Projects

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• Axon Growth

  Axon Growth

  Measuring morphogenesis of the embryonic brain.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Michael Barresi (Smith College)

  Project description
  

  After a neuron is born in the developing brain, it sends out a long axon, led by a dynamically motile growth cone. Pathfinding axons must decide whether or not to cross the midline from one hemisphere of the brain to the other, thus forming a commissure. Using transgenic tools to label axons and glial cells in vivo, we are proposing to conduct high-resolution laser scanning confocal time lapse microscopy of commissure formation. This type of imaging will generate enormous 4D data sets to analyze. Mathematical analysis of the data sets, as well as modeling of glial cell morphology and movements in response to growing axons will be critical to understanding the biological formation of commissures.

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• Bioacoustics

  Bioacoustics

  Bioacoustics and the architecture of human hearing

  Statistics: Nicholas Horton, (Smith College)
  Engineering: Susan Voss, (Smith College)

  Project description
  

  One long-term project aims to use emissions from the inner ear to monitor non-invasively changes in intracranial pressure (ICP). We make distortion product otoacoustic emission measurements on both normal subjects and hospitalized subjects who are undergoing invasive ICP monitoring. This work requires both new strategies for defining and lowering the noise floor and optimizing how the magnitude and phase of the responses are combined into a single clinically-relevant measure. A second long-term project aims to include ear-canal based acoustic reflectance measurements in newborn hearing screening protocols with the goal of determining when middle-ear fluid prevents an accurate assessment of inner-ear function. This project relies on a mathematical model for understanding the response of the ear, and analyzes the results from a statistical perspective.

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• Biological Clocks

  Biological Clocks

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

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• Cluster Analysis

  Cluster Analysis

  Unfolding Proteins to Learn Nature’s Origami and Process Statistical Fingerprints of Folding Landscapes

  Chemistry: Sheila Jaswal (Amherst College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Community Dynamics

  Community Dynamics

  Ecohydrology and forest community change

  Biological Sciences: Jesse Bellemare (Smith College)
  Engineering: Andrew Guswa (Smith College)

  Project description
  

  In the face of climate change, land-use modification, and exotic species invasions, gaining a clear understanding of the connections and interactions between hydrology and ecology is vital for effective environmental planning and decision-making. This project, led by a plant ecologist and a hydrologist, will engage students in the measurement and modeling of plant-water interactions from the scale of individual trees to whole forest communities and landscapes. Of particular interest are the divergent ecological and hydrological impacts of coniferous hemlock (Tsuga canadensis) vs. deciduous forest canopies on key ecosystem-level processes in southern New England. This study system is currently in flux, as hemlock faces imminent decline due to attack by the invasive insect hemlock wooly adelgid (Adelges tsugae), while other substantial changes are expected due to rapid climate change in coming decades. Field investigations will be carried out at the Ada and Archibald MacLeish Field Station, a two-hundred acre property managed by Smith College’s Center for the Environment, Ecological Design and Sustainability, that supports environmental research and education. Field projects for students will range from measurement of sap-flux on individual trees, to quantification of forest community structure and dynamics, to assessment of stand-level throughfall, and snow sampling in hemlock and deciduous forest areas. To complement these field studies, students will also employ mathematical models to explore the effects of species, functional type, spatial variability, hydraulic lift, and other factors on plant-water relations and hydrologic processes in the landscape. Using these techniques, students will explore how the hydrologic cycle may change due to changes in forest composition (for example, loss of dominant hemlock), or, conversely, how forest composition may change as a result of modifications in the hydrologic cycle (for example, via climate change), along with consideration of the inherent feedbacks in these processes.

  Invasion, disturbance and community dynamics

  Biology: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

  Propagule pressure, disturbance, and invasion dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Disturbance

  Disturbance

  Propagule pressure, disturbance, and invasion dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Dynamical Systems

  Dynamical Systems

  Geometry of an ecological arms race

  Biological Sciences: L. David Smith (Smith College)
  Mathematics: Christophe Golé (Smith College)

  Project description
  

  This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

  Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

  This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

  Spatial parasitoid community dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)

  Project description
  

  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.

