Projects

Invasive species alter community dynamics by changing access to resources and potentially altering abiotic environments. We can assess these changes with the experimental removal of invaders from natural communities or with common garden or greenhouse experiments that create communities. The field removals start with random replicates containing very different initial communities and then remove different relative proportions of the community. Analyzing subsequent community responses offers possibilities for basic factorial statistical analysis, as well as matrix geometric approaches of community characterization. Students will collect data in the field and greenhouse and explore statistical analysis and community characterization.

In mice, the source of the internal clock that maintains internal physiological rhythms in the absence of external cues, is a region of the hypothalamus called the suprachiasmatic nucleus (SCN). Neurons in the SCN exhibit oscillations in mRNA and proteins levels of “clock genes” generated through negative feedback loops in the expression of these genes. Recently, oscillations in clock gene expression have been observed in tissues throughout the body, including lung, liver, and muscle, implying that clocks are in fact distributed throughout the body, synchronized by the master pacemaker in the SCN. This project combines experiments, statistical analysis, and mathematical modeling to explore the effects of shifts of the light-dark cycle on the SCN, and several peripheral tissues (thymus, spleen, esophagus, and liver), of mice. Students with appropriate background will design and run experiments, and the data generated by these experiments will be analyzed using mathematical tools such as wavelets. Deeper implications will be explored through modeling the circadian clock as a dynamical system using differential equations.

Species composition in a local habitat reflects the regional species pool and any transport and disturbance mechanisms that disperse species between local patches to colonize new sites. This project examines plant community composition in wet and dry meadows in areas open to recreational use and closed to the public. The data offer insight into the effect of disturbance, propagule pressure, and regional species richness on invasion and community dynamics. Students will collect plant community data and analyze it. There is also the possibility of testing metacommunity theories in a terrestrial system, a gap in the current ecological literature. Mathematical approaches include basic factorial statistical analysis, robust methods for variable selection and clustering for multivariate responses, and examination of several measures of similarity and dissimilarity, model optimization, matrix geometric approaches.

Mechanisms underlying protein stability are not well-understood, but are intimately related to geometric and structural properties. We consider a set of homologous serine proteases that demonstrate a continuum of stabilization (aLP, Nocardiopsis alba Protease A, Thermobifida fusca protease A, S. griseus protease B, chymotrypsin, and trypsin).  At one extreme is trypsin, a typical protein whose folded state is thermodynamically stable.  At the other extreme is alpha-lytic protease, whose folded state is thermodynamically unstable, and is instead stabilized through a large barrier to unfolding.  This strategy of kinetic stability provides the extracellular aLP with vastly improved longevity over chymotrypsin and trypsin, and appears to derive in part from an increased rigidity of its native state (Jaswal, Nature, 2002).  Molecular dynamics simulations on aLP and trypsin suggest key regions that may contribute to the differences in their stabilization mechanisms (Salimi, PLOS Comp. Biol., 2010).  Rigidity theory offers a less computationally expensive approach to probe the whole set, by mathematically analyzing 3-dimensional structural properties implied by chemical interactions.  We will use rigidity theory to derive measures of rigidity and flexibility all of the proteins.  Confirmation of the MD results for aLP and trypsin will provide confidence that this static approach can be used to compare the full set. Furthermore, additional development of novel rigidity theory techniques may offer new insights into the degree of difference between proteins along the spectrum and the origin of those differences.  Alternatively, this system may identify limitations to the rigidity theory based on structural information alone, as currently configured, and may provide a good testing ground for improving rigidity theory through incorporation of additional experimental features relevant to structural flexibility.

Information on protein stability and folding kinetics is critical to understanding the normal biological function of a protein, as well as the misfolding and aggregation properties of a growing number of proteins found to be involved in neurodegenerative and other diseases of conformation. We are conducting a large-scale analysis of more than one hundred proteins, and investigating new experimental methods (Hydrogen exchange mass spectrometry) to reveal insights relating to protein folding landscapes.

