.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

germs-lab/LAMPS-miscanthus-microbiome

Data and analysis to accompany our submitted paper characterizing the LAMPS Miscanthus Microbiome comparing 16S rRNA gene DNA sequencing of Miscanthus in a staggered-start experiment. Authors for this analysis include Fernando Igne Rocha, Lanying Ma, and Adina Howe.

Igne Rocha, Fernando↗
DOE OSTI2022

RNAseq-based transcriptome assembly of Clostridium acetobutylicum for functional genome annotation and discovery

Accurate genome annotations are essential in modern biology and biotechnology, yet they are still largely based on genome sequencing and comparative analyses. We show that the Clostridium acetobutylicum genome annotation can be markedly improved by integrating bioinformatic predictions with RNA sequencing (RNAseq) data. Samples were acquired under butanol, butyrate, and unstressed treatments across various growth conditions. Analysis of an initial assembly revealed errors due to background signals and limitations of assembly algorithms. Hurdles for RNAseq transcriptome mapping include optimizing library complexity and sequencing depth, yet most studies report low sequencing depth and ignore the effect of ribosomal RNA abundance. An integrative analysis was developed to combine motif predictions, single-nucleotide resolution sequencing depth, and library complexity to resolve difficulties in assembly curation. This minimized false positive error and determined gene boundaries, in some cases, to the exact base-pair of prior studies. This will be the first strand-specific transcriptome assembly in a Clostridium organism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Isolation and characterization of a novel mycovirus from Penicillium digitatum

A novel double-stranded RNA virus designated Penicillium digitatum virus 1 (PdV1) was isolated from the citrus fruit rot pathogen P. digitatum (HS-RH1). The full-length cDNA sequence of the dsRNA/PdV1 (5211 bp) possesses two partially overlapping open reading frames, which encode a coat protein (CP) and a putative RNA-dependent RNA polymerase (RdRp), respectively. Phylogenetic analysis based on multiple alignments of the amino acid sequences of the RdRp and CP indicated that PdV1 tentatively belongs to the genus Victorivirus in the Totiviridae family. Electron micrographs of negatively stained viral particles purified from the peak fraction of sucrose density gradient centrifugation showed spherical particles ~35 nm in diameter. Transfection experiments with purified virions indicated that PdV1 could reduce the vegetative growth and virulence of P. digitatum strain HS-F6. In summary, we report the first isolation and characterization of a mycovirus from P. digitatum that contributes to the hypovirulence phenotypes of the host strain. - Highlights: • A novel victorivirus designated Penicillium digitatum virus 1 (PdV1) was isolated fromP. digitatum. • The dsRNA genome of PdV1 are 5211 bp long, two ORFs encoding CP and RdRp, and are encased in virions of ~35 nm in diameter. • PdV1 infection led to hypovirulent effect on P. digitatum. PdV1 may potentially be used for citrus green mold biocontrol. • Our study provides a research basis for establishing a model system for the study of P. digitatum–mycovirus interactions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Riemann solutions for counterflow combustion in light porous foam

The paper is motivated by a model for the injection of air into a porous medium that contains a solid fuel. In previous work, a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection was considered. The existence and uniqueness of traveling waves were studied and the wave sequences appearing in Riemann solutions were identified. This analysis was done under assumption that the combustion wave velocity is positive. In the present work, this hypothesis was neglected and the results generalized including the case of negative combustion wave speed. The existence of such waves was proved and the uniqueness investigated for some particular cases using Melnikov’s integral. The wave sequences appearing in Riemann solutions were identified and the numerical examples using finite difference scheme were presented.

97 MATHEMATICS AND COMPUTING↗