Matematiska vetenskaper // Mathematical Sciences

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https://odr.chalmers.se/handle/20.500.12380/17

Studerar matematikens strukturer och utvecklar dem för att bättre förstå vår värld, och till nytta för forskning och teknisk utveckling.
De matematiska vetenskaperna utforskar tankens grundläggande begrepp och lagar. De är oumbärliga för modern naturvetenskap och teknik. Även inom andra vetenskaper spelar matematisk och statistisk metodik en alltmer framträdande roll. Matematik är också en vetenskap i sig själv och grundforskning i matematik är en förutsättning för dess många tillämpningar. Institutionen är gemensam för Chalmers tekniska högskola och Göteborgs universitet.

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För forskning och forskningspublikationer, se https://research.chalmers.se/organisation/matematiska-vetenskaper/

Studies mathematical structures, developing them to better understand our world and to benefit from research and technological development.
The mathematical sciences are fundamental and indispensable to a large part of modern science and engineering. Progress in other disciplines is often linked to an increased use of mathematics. Mathematics is also a subject in itself, and fundamental research is a necessary condition for its many applications. The Department is joint for the Chalmers University of Technology and University of Gothenburg.

Studying at the Department of Mathematical Sciences at Chalmers

For research and research output, please visit https://research.chalmers.se/en/organization/mathematical-sciences/

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Compatibility patterns in antibiotic resistant genes in pathogens
(2020) Lindbom, Agnes; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Kristiansson, Erik; Kristiansson, Erik
Antibiotic resistance is increasing globally and is a substantial threat to the public health with higher costs and longer hospital stays. Infections of antibiotic resistant bacteria are harder to treat and without actions, there is a risk common infections eventually can become life-threatening again. Antibiotic resistance can be acquired by mutations in existing genes or from resistance genes transferred from other bacteria by horizontal gene transfer. The reason why some genes are transferred could be explained by the compatibility of the gene, but currently, there is not so much information what would be needed to make a gene compatible and able to be transferred and make new antibiotic resistant bacteria. The aim of this project is to investigate whether there are compatibility patterns in antibiotic resistant genes in the pathogens Escherichia coli and Klebsiella pneumoniae. This was done by three analyses, kmer analysis, frequency analysis and analysis of regions surrounding the gene. The project also included predictive models to investigate the predictive ability of a logistic regression model. The data was collected from NCBI and ResFinder and core genomes from the species were used. The antibiotic resistant genes were divided into groups whether they were present or not in the species after using BLAST. The kmer analysis used the kmer distributions of different kmer lengths in three methods; squared Euclidean distance, absolute maximum values and maximum value and gave similar results for both species. For smaller kmer lengths, differences could be seen for the species in the median and p-values between the antibiotic resistant genes and the core genome genes. For increasing kmer lengths less differences could be seen. In the frequency analysis the genes were merged into genes groups and the values from kmer analysis were compared against the number of hits from the BLAST results. Many values clustered around the median values and the gene groups with the most hits were close to the median values while the values far away from the median values did not have many hits. No clear conclusion about different antibiotic classes could be seen. In the analysis of regions surrounding the gene, sequences of 100 bp upstream and downstream of each gene were cut and the genes were divided into groups whether they were present in both or one species. There could be seen differences between the unique groups of the species, while the difference between the shared groups were surprisingly low. On kmer level, the kmers that differed most between the species had no clear correlation, potentially they could be related to the higher GC content in K. pneumoniae. Predictive models were created with logistic regression for all genes and three different antibiotic classes. The model for all genes included the length and 21 kmers out of 64 possible kmers. The model performed better than a random classification with the best values of true positive rate of 72% and false positive rate of 11%. The other models included fewer kmers and most of the classifier performed better than a random classification. In this project analyses have developed and from the results it has been found compatibility patterns of the antibiotic resistant genes by looking at the gene sequences and the regions surrounding the genes. From the gene sequences it has also been possible to predict the gene compatibility in a predictive model.