For the analysis side, we are investigating relationships between energetic quantities related to protein folding thermodynamics and kinetics (beyond the known formulaic relationships) and protein structure and function.  We are also investigating certain “outlier” proteins in terms of kinetics/thermodynamics in depth to see if we can ascertain from structural properties why they are outliers (do they have a different protein “fingerprint” than other proteins?). Several possible spin-off problems exist where studying homologues and protein families may be of interest.  A variety of multivariate statistical tools are necessary for the analysis including regression and clustering methods. There is also some possible application of dimension reduction methods, as we are still dealing with a large variable selection problem, due to the size of our database.

Traditional protein folding approaches destabilize the native state.  However, for many proteins, including amyloid precursor proteins and chaperone substrates, significant destabilization of the native state leads to aggregation.  For such proteins, Hydrogen Exchange Mass Spectrometry (HXMS) offers an equilibrium approach to explore their folding landscape at equilibrium. We have developed a numerical simulations approach to model simple HXMS behavior for proteins. By systematically varying conditions of the simulation in analogy to the experimental conditions of temperature and pH, we will probe the relationship between the experimental observables of HXMS and the underlying folding landscape.   This will allow us to optimize methods of analysis to extract folding information from experimental HXMS profiles of proteins. To validate our simulations and analysis, we will first perform HXMS on simple proteins whose landscapes have already been determined through traditional methods.  After validation, we will apply our HXMS approach to proteins not accessible to tradition folding approaches.

Evolutionary and ecological processes (selection, assortative mating, etc) often must be inferred from patterns of variation in nature. These patterns may vary in time and space, and they may vary within vs. between groups. Additionally, the relationship among different kinds of variation (genetic vs geographic vs. ecological) may provide useful insight. Unfortunately, the same pattern may point to different potential explanations, different patterns may point to the same explanation, or the patterns of variation may not fit any current explanation. Consequently, an ongoing challenge is to develop models that may link evolutionary and ecological processes to patterns of variation in actual biological systems. Spatial analysis of variation in biological systems currently is an especially active area or research (landscape genetics, for example).

Hybrid zones, spatial areas where two distinct groups (eg. species) produce hybrid offspring, may be considered a special case of spatial variation. Hybrid zones have great advantages for understanding evolutionary forces because of the particular nature of their structure: linking hybrid zone structure (pattern) and maintenance (process) can reveal how evolution leads to adaptation and how speciation works. Currently, hybrid zone models focus on simple, one-dimensional zones, but even these are limited. Two perspectives of investigation are needed. First, exploring models of hybrid zone structure as a function of dimensionality, complexity, scale, and heterogeneity of the system, are interesting and productive directions. Second, testing candidate models with biological data will provide insight into the connection between spatial patterns and evolutionary parameters.

Using a mouse model of AIDS (called MAIDS) to study genetic and cellular determinants of susceptibility to immune deficiency, we can create infection resulting in a chronic and life-threatening AIDS-like disease in one strain (C57BL/6) and a mild, resolvable illness in the other strain (BALB/c).  We study differential responses within the lymphoid tissues (spleen and lymph node) between the two strains in the first 2 weeks post infection for clues to productive immune response pathways. These studies have involved using DNA microarrays to identify differential gene expression, followed by some limited real time PCR assays and protein-based assays on individual genes/proteins in an attempt to confirm these differences. We published our first joint math and biology collaboration on this work in Immunogenetics (Tepsuporn et al. 2008). We would now like to evaluate the methods used for computational analysis and how these relate to biological outcome. For each of methods, we would convert the statistic to an estimated false discovery rate and use this value to identify differentially expressed genes. Using a systematically varying collection of artificial data, each method can then be compared for accuracy of FDR estimation and success at identifying differentially expressed genes. These alternative methods can also be used to reanalyze our actual data sets and compare the outcomes. We used the permutation methods in our statistical analysis of differential expression and would like to compare this with a principle component analysis, an empirical Bayes procedure, and a hierarchical Bayesian analysis. Students would be involved in all laboratory work and analysis.

Invasive species alter community dynamics by changing access to resources and potentially altering abiotic environments. We can assess these changes with the experimental removal of invaders from natural communities or with common garden or greenhouse experiments that create communities. The field removals start with random replicates containing very different initial communities and then remove different relative proportions of the community. Analyzing subsequent community responses offers possibilities for basic factorial statistical analysis, as well as matrix geometric approaches of community characterization. Students will collect data in the field and greenhouse and explore statistical analysis and community characterization.