  Spirals in nature: Phyllotaxis.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Denise Lello ( Smith College)

  Project description
  

  The majority of plants display Fibonacci phyllotaxis, featuring Fibonacci numbers of spirals in the arrangement of their organs. We study a dynamical model that offers an explanation of why Fibonacci phyllotaxis is so predominant. Recent advances in our understanding of the biochemistry of plant pattern formation provide a crucial link between models and natural history. We study the transitions between the different kinds of patterns observed in the models and in nature. Students work on growing and dissecting the plants, microscopic imaging, data gathering, modeling, programming and mathematical analysis. Dynamical systems, geometry, number and group theory are some of the mathematics involved.

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• Eco-hydrology

  Eco-hydrology

  Ecohydrology and forest community change

  Biological Sciences: Jesse Bellemare (Smith College)
  Engineering: Andrew Guswa (Smith College)

  Project description
  

  In the face of climate change, land-use modification, and exotic species invasions, gaining a clear understanding of the connections and interactions between hydrology and ecology is vital for effective environmental planning and decision-making. This project, led by a plant ecologist and a hydrologist, will engage students in the measurement and modeling of plant-water interactions from the scale of individual trees to whole forest communities and landscapes. Of particular interest are the divergent ecological and hydrological impacts of coniferous hemlock (Tsuga canadensis) vs. deciduous forest canopies on key ecosystem-level processes in southern New England. This study system is currently in flux, as hemlock faces imminent decline due to attack by the invasive insect hemlock wooly adelgid (Adelges tsugae), while other substantial changes are expected due to rapid climate change in coming decades. Field investigations will be carried out at the Ada and Archibald MacLeish Field Station, a two-hundred acre property managed by Smith College’s Center for the Environment, Ecological Design and Sustainability, that supports environmental research and education. Field projects for students will range from measurement of sap-flux on individual trees, to quantification of forest community structure and dynamics, to assessment of stand-level throughfall, and snow sampling in hemlock and deciduous forest areas. To complement these field studies, students will also employ mathematical models to explore the effects of species, functional type, spatial variability, hydraulic lift, and other factors on plant-water relations and hydrologic processes in the landscape. Using these techniques, students will explore how the hydrologic cycle may change due to changes in forest composition (for example, loss of dominant hemlock), or, conversely, how forest composition may change as a result of modifications in the hydrologic cycle (for example, via climate change), along with consideration of the inherent feedbacks in these processes.

  Go with the flow: Modeling in eco-hydrology

  Engineering: Andrew Guswa (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  This project focuses on the quantitative prediction of linkages among climate, soil-moisture dynamics, and the function of plant roots. Recent work employs a stochastic model of soil-moisture dynamics to determine a water-optimal root depth for plants as a function of rainfall intermittency and intensity. The overarching goal of this work is to improve understanding and representation of hydrologic processes to facilitate informed resource management. The project will include field investigations of throughfall and sapflux at Smith’s recently dedicated Ada and Archibald MacLeish Field Station in West Whately, MA. Mathematical modeling, including stochastic partial differential equations and statistics are integral parts of the project.

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• Ecology

  Ecology

  Ecohydrology and forest community change

  Biological Sciences: Jesse Bellemare (Smith College)
  Engineering: Andrew Guswa (Smith College)

  Project description
  

  In the face of climate change, land-use modification, and exotic species invasions, gaining a clear understanding of the connections and interactions between hydrology and ecology is vital for effective environmental planning and decision-making. This project, led by a plant ecologist and a hydrologist, will engage students in the measurement and modeling of plant-water interactions from the scale of individual trees to whole forest communities and landscapes. Of particular interest are the divergent ecological and hydrological impacts of coniferous hemlock (Tsuga canadensis) vs. deciduous forest canopies on key ecosystem-level processes in southern New England. This study system is currently in flux, as hemlock faces imminent decline due to attack by the invasive insect hemlock wooly adelgid (Adelges tsugae), while other substantial changes are expected due to rapid climate change in coming decades. Field investigations will be carried out at the Ada and Archibald MacLeish Field Station, a two-hundred acre property managed by Smith College’s Center for the Environment, Ecological Design and Sustainability, that supports environmental research and education. Field projects for students will range from measurement of sap-flux on individual trees, to quantification of forest community structure and dynamics, to assessment of stand-level throughfall, and snow sampling in hemlock and deciduous forest areas. To complement these field studies, students will also employ mathematical models to explore the effects of species, functional type, spatial variability, hydraulic lift, and other factors on plant-water relations and hydrologic processes in the landscape. Using these techniques, students will explore how the hydrologic cycle may change due to changes in forest composition (for example, loss of dominant hemlock), or, conversely, how forest composition may change as a result of modifications in the hydrologic cycle (for example, via climate change), along with consideration of the inherent feedbacks in these processes.