Development of 3D Finite Element Model of Human head
(2017) Kim, Li Jung; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
Bone-Anchored Hearing Aid (BAHA) is known as the surgically implantable hearing aid for patients whose medical conditions are beyond the stage of wearing the conventional air conductive hearing aid (ACHA) or those who suffer from bone diseases or chronic inflammation of the outer or middle ear. Numerous studies have been conducted to investigate the bone conduction mechanism. Nowadays, with the help of computational mechanics such as the Finite-Element Method (FEM), the performance of BAHA can be improved before the actual costly physical models are built. This thesis aims to develop FE head models that are readily available for commercial use. This thesis presents two different head models, which enable the simulation of the vibration phenomenon, specifically the mechanical point impedance of the skull bone. One model addresses the artificial head model, and the other originates from the direct segmentation of CT scan with new segmentation software. The final goal is to identify critical parameters for effective bone conduction as well as to improve the current BAHA model. The simulation results were compared with both test data and literature. This study concludes that both models were successfully able to reproduce results with the test data. Antiresonance frequencies in the simulation results were present at approximately 70 — 90 Hz in the simulator FE model and approximately 200 Hz in the actual human FE model. The proposed modelling approach will be a stepping stone to quantitatively investigate the biomechanical behavior of bone conduction and provide platforms for the patient-specific optimization of the BAHA configuration with future improvements.
Development of 3D Finite Element Model of Human head
(2017) Kim, Li Jung; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
Bone-Anchored Hearing Aid (BAHA) is known as the surgically implantable hearing aid for patients whose medical conditions are beyond the stage of wearing the conventional air conductive hearing aid (ACHA) or those who suffer from bone diseases or chronic inflammation of the outer or middle ear. Numerous studies have been conducted to investigate the bone conduction mechanism. Nowadays, with the help of computational mechanics such as the Finite-Element Method (FEM), the performance of BAHA can be improved before the actual costly physical models are built. This thesis aims to develop FE head models that are readily available for commercial use. This thesis presents two different head models, which enable the simulation of the vibration phenomenon, specifically the mechanical point impedance of the skull bone. One model addresses the artificial head model, and the other originates from the direct segmentation of CT scan with new segmentation software. The final goal is to identify critical parameters for effective bone conduction as well as to improve the current BAHA model. The simulation results were compared with both test data and literature. This study concludes that both models were successfully able to reproduce results with the test data. Antiresonance frequencies in the simulation results were present at approximately 70 — 90 Hz in the simulator FE model and approximately 200 Hz in the actual human FE model. The proposed modelling approach will be a stepping stone to quantitatively investigate the biomechanical behavior of bone conduction and provide platforms for the patient-specific optimization of the BAHA configuration with future improvements.
Evolutionarily Conserved Drug Targets
(2016) Palm, Yvette; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
Extensive Screening of Genomic and Metagenomic Data Identifies Novel Components of the Macrolide Resistome
(2020) Lund, David; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Kristiansson, Erik; Kristiansson, Erik
Antibiotic resistance is growing among pathogenic bacteria all across the world, and has been called one of the most serious threats that humanity is facing. Typically, bacteria are able to develop resistance as a result of acquiring specific antibiotic resistance genes from other bacteria though so called horizontal gene transfer. One commonly used class of antibiotics for which resistance is spreading rapidly is macrolides. While a lot of research has been devoted to studying the genes that confer resistance to these antibiotics, the evolution of these macrolide resistance genes has not been determined. It has been suggested that resistance determinants that eventually find their way into the clinical environment originate from external environments, however the mechanisms behind this flow of resistance is not known. To prevent resistance to macrolide antibiotics from spreading further, it is therefore important to characterize how the resistance genes have evolved. Furthermore, knowledge about which genes are present in what environments will help with anticipating which genes might mobilize into the clinical environment in the future, and facilitate preemptive measures being taken. This project aims to use a bioinformatic approach to characterize novel macrolide resistance genes, applying a computational method called fARGene. To achieve this, profile hidden Markov models have been developed that are able to identify two types of genes that confer resistance to macrolides, mediated by enzymes called Erm 23S rRNA methyltransferases and Mph macrolide phosphotransferases respectively, from biological sequencing data. The models have been used to analyze data representing over 400,000 bacterial genomes, and over 14 terabases of metagenomic data. Hundreds of gene families have been identified from the bacterial genomes, most of which are previously uncharacterized, and these have been analyzed based on their phylogenetic relationships. The results revealed a large variety of uncharacterized macrolide resistance genes that seem to have evolved primarily in bacteria from the phyla Firmicutes and Actinobacteria. In addition, several uncharacterized resistance genes that have potentially been mobilized have been identified from the results. No singular origin was determined for either of the analyzed gene classes, however the previously hypothesized evolutionary relationship between Erm methyltransferases and the housekeeping methyltransferase KsgA is supported by the results. In addition, the results from the analysis of metagenomic data indicate that the studied macrolide resistance genes are likely to mobilize from the human gut, naturally presenting a way through which the genes may enter the clinical environment.