Species composition in a local habitat reflects the regional species pool and any transport and disturbance mechanisms that disperse species between local patches to colonize new sites. This project examines plant community composition in wet and dry meadows in areas open to recreational use and closed to the public. The data offer insight into the effect of disturbance, propagule pressure, and regional species richness on invasion and community dynamics. Students will collect plant community data and analyze it. There is also the possibility of testing metacommunity theories in a terrestrial system, a gap in the current ecological literature. Mathematical approaches include basic factorial statistical analysis, robust methods for variable selection and clustering for multivariate responses, and examination of several measures of similarity and dissimilarity, model optimization, matrix geometric approaches.

There is a long history of examining host-parasitoid dynamics in ecology and particularly of looking for factors that help to stabilize the dynamics of these interactions. The consideration of spatial dynamics and additional species interactions has suggested several ways in which dispersal, aggregation, and competition or hyperparasitism can contribute to stabilization. Theory has significantly outstripped empirical studies in this area, but confronting the theory with data leads to very complicated analyses. We have a 28 generation data set exploring the dynamics of a specialist galling midge and a community of parasitoids and hyperparasitoids in a factorial experimental design. We crossed two plant community sizes with caged and uncaged treatments (as well as a cage control) in five blocks across two sites. Even the simplest parametrical statistical analysis of this dataset is somewhat complex because it forces confrontation with response variables that indicate stability (outbreak number and type, cycling) but also because the data are field data and are unavoidably messy and nested. These difficulties in analysis present rich opportunities for student challenges. More complex analyses offer insight into ways to combine statistics with dynamic population and community models. Students work on dissecting galls and identifying larvae, data management, statistical analysis, and modeling. Differential equations in dynamical systems, time-series analysis, and multivariate non-parametric statistical analyses that are robust against contamination are some of the mathematical techniques necessary for this project.

Mechanisms underlying protein stability are not well-understood, but are intimately related to geometric and structural properties. We consider a set of homologous serine proteases that demonstrate a continuum of stabilization (aLP, Nocardiopsis alba Protease A, Thermobifida fusca protease A, S. griseus protease B, chymotrypsin, and trypsin).  At one extreme is trypsin, a typical protein whose folded state is thermodynamically stable.  At the other extreme is alpha-lytic protease, whose folded state is thermodynamically unstable, and is instead stabilized through a large barrier to unfolding.  This strategy of kinetic stability provides the extracellular aLP with vastly improved longevity over chymotrypsin and trypsin, and appears to derive in part from an increased rigidity of its native state (Jaswal, Nature, 2002).  Molecular dynamics simulations on aLP and trypsin suggest key regions that may contribute to the differences in their stabilization mechanisms (Salimi, PLOS Comp. Biol., 2010).  Rigidity theory offers a less computationally expensive approach to probe the whole set, by mathematically analyzing 3-dimensional structural properties implied by chemical interactions.  We will use rigidity theory to derive measures of rigidity and flexibility all of the proteins.  Confirmation of the MD results for aLP and trypsin will provide confidence that this static approach can be used to compare the full set. Furthermore, additional development of novel rigidity theory techniques may offer new insights into the degree of difference between proteins along the spectrum and the origin of those differences.  Alternatively, this system may identify limitations to the rigidity theory based on structural information alone, as currently configured, and may provide a good testing ground for improving rigidity theory through incorporation of additional experimental features relevant to structural flexibility.

Using a mouse model of AIDS (called MAIDS) to study genetic and cellular determinants of susceptibility to immune deficiency, we can create infection resulting in a chronic and life-threatening AIDS-like disease in one strain (C57BL/6) and a mild, resolvable illness in the other strain (BALB/c).  We study differential responses within the lymphoid tissues (spleen and lymph node) between the two strains in the first 2 weeks post infection for clues to productive immune response pathways. These studies have involved using DNA microarrays to identify differential gene expression, followed by some limited real time PCR assays and protein-based assays on individual genes/proteins in an attempt to confirm these differences. We published our first joint math and biology collaboration on this work in Immunogenetics (Tepsuporn et al. 2008). We would now like to evaluate the methods used for computational analysis and how these relate to biological outcome. For each of methods, we would convert the statistic to an estimated false discovery rate and use this value to identify differentially expressed genes. Using a systematically varying collection of artificial data, each method can then be compared for accuracy of FDR estimation and success at identifying differentially expressed genes. These alternative methods can also be used to reanalyze our actual data sets and compare the outcomes. We used the permutation methods in our statistical analysis of differential expression and would like to compare this with a principle component analysis, an empirical Bayes procedure, and a hierarchical Bayesian analysis. Students would be involved in all laboratory work and analysis.