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• Environmentally Induced Responses

  Environmentally Induced Responses

  Geometry of an ecological arms race

  Biological Sciences: L. David Smith (Smith College)
  Mathematics: Christophe Golé (Smith College)

  Project description
  

  This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

  Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

  This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.

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• Fibonacci

  Fibonacci

  Spirals in nature: Phyllotaxis.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Denise Lello ( Smith College)

  Project description
  

  The majority of plants display Fibonacci phyllotaxis, featuring Fibonacci numbers of spirals in the arrangement of their organs. We study a dynamical model that offers an explanation of why Fibonacci phyllotaxis is so predominant. Recent advances in our understanding of the biochemistry of plant pattern formation provide a crucial link between models and natural history. We study the transitions between the different kinds of patterns observed in the models and in nature. Students work on growing and dissecting the plants, microscopic imaging, data gathering, modeling, programming and mathematical analysis. Dynamical systems, geometry, number and group theory are some of the mathematics involved.

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• Foraging

  Foraging

  Geometry of an ecological arms race

  Biological Sciences: L. David Smith (Smith College)
  Mathematics: Christophe Golé (Smith College)

  Project description
  

  This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

  Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

  This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.

  << view all topics

• Forest Dynamics

  Forest Dynamics

  Ecohydrology and forest community change

  Biological Sciences: Jesse Bellemare (Smith College)
  Engineering: Andrew Guswa (Smith College)

  Project description
  

  In the face of climate change, land-use modification, and exotic species invasions, gaining a clear understanding of the connections and interactions between hydrology and ecology is vital for effective environmental planning and decision-making. This project, led by a plant ecologist and a hydrologist, will engage students in the measurement and modeling of plant-water interactions from the scale of individual trees to whole forest communities and landscapes. Of particular interest are the divergent ecological and hydrological impacts of coniferous hemlock (Tsuga canadensis) vs. deciduous forest canopies on key ecosystem-level processes in southern New England. This study system is currently in flux, as hemlock faces imminent decline due to attack by the invasive insect hemlock wooly adelgid (Adelges tsugae), while other substantial changes are expected due to rapid climate change in coming decades. Field investigations will be carried out at the Ada and Archibald MacLeish Field Station, a two-hundred acre property managed by Smith College’s Center for the Environment, Ecological Design and Sustainability, that supports environmental research and education. Field projects for students will range from measurement of sap-flux on individual trees, to quantification of forest community structure and dynamics, to assessment of stand-level throughfall, and snow sampling in hemlock and deciduous forest areas. To complement these field studies, students will also employ mathematical models to explore the effects of species, functional type, spatial variability, hydraulic lift, and other factors on plant-water relations and hydrologic processes in the landscape. Using these techniques, students will explore how the hydrologic cycle may change due to changes in forest composition (for example, loss of dominant hemlock), or, conversely, how forest composition may change as a result of modifications in the hydrologic cycle (for example, via climate change), along with consideration of the inherent feedbacks in these processes.

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• Gene Expression

  Gene Expression

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

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• Genetics

  Genetics

  Genetic and cellular determinants of susceptibility to immune deficiency

  Biological Sciences: Sharon Stranford (Mount Holyoke College)

  Project description
  

   

   

  
  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.

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• Geometry

  Geometry

  Geometry of an ecological arms race

  Biological Sciences: L. David Smith (Smith College)
  Mathematics: Christophe Golé (Smith College)

  Project description
  

  This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

  Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

  This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.

  Protein Function from Rigidity, Flexibility and Motion

  
  Biology: Robert Dorit (Smith College)
  Mathematics and Computer Science: Ileana Streinu (Smith College)

  Project description
  

  Proteins and other large biomolecules can be modeled as mechanical linkages, reminiscent in many ways of articulated robot arms. To simulate their motions, the existing mathematical theories and computational tools do not scale up: the entire process of folding or unfolding of a protein is a problem that poses formidable computational challenges. Useful information about the molecule’s “potential to flex” can be gathered through rigidity analysis, and in turn this can shed light on questions concerning its function.