Improving Genome Scale Metabolic Models using Gene Regulatory Networks
(2024) Davidsson, Liam; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Cvijovic, Marija; Brunnsåker, Daniel
This thesis aims to enhance Genome Scale Metabolic Models (GEMs) by integrating Gene Regulatory Networks (GRNs) to improve modeling capabilities for the yeast Saccharomyces cerevisiae. The project involved constructing a pipeline to incorporate gene expression data into GEMs, resulting in a constrained metabolic model with a more diverse and characteristic flux distribution. By utilizing transcription data and transcription factor interactions, the integration aims to provide a more comprehensive understanding of cellular processes. The research demonstrates that incorporating GRNs can enhance the predictive accuracy of GEMs, despite the challenges associated with data complexity and integration methodologies. Potential future work includes upgrading the GRN to a dynamic Bayesian network and exploring the effects of network size on model outcomes.
Large-scale screening of genomic data identifies novel mobile colistin resistance genes and reveals high over-representation in Pseudomonadota
(2023) Schiller, Alice; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Kristiansson, Erik; Lund , David; Johnning, Anna
The emergence of antibiotic-resistant bacteria is a health problem of great concern. Antibiotic resistance development is driven by selection pressure and the environment is believed to be the origin of most antibiotic resistance genes, from where they can mobilize into pathogens. In order to be prepared when novel antibiotic resistance genes reach pathogens and prevent further transmission, early detection and knowledge about the spread is of high importance. One specific type of antibiotic that is of high interest to characterize is colistin. Colistin is an antibiotic that targets gram-negative bacteria and is sometimes seen as the last alternative to treat dangerous infections caused by multi-drug resistance gram-negative bacteria. The emergence of mobile colistin resistance genes hence threatens the efficiency of treating these types of infections. The aim of this thesis is to identify potential novel colistin resistance genes and evaluate them in terms of gene mobility and phylogeny. In order to achieve this, a gene model optimized for colistin resistance genes has been created with fARGene. This model was then used to screen large-scale bacterial genomic data for potential novel colistin resistance genes. The predicted genes were analyzed in terms of mobility and phylogeny. This resulted in 680 257 predicted genes, over-represented in the class Gammaproteobacteria within the phylum Pseudomonadota, that could be summarized into 1611 clusters. Out of these clusters, 104 showed signs of mobility, and many were closely related to the already known mobile colistin resistance genes. Additionally, 13 clusters comprising potential mobile novel colistin resistance genes that are present, or at risk of ending up, in pathogenic hosts could be identified.
The abundance and selection of antibiotic resistance genes: A metagenomic study based on wastewater and human gut data.
