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While students progress through their school years, they are expected to develop reading skills in all academic subjects, including mathematics. Mathematics texts, being multisemiotic, require readers to make meaning not only from written language but also from mathematical symbols and visualizations. Integrating content presented through different sign systems is essential for creating coherence. Thus, the organizational structure of these texts becomes critically important when designing texts for learning. The purpose of this thesis is to build knowledge of the organization of mathematical symbols and written language, and to achieve better understanding of how this organization influences the reading of mathematics texts. 

First, the structural connections between mathematical symbols and written language in mathematics texts designed for students are characterized. Five distinct categories of such connections—Interwoven, Chunked, Marked, Adjoined, and Referenced—are identified, ranging from connections in which mathematical symbols are integrated into sentences (Interwoven), to those based solely on the proximity between two text sequences (Adjoined). The prevalence of these connection categories in textbooks from different school levels is also investigated. The results indicate a progression in the use of structural connections, with a shift from reliance on proximity in early school years towards a preference for symbols interwoven in sentences between years 2 and 5, suggesting that all students eventually need to navigate texts with interwoven symbols. Additionally, changes can be seen in how symbols are being connected to more detailed meanings. Second, the reading of mathematics texts employing two distinct text designs inspired by the new framework is compared: one design features only sentences with interwoven symbols, whereas the other uses a graphic to highlight key connections between symbols and words. The reading processes and experiences of students are investigated by analyzing gaze measurements and interviews. The results indicate that the two designs have different advantages depending on the situation. While the graphic design can facilitate reading and interpretation by drawing attention to the connections between symbols and words, enabling quicker content matching, the symbols interwoven in sentences might provide better access to details or allow more efficient reading in other contexts. Moreover, individual differences in processing and experiences were noted: while some readers benefitted from the graphic design, others did not. Yet, as reading becomes more complex, the graphic is increasingly appreciated. It is concluded that while readers generally prefer text designs that enhance readability, the optimal design varies based on the reader and the context. The discussion includes what text design benefits whom and under what circumstances. 

Spoken mathematical symbols are part of oral communication in mathematics classrooms. The transition from written mathematical symbols into spoken sound is an intricate process that, in some respects, parallels the translation of one language into another. This study focuses on strategy use in the reading aloud of mathematical symbols and compares them to strategies found in second language communication (SLC). In an analysis of sound recordings of university students who read symbolic expressions aloud, SLC strategies were found to be abundant. This indicates that some obstacles encountered when transforming written symbols into spoken words are similar to problems occurring in SLC. It is suggested that mathematics teaching should include some instructions on how to read symbolic expressions.

To engage with specialized subject content, students must develop adequate reading skills. In mathematics, this includes to integrate information from different semiotic resources. This study elucidates how differences in the structural connections between mathematical symbols and written language in mathematics texts can affect the reading process. With the help of eye-tracking techniques, we investigated differences in focus and navigation when 15-year-olds read task texts in two distinct designs: a traditional design with written language presented in lines and all connections based on semantics; and a design including a graphic emphasizing links between symbols and explanations. While the graphic design was found to facilitate fast interpretation of the symbol–language connections, the traditional design seemed to encourage global reading, involving more text parts. When designing texts for mathematics learning, structural connections may be chosen to adapt texts to various student groups and purposes.

A reader of mathematical text must often switch between reading mathematical symbols and reading words. In this study, five different categories of structural connections between symbols and language, which invite such switches, are presented in a framework. The framework was applied in a study of Swedish mathematics textbooks, where 180 randomly selected pages from different educational stages were analyzed. The results showed a significant change in communication patterns as students progress through school. From a predomination of connections based on proximity found in year two, there is a gradual change to a predomination of symbols interwoven in sentences in year eight. Furthermore, more qualitative investigations of the different connections complemented the quantification, both through further explanations of the quantitative results, and through more examples of differences in communication patterns. The implications for readers of mathematics texts are discussed.

In mathematical text and talk, natural language is a constant companion to mathematical symbols. The purpose of this study is to identify different types of relations between natural language and symbolic language in mathematics textbooks. Here we focus on the level of integration. We have identified examples of high integration (e.g., when symbols are part of a sentence), medium integration (e.g., when the shifts between natural and symbolic language occurs when switching to a new line), and low integration (e.g., when symbols and written words are connected by the layout).

In this study, we examine how the use of natural language varies, considering the symbolic language in procedural and conceptual aspects of mathematics.

The transcription factor FocB belongs to a family of regulators encoded by several different fimbriae gene clusters in uropathogenic Escherichia coli. Recent findings suggest that FocB-family proteins may form different protein-protein complexes and that they may exert both positive and negative effects on the transcription of fimbriae genes. However, little is known about the actual role and mode of action when these proteins interact with the fimbriae operons. The 109-amino-acid FocB transcription factor from the foc gene cluster in E. coli strain J96 has been cloned, expressed and purified. The His₆-tagged fusion protein was captured by Ni²⁺-affinity chromatography, cleaved with tobacco etch virus protease and purified by gel filtration. The purified protein is oligomeric, most likely in the form of dimers. NMR analysis guided the crystallization attempts by showing that probable conformational exchange or oligomerization is reduced at temperatures above 293 K and that removal of the highly flexible His₆ tag is advantageous. The protein was crystallized using the hanging-drop vapour-diffusion method at 295 K. A native data set to 2.0 Å resolution was collected at 100 K using synchrotron radiation.

The molecular structure of a protein decides its function, its way to interact with other molecules. Using X-ray crystallography methods, a 3-dimensional, atomic model of a macromolecule can be determined. In this thesis work, the X-ray structures of two different proteins involved in human diseases were studied: FocB, which is associated with urinary tract infections, and transthyretin, which is the causative of hereditary systemic transthyretin amyloidosis.

FocB is a 12 kDa protein which binds DNA in an oligomeric fashion. It is involved in the regulation of the expression of bacterial surface organelles (fimbriae), responsible for the adhesion to specific receptors in host tissue. Specifically, FocB regulates the expression of one fimbrial type found in uropathogenic E. coli (UPEC): F1C. Our FocB structure revealed it to be an all-alpha helical protein with an atypical helix-turn-helix (HTH) motif. Residues previously found important for DNA-binding in the FocB homologue PapB, were not located in the putative “recognition helix” of the HTH-motif. FocB was also found to bind to the minor groove of the DNA. Together with homology searches showing that the DNA-interactions possible for FocB are greatly diversified, these findings indicated a DNA-interaction different from the typical DNA-interaction of a HTH-protein.

Transthyretin (TTR) is a plasma protein involved in transport of thyroxin (T₄) and retinol. Mutated TTR is also the cause of the neurodegenerative disease hereditary systemic transthyretin amyloidosis, which is characterized by systemic deposition of TTR amyloid fibrils. The amyloid occurs through a process of TTR tetramer destabilization and partial unfolding. A common way to inhibit amyloid formation is to design small molecules that bind unoccupied thyroxin binding sites and stabilize the tetrameric form of the protein. The structural characterization of the binding of chloride and iodide ions to TTR revealed that two of three previously identified halogen binding pockets in the T₄-binding site were just as optimal for halide binding. In addition, a third halide-binding site, bridging two TTR subunits, was found. In biochemical experiments, chloride and iodide ions were shown to stabilize the TTR structure and inhibit the TTR aggregation and/or amyloid formation, with iodide ions doing so more efficiently than the chloride ions. In the search for new TTR amyloid-inhibiting drugs, the identified halide-binding sites in the T₄-binding pocket are possible starting points for structure-based drug design.