  Students engaged in this project explore questions directly motivated by protein geometry, and participate in the design and development of prototype computer simulations. The underlying mathematics includes graph theory, computational geometry, rigidity theory and kinematics.

  Spirals in nature: Phyllotaxis.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Denise Lello ( Smith College)

  Project description
  

  The majority of plants display Fibonacci phyllotaxis, featuring Fibonacci numbers of spirals in the arrangement of their organs. We study a dynamical model that offers an explanation of why Fibonacci phyllotaxis is so predominant. Recent advances in our understanding of the biochemistry of plant pattern formation provide a crucial link between models and natural history. We study the transitions between the different kinds of patterns observed in the models and in nature. Students work on growing and dissecting the plants, microscopic imaging, data gathering, modeling, programming and mathematical analysis. Dynamical systems, geometry, number and group theory are some of the mathematics involved.

  Vacancy: Distribution of biological objects in shape space

  Biological Sciences: Robert Dorit (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  Biological objects, from ecosystems to molecules, exist in three-dimensional space. Over the past century, considerable progress has been made not only in the measurement and description of these objects, but in the elucidation of the underlying rules that generate their form. The mathematical description of biological shape, whether in the form of coupled equations describing gastropod coiling or of folding algorithms for RNA secondary structure, make it possible to describe a “shape space” for the relevant objects. That description of shape space, in turn, makes it possible to examine the occupancy of that space. The data suggest that existing objects are not isotropically distributed in shape space, but are instead clumped and that large amounts of shape space are unoccupied. We are exploring the underlying reasons for that non-isotropic distribution, which may be functional, historical, stochastic or developmental. mathematical statistics and geometry are integral parts of this project.

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• Glial Cells

  Glial Cells

  Measuring morphogenesis of the embryonic brain.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Michael Barresi (Smith College)

  Project description
  

  After a neuron is born in the developing brain, it sends out a long axon, led by a dynamically motile growth cone. Pathfinding axons must decide whether or not to cross the midline from one hemisphere of the brain to the other, thus forming a commissure. Using transgenic tools to label axons and glial cells in vivo, we are proposing to conduct high-resolution laser scanning confocal time lapse microscopy of commissure formation. This type of imaging will generate enormous 4D data sets to analyze. Mathematical analysis of the data sets, as well as modeling of glial cell morphology and movements in response to growing axons will be critical to understanding the biological formation of commissures.

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• Host-parasitoid Interactions

  Host-parasitoid Interactions

  Spatial parasitoid community dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)

  Project description
  

  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.

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• Immune Deficiency

  Immune Deficiency

  Genetic and cellular determinants of susceptibility to immune deficiency

  Biological Sciences: Sharon Stranford (Mount Holyoke College)

  Project description
  

   

   

  
  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.

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• Introduced Species

  Introduced Species

  Geometry of an ecological arms race

  Biological Sciences: L. David Smith (Smith College)
  Mathematics: Christophe Golé (Smith College)

  Project description
  

  This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

  Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

  This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.

  Invasion, disturbance and community dynamics

  Biology: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

  Propagule pressure, disturbance, and invasion dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Invasive Species

  Invasive Species

  Ecohydrology and forest community change

  Biological Sciences: Jesse Bellemare (Smith College)
  Engineering: Andrew Guswa (Smith College)

  Project description
  

  In the face of climate change, land-use modification, and exotic species invasions, gaining a clear understanding of the connections and interactions between hydrology and ecology is vital for effective environmental planning and decision-making. This project, led by a plant ecologist and a hydrologist, will engage students in the measurement and modeling of plant-water interactions from the scale of individual trees to whole forest communities and landscapes. Of particular interest are the divergent ecological and hydrological impacts of coniferous hemlock (Tsuga canadensis) vs. deciduous forest canopies on key ecosystem-level processes in southern New England. This study system is currently in flux, as hemlock faces imminent decline due to attack by the invasive insect hemlock wooly adelgid (Adelges tsugae), while other substantial changes are expected due to rapid climate change in coming decades. Field investigations will be carried out at the Ada and Archibald MacLeish Field Station, a two-hundred acre property managed by Smith College’s Center for the Environment, Ecological Design and Sustainability, that supports environmental research and education. Field projects for students will range from measurement of sap-flux on individual trees, to quantification of forest community structure and dynamics, to assessment of stand-level throughfall, and snow sampling in hemlock and deciduous forest areas. To complement these field studies, students will also employ mathematical models to explore the effects of species, functional type, spatial variability, hydraulic lift, and other factors on plant-water relations and hydrologic processes in the landscape. Using these techniques, students will explore how the hydrologic cycle may change due to changes in forest composition (for example, loss of dominant hemlock), or, conversely, how forest composition may change as a result of modifications in the hydrologic cycle (for example, via climate change), along with consideration of the inherent feedbacks in these processes.