(2024) Holmström, Michaela; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Kristiansson, Erik; Johnning, Anna; Lund, David
Antibiotic resistance is a global issue, with many consequences for the individual person and society as a whole. Studying potential new genes conferring resistance (latent ARGs) and the flow of resistance genes through environments could be crucial for the prevention and control of ARGs. This project aimed firstly to investigate how antibiotic usage affects new antibiotic resistance genes in the human gut. A metagenomic pipeline including mapping of reads and statistical models using a study of 12 healthy individuals treated with three broad-spectrum antibiotics enabled analysis of ARGs and taxonomy abundances. It was shown that after treatment with the broad-spectrum antibiotics, several latent ARGs were more abundant in the short term, implying the potential selection of these ARGs. The change in ARGs can not be ruled out as being due to the recolonization of fast-growing bacterial species, normally carrying such genes, as also the taxonomy composition was largely affected. This effect was not seen on the last sampling day, after 180 days, in which only one single ARG was found at higher abundance. The short-term effect could, nevertheless, impact the spread of ARGs due to the potential for these ARGs to spread in the disrupted microbiota. Secondly, this project aimed to investigate the flow of ARGs between the human gut and wastewater. For this, a large number of metagenomic samples were used. Similarly to the first part, a metagenomic pipeline was utilized for ARG and taxonomy analysis. Contrary to previous findings, the results implied that ARGs flow from the human gut to the wastewater, while not the other way around. Furthermore, pathogenic presence was highest for ARGs found at high prevalence in both the human gut and wastewater. Interestingly, ARGs present only in wastewater were more prevalent in pathogens compared to ARGs present only in the human gut. This implies that the spread of ARGs to pathogens could be linked to presence in wastewater environments. Moreover, the taxonomy of the human gut and wastewater differed. The results of this project can inform several future research directions, from broadening the data of longitudinal studies to a deeper dive into the flow of ARGs.
The Role of Wnt Signaling in an Embryoid Body Generation Protocol for Hematopoiesis Studies: Investigating the Emergence of Endothelial and Hematopoietic Stem and Progenitor Cells in hiPSC-Derived Embryoid Bodies through RT-qPCR and Flow Cytometry Analysis
(2024) Hilpold Berntsson, Elin; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Kristiansson, Erik; Guibentif, Carolina
Research indicates that childhood leukemia originates in utero during hematopoietic development, emphasizing the importance of understanding embryonic hematopoiesis to identify disruptions leading to diseases such as leukemia. However, studying human embryonic hematopoiesis in vivo faces significant ethical and technical challenges. As an alternative, embryoid bodies (EBs) derived from human induced pluripotent stem cells (hiPSCs) offer a promising in vitro model for studying human developmental processes and hematological diseases. This thesis evaluates an established EB generation protocol for its efficacy in differentiating hiPSCs into hematopoietic stem and progenitor cells (HSPCs). Through the application of real-time quantitative PCR, this study investigates the activation of the Wnt signaling pathway, marked by RSPO3 gene expression, assessing its impact on cell fate decisions within the EBs. Key findings reveal that activation of the Wnt pathway not only induces the emergence of endothelial cells but also facilitates the specification of HSPCs. The robust upregulation of genes such as SOX17, CDH5, RUNX1, GATA2, and HOXA9 over time validates the progressive development of endothelial and hematopoietic lineages. Flow cytometry analysis results also confirm the emergence of endothelial and blood cell populations. However, the response of differentiating hiPSCs to Wnt signaling varies between independent experiments, suggesting that further optimization of the EB generation protocol can be implemented. Overall, the results underscore the role of Wnt signaling in lineage specification, offering valuable insights into hematopoietic differentiation and development in a controlled environment.
Validation of a Damage Accumulation Model of Replicative Ageing in S.cerevisiae.