Invasive species alter community dynamics by changing access to resources and potentially altering abiotic environments. We can assess these changes with the experimental removal of invaders from natural communities or with common garden or greenhouse experiments that create communities. The field removals start with random replicates containing very different initial communities and then remove different relative proportions of the community. Analyzing subsequent community responses offers possibilities for basic factorial statistical analysis, as well as matrix geometric approaches of community characterization. Students will collect data in the field and greenhouse and explore statistical analysis and community characterization.

Species composition in a local habitat reflects the regional species pool and any transport and disturbance mechanisms that disperse species between local patches to colonize new sites. This project examines plant community composition in wet and dry meadows in areas open to recreational use and closed to the public. The data offer insight into the effect of disturbance, propagule pressure, and regional species richness on invasion and community dynamics. Students will collect plant community data and analyze it. There is also the possibility of testing metacommunity theories in a terrestrial system, a gap in the current ecological literature. Mathematical approaches include basic factorial statistical analysis, robust methods for variable selection and clustering for multivariate responses, and examination of several measures of similarity and dissimilarity, model optimization, matrix geometric approaches.

There is a long history of examining host-parasitoid dynamics in ecology and particularly of looking for factors that help to stabilize the dynamics of these interactions. The consideration of spatial dynamics and additional species interactions has suggested several ways in which dispersal, aggregation, and competition or hyperparasitism can contribute to stabilization. Theory has significantly outstripped empirical studies in this area, but confronting the theory with data leads to very complicated analyses. We have a 28 generation data set exploring the dynamics of a specialist galling midge and a community of parasitoids and hyperparasitoids in a factorial experimental design. We crossed two plant community sizes with caged and uncaged treatments (as well as a cage control) in five blocks across two sites. Even the simplest parametrical statistical analysis of this dataset is somewhat complex because it forces confrontation with response variables that indicate stability (outbreak number and type, cycling) but also because the data are field data and are unavoidably messy and nested. These difficulties in analysis present rich opportunities for student challenges. More complex analyses offer insight into ways to combine statistics with dynamic population and community models. Students work on dissecting galls and identifying larvae, data management, statistical analysis, and modeling. Differential equations in dynamical systems, time-series analysis, and multivariate non-parametric statistical analyses that are robust against contamination are some of the mathematical techniques necessary for this project.

Mechanisms underlying protein stability are not well-understood, but are intimately related to geometric and structural properties. We consider a set of homologous serine proteases that demonstrate a continuum of stabilization (aLP, Nocardiopsis alba Protease A, Thermobifida fusca protease A, S. griseus protease B, chymotrypsin, and trypsin).  At one extreme is trypsin, a typical protein whose folded state is thermodynamically stable.  At the other extreme is alpha-lytic protease, whose folded state is thermodynamically unstable, and is instead stabilized through a large barrier to unfolding.  This strategy of kinetic stability provides the extracellular aLP with vastly improved longevity over chymotrypsin and trypsin, and appears to derive in part from an increased rigidity of its native state (Jaswal, Nature, 2002).  Molecular dynamics simulations on aLP and trypsin suggest key regions that may contribute to the differences in their stabilization mechanisms (Salimi, PLOS Comp. Biol., 2010).  Rigidity theory offers a less computationally expensive approach to probe the whole set, by mathematically analyzing 3-dimensional structural properties implied by chemical interactions.  We will use rigidity theory to derive measures of rigidity and flexibility all of the proteins.  Confirmation of the MD results for aLP and trypsin will provide confidence that this static approach can be used to compare the full set. Furthermore, additional development of novel rigidity theory techniques may offer new insights into the degree of difference between proteins along the spectrum and the origin of those differences.  Alternatively, this system may identify limitations to the rigidity theory based on structural information alone, as currently configured, and may provide a good testing ground for improving rigidity theory through incorporation of additional experimental features relevant to structural flexibility.