  Propagule pressure, disturbance, and invasion dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Kinetics

  Kinetics

  The Geometry Behind Protein Stability

  Chemistry:  Sheila Jaswal  (Amherst College)
  Computer Science: Audrey Lee-St.John (Mount Holyoke College)

  Project description
  

  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.

  Unfolding Proteins to Learn Nature’s Origami and Process Statistical Fingerprints of Folding Landscapes

  Chemistry: Sheila Jaswal (Amherst College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• MRNA

  MRNA

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

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• Matrix Geometry

  Matrix Geometry

  Invasion, disturbance and community dynamics

  Biology: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

  << view all topics

• Metacommunity Dynamics

  Metacommunity Dynamics

  Propagule pressure, disturbance, and invasion dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)
  Math and Statistics: Matt Noonan (Mount Holyoke College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

  << view all topics

• Morphogenesis

  Morphogenesis

  Measuring morphogenesis of the embryonic brain.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Michael Barresi (Smith College)

  Project description
  

  After a neuron is born in the developing brain, it sends out a long axon, led by a dynamically motile growth cone. Pathfinding axons must decide whether or not to cross the midline from one hemisphere of the brain to the other, thus forming a commissure. Using transgenic tools to label axons and glial cells in vivo, we are proposing to conduct high-resolution laser scanning confocal time lapse microscopy of commissure formation. This type of imaging will generate enormous 4D data sets to analyze. Mathematical analysis of the data sets, as well as modeling of glial cell morphology and movements in response to growing axons will be critical to understanding the biological formation of commissures.

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• Multi-dimensional Scaling

  Multi-dimensional Scaling

  Unfolding Proteins to Learn Nature’s Origami and Process Statistical Fingerprints of Folding Landscapes

  Chemistry: Sheila Jaswal (Amherst College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Non-isotropic Distribution

  Non-isotropic Distribution

  Vacancy: Distribution of biological objects in shape space

  Biological Sciences: Robert Dorit (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  Biological objects, from ecosystems to molecules, exist in three-dimensional space. Over the past century, considerable progress has been made not only in the measurement and description of these objects, but in the elucidation of the underlying rules that generate their form. The mathematical description of biological shape, whether in the form of coupled equations describing gastropod coiling or of folding algorithms for RNA secondary structure, make it possible to describe a “shape space” for the relevant objects. That description of shape space, in turn, makes it possible to examine the occupancy of that space. The data suggest that existing objects are not isotropically distributed in shape space, but are instead clumped and that large amounts of shape space are unoccupied. We are exploring the underlying reasons for that non-isotropic distribution, which may be functional, historical, stochastic or developmental. mathematical statistics and geometry are integral parts of this project.

  << view all topics

• Oscillations

  Oscillations

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

  << view all topics

• Phyllotaxis

  Phyllotaxis

  Spirals in nature: Phyllotaxis.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Denise Lello ( Smith College)

  Project description
  

  The majority of plants display Fibonacci phyllotaxis, featuring Fibonacci numbers of spirals in the arrangement of their organs. We study a dynamical model that offers an explanation of why Fibonacci phyllotaxis is so predominant. Recent advances in our understanding of the biochemistry of plant pattern formation provide a crucial link between models and natural history. We study the transitions between the different kinds of patterns observed in the models and in nature. Students work on growing and dissecting the plants, microscopic imaging, data gathering, modeling, programming and mathematical analysis. Dynamical systems, geometry, number and group theory are some of the mathematics involved.