(2019) Olmin, Amanda; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Chalmers University of Technology / Department of Mathematical Sciences
Age-related diseases and conditions give rise to societal challenges and pose a threat to healthy ageing. At the same time, the more recent evolutionary theories of ageing hypothesise that the process of ageing is a consequence of living rather than an evolutionary strategy. Consequently, it is implied that ageing is not as inevitable as many might believe and, as a consequence, it is of interest to study this biological process and its underlying mechanisms. On a cellular level, accumulation of damage is often regarded as the main cause of ageing. Since the basic properties of ageing between unicellular and multicellular organisms are similar on this level, it is common to use the unicellular yeast Saccharomyces cerevisiae as a model organism in the field of ageing research. The aim of this project is to validate a mathematical damage accumulation model of replicative ageing in yeast. The model represents a cell by intact protein and damage and describes how these quantities change as the cell grows. In addition to cell growth, the model takes asymmetric division, retention and cell death into account. For the purpose of validating the model of replicative ageing, structural and numerical identifiability methods are applied and continuous optimisation is performed using single-cell area data. The model is fit to experimental data obtained for wildtype yeast and the two deletion strains sir2 and fob1. Moreover, replicative lifespan data of 4,698 single-gene deletion strains is analysed and, in conjunction to this, it is investigated how the model parameters affect the replicative lifespan of the simulations. The results show that the parameters in the model of replicative ageing that describes the rate of change of intact protein and damage in the cell, are structurally identifiable. In spite of this, they are not numerically identifiable based on the experimental data available; the parameter estimates obtained have high variances and are moderately or highly correlated with each other. Likewise, it is possible to generate parameter sets that make the mathematical model reproduce the replicative lifespans of the investigated strains, if a replicative lifespan constraint is inferred on the optimisation. For future work, it is suggested that new experimental data is generated as to fit the model of replicative ageing to growth curves belonging to cells of later life stages. Ultimately, the data should be sufficient enough for the optimisation to generate parameter sets that make the model adapt to the characteristics of the investigated strains, without having additional constraints added to the objective function.
What is a successful antibiotic resistance gene? A conceptual model and machine learning predictions
(2024) Einarsson, Elinor; Torell, Stina; Chalmers tekniska högskola / Institutionen för matematiska vetenskaper; Kristiansson, Erik; Lund, David
Antibiotic resistance is a global public health threat and it causes bacterial infections to become more difficult to treat. The spread of antibiotic resistance genes (ARGs) is predominantly driven by horizontal gene transfer (HGT) that enables bacteria to share genetic information directly between cells. The ability of an ARG to spread is influenced by a range of factors, and has become a popular field of research, aiming to find characteristics that enable rapid antibiotic resistance dissemination. This facilitates the identification of ARGs that possess the ability to disseminate rapidly, and for proactive measures against the dissemination to be implemented. Bioinformatics tools were used to study the prevalence of 4775 known ARGs in 867 318 bacterial genomes. A conceptual model describing the success of an ARG was developed containing four different measures of dissemination, over taxonomic barriers, in different GC-environments, geographical dissemination, and dissemination to pathogenic bacteria. By using a top-down approach studying the success of a gene, the thesis complements research studying factors that characterizes successful and rapid HGT. The conceptual model resulted in a success-score for each ARG that reflected the overall performance in the four components. Among the ARGs found to be highly successful the most common class was multidrug resistance, followed by aminoglycoside, β-lactam, and MLS antibiotic resistance. Furthermore, the success-score together with information about the genes, were used to investigate the possibility to predict the success of an ARG with the use of machine learning in a binary classification Random forest algorithm. The model was built to evaluate the predictive performance using decreasing amounts of observations of each gene. As expected, the predictive performance of the model improved as the number of observation increased. Based on only one observation, it was possible to predict the class of each gene with an average sensitivity of ~70% at 90% specificity, and with 250 observations a sensitivity of 98% could be attained. Sequence related features such as gene length and codon usage were important when only a few observations of a gene were used, but as the number of observations grew, non-sequence related features such as number of countries and pathogens a gene was found in, became more relevant. A meta-analysis also aims to explore the managerial and policy implications of antibiotics resistance, and findings include that policies facilitating for machine learning are important to implement. This study can be used as a starting point in the modelling of antibiotic resistance gene success, aiming to help identify emerging ARGs that have the possibility to become future threats.

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