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• Predator-prey

  Predator-prey

  Geometry of an ecological arms race

  Biological Sciences: L. David Smith (Smith College)
  Mathematics: Christophe Golé (Smith College)

  Project description
  

  This project examines the geometry of a predator-prey arms race between populations of introduced crabs and native snails along the New England coast. In particular, we are interested in understanding the role that phenotypic plasticity (environmentally induced change in a character during an organism’s lifetime) plays in this ecological interaction.

  Experiments using diverse taxonomic groups have shown that both predator trophic (feeding) structures and prey morphological defenses can change in response to environmental cues during development. In our system, invasive crabs fed thick-shelled snails develop relatively larger, stronger claws after molting than do crabs fed thin-shelled snails. In turn, snails reared in the presence of crabs build, over the course of weeks, thicker, more resistant shells than in their absence. Thus, phenotypic plasticity provides a means by which an invader can respond relatively quickly to its new environment, and induced defenses may allow resident prey species to mitigate impacts of the invader. Predicting the consequences of a predator introduction, however, requires an understanding of how key environmental variables (e.g., predator density, shell defenses, water temperature) influence both the magnitude and rate of induced responses in antagonists over the invader’s range.

  This project will use field and lab experiments to compare crab foraging performance and defensive effectiveness of shells with respect to the geometric parameters of growth, environmental cues, and functional trade-offs. Mathematical modeling for this project includes geometry, size scaling of predator-prey interactions (allometry), dynamical systems, game theory, programming in Mathematica, and statistics.

  << view all topics

• Protein Folding

  Protein Folding

  The Geometry Behind Protein Stability

  Chemistry:  Sheila Jaswal  (Amherst College)
  Computer Science: Audrey Lee-St.John (Mount Holyoke College)

  Project description
  

  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.

  Unfolding Proteins to Learn Nature’s Origami and Process Statistical Fingerprints of Folding Landscapes

  Chemistry: Sheila Jaswal (Amherst College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

  << view all topics

• Shape Space

  Shape Space

  Vacancy: Distribution of biological objects in shape space

  Biological Sciences: Robert Dorit (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  Biological objects, from ecosystems to molecules, exist in three-dimensional space. Over the past century, considerable progress has been made not only in the measurement and description of these objects, but in the elucidation of the underlying rules that generate their form. The mathematical description of biological shape, whether in the form of coupled equations describing gastropod coiling or of folding algorithms for RNA secondary structure, make it possible to describe a “shape space” for the relevant objects. That description of shape space, in turn, makes it possible to examine the occupancy of that space. The data suggest that existing objects are not isotropically distributed in shape space, but are instead clumped and that large amounts of shape space are unoccupied. We are exploring the underlying reasons for that non-isotropic distribution, which may be functional, historical, stochastic or developmental. mathematical statistics and geometry are integral parts of this project.

  << view all topics

• Soil-moisture Dynamics

  Soil-moisture Dynamics

  Go with the flow: Modeling in eco-hydrology

  Engineering: Andrew Guswa (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  This project focuses on the quantitative prediction of linkages among climate, soil-moisture dynamics, and the function of plant roots. Recent work employs a stochastic model of soil-moisture dynamics to determine a water-optimal root depth for plants as a function of rainfall intermittency and intensity. The overarching goal of this work is to improve understanding and representation of hydrologic processes to facilitate informed resource management. The project will include field investigations of throughfall and sapflux at Smith’s recently dedicated Ada and Archibald MacLeish Field Station in West Whately, MA. Mathematical modeling, including stochastic partial differential equations and statistics are integral parts of the project.

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• Spatial Dynamics

  Spatial Dynamics

  Spatial parasitoid community dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)

  Project description
  

  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.

  << view all topics

• Species Interactions

  Species Interactions

  Spatial parasitoid community dynamics

  Biological Sciences: Martha Hoopes (Mount Holyoke College)
  Math and Statistics: Janice Gifford (Mount Holyoke College)
  Math and Statistics: Ji Young Kim (Mount Holyoke College)

  Project description
  

  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.

  << view all topics

• Statistics

  Statistics

  Bioacoustics and the architecture of human hearing

  Statistics: Nicholas Horton, (Smith College)
  Engineering: Susan Voss, (Smith College)

  Project description
  

  One long-term project aims to use emissions from the inner ear to monitor non-invasively changes in intracranial pressure (ICP). We make distortion product otoacoustic emission measurements on both normal subjects and hospitalized subjects who are undergoing invasive ICP monitoring. This work requires both new strategies for defining and lowering the noise floor and optimizing how the magnitude and phase of the responses are combined into a single clinically-relevant measure. A second long-term project aims to include ear-canal based acoustic reflectance measurements in newborn hearing screening protocols with the goal of determining when middle-ear fluid prevents an accurate assessment of inner-ear function. This project relies on a mathematical model for understanding the response of the ear, and analyzes the results from a statistical perspective.

  Genetic and cellular determinants of susceptibility to immune deficiency

  Biological Sciences: Sharon Stranford (Mount Holyoke College)

  Project description
  

   

   

  
  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.

  Go with the flow: Modeling in eco-hydrology

  Engineering: Andrew Guswa (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  This project focuses on the quantitative prediction of linkages among climate, soil-moisture dynamics, and the function of plant roots. Recent work employs a stochastic model of soil-moisture dynamics to determine a water-optimal root depth for plants as a function of rainfall intermittency and intensity. The overarching goal of this work is to improve understanding and representation of hydrologic processes to facilitate informed resource management. The project will include field investigations of throughfall and sapflux at Smith’s recently dedicated Ada and Archibald MacLeish Field Station in West Whately, MA. Mathematical modeling, including stochastic partial differential equations and statistics are integral parts of the project.

  Vacancy: Distribution of biological objects in shape space

  Biological Sciences: Robert Dorit (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  Biological objects, from ecosystems to molecules, exist in three-dimensional space. Over the past century, considerable progress has been made not only in the measurement and description of these objects, but in the elucidation of the underlying rules that generate their form. The mathematical description of biological shape, whether in the form of coupled equations describing gastropod coiling or of folding algorithms for RNA secondary structure, make it possible to describe a “shape space” for the relevant objects. That description of shape space, in turn, makes it possible to examine the occupancy of that space. The data suggest that existing objects are not isotropically distributed in shape space, but are instead clumped and that large amounts of shape space are unoccupied. We are exploring the underlying reasons for that non-isotropic distribution, which may be functional, historical, stochastic or developmental. mathematical statistics and geometry are integral parts of this project.

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• Stochastic Models

  Stochastic Models

  Go with the flow: Modeling in eco-hydrology

  Engineering: Andrew Guswa (Smith College)
  Statistics: Nicholas Horton (Smith College)

  Project description
  

  This project focuses on the quantitative prediction of linkages among climate, soil-moisture dynamics, and the function of plant roots. Recent work employs a stochastic model of soil-moisture dynamics to determine a water-optimal root depth for plants as a function of rainfall intermittency and intensity. The overarching goal of this work is to improve understanding and representation of hydrologic processes to facilitate informed resource management. The project will include field investigations of throughfall and sapflux at Smith’s recently dedicated Ada and Archibald MacLeish Field Station in West Whately, MA. Mathematical modeling, including stochastic partial differential equations and statistics are integral parts of the project.

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• Suprachiasmic Nucleus

  Suprachiasmic Nucleus

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

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• Thermodynamics

  Thermodynamics

  Unfolding Proteins to Learn Nature’s Origami and Process Statistical Fingerprints of Folding Landscapes

  Chemistry: Sheila Jaswal (Amherst College)
  Mathematics: Amy Wagaman (Amherst College)

  Project description
  

  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.

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• Transitions

  Transitions

  Spirals in nature: Phyllotaxis.

  Mathematics: Christophe Gole (Smith College)
  Biological Sciences: Denise Lello ( Smith College)

  Project description
  

  The majority of plants display Fibonacci phyllotaxis, featuring Fibonacci numbers of spirals in the arrangement of their organs. We study a dynamical model that offers an explanation of why Fibonacci phyllotaxis is so predominant. Recent advances in our understanding of the biochemistry of plant pattern formation provide a crucial link between models and natural history. We study the transitions between the different kinds of patterns observed in the models and in nature. Students work on growing and dissecting the plants, microscopic imaging, data gathering, modeling, programming and mathematical analysis. Dynamical systems, geometry, number and group theory are some of the mathematics involved.

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• Wavelet Analysis

  Wavelet Analysis

  Oscillations in biological clock gene expression

  Life Sciences: Mary Harrington (Smith College)
  Mathematics: Tanya Leise (Amherst College)

  Project description
  

  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.

  << view all topics