Changing the Nature of Quantitative Biology Education: Data Science as a Driver.

We live in a data-rich world with rapidly growing databases with zettabytes of data. Innovation, computation, and technological advances have now tremendously accelerated the pace of discovery, providing driverless cars, robotic devices, expert healthcare systems, precision medicine, and automated discovery to mention a few. Even though the definition of the term data science continues to evolve, the sweeping impact it has already produced on society is undeniable. We are at a point when new discoveries through data science have enormous potential to advance progress but also to be used maliciously, with harmful ethical and social consequences. Perhaps nowhere is this more clearly exemplified than in the biological and medical sciences. The confluence of (1) machine learning, (2) mathematical modeling, (3) computation/simulation, and (4) big data have moved us from the sequencing of genomes to gene editing and individualized medicine; yet, unsettled policies regarding data privacy and ethical norms could potentially open doors for serious negative repercussions. The data science revolution has amplified the urgent need for a paradigm shift in undergraduate biology education. It has reaffirmed that data science education interacts and enhances mathematical education in advancing quantitative conceptual and skill development for the new generation of biologists. These connections encourage us to strive to cultivate a broadly skilled workforce of technologically savvy problem-solvers, skilled at handling the unique challenges pertaining to biological data, and capable of collaborating across various disciplines in the sciences, the humanities, and the social sciences. To accomplish this, we suggest development of open curricula that extend beyond the job certification rhetoric and combine data acumen with modeling, experimental, and computational methods through engaging projects, while also providing awareness and deep exploration of their societal implications. This process would benefit from embracing the pedagogy of experiential learning and involve students in open-ended explorations derived from authentic inquiries and ongoing research. On this foundation, we encourage development of flexible data science initiatives for the education of life science undergraduates within and across existing models.

Mathematics and evolutionary biology make bioinformatics education comprehensible.

The patterns of variation within a molecular sequence data set result from the interplay between population genetic, molecular evolutionary and macroevolutionary processes-the standard purview of evolutionary biologists. Elucidating these patterns, particularly for large data sets, requires an understanding of the structure, assumptions and limitations of the algorithms used by bioinformatics software-the domain of mathematicians and computer scientists. As a result, bioinformatics often suffers a 'two-culture' problem because of the lack of broad overlapping expertise between these two groups. Collaboration among specialists in different fields has greatly mitigated this problem among active bioinformaticians. However, science education researchers report that much of bioinformatics education does little to bridge the cultural divide, the curriculum too focused on solving narrow problems (e.g. interpreting pre-built phylogenetic trees) rather than on exploring broader ones (e.g. exploring alternative phylogenetic strategies for different kinds of data sets). Herein, we present an introduction to the mathematics of tree enumeration, tree construction, split decomposition and sequence alignment. We also introduce off-line downloadable software tools developed by the BioQUEST Curriculum Consortium to help students learn how to interpret and critically evaluate the results of standard bioinformatics analyses.

Ka-me: a Voronoi image analyzer.

SUMMARY: Ka-me is a Voronoi image analyzer that allows users to analyze any image with a convex polygonal tessellation or any spatial point distribution by fitting Voronoi polygons and their dual, Delaunay triangulations, to the pattern. The analytical tools include a variety of graph theoretic and geometric tools that summarize the distribution of the numbers of edges per face, areas, perimeters, angles of Delaunay triangle edges (anglograms), Gabriel graphs, nearest neighbor graphs, minimal spanning trees, Ulam trees, Pitteway tests, circumcircles and convexhulls, as well as spatial statistics (Clark-Evans Nearest Neighborhood and Variance to Mean Ratio) and export functions for standard relationships (Lewis's Law, Desch's Law and Aboav-Weaire Law). AVAILABILITY: Ka-me: a Voronoi image analyzer is available as an executable with documentation and sample applications from the BioQUEST Library (http://bioquest.org/downloads/kame_1.0.rar).

An international consensus on effective, inclusive, and career-spanning short-format training in the life sciences and beyond.

Science, technology, engineering, mathematics, and medicine (STEMM) fields change rapidly and are increasingly interdisciplinary. Commonly, STEMM practitioners use short-format training (SFT) such as workshops and short courses for upskilling and reskilling, but unaddressed challenges limit SFT's effectiveness and inclusiveness. Education researchers, students in SFT courses, and organizations have called for research and strategies that can strengthen SFT in terms of effectiveness, inclusiveness, and accessibility across multiple dimensions. This paper describes the project that resulted in a consensus set of 14 actionable recommendations to systematically strengthen SFT. A diverse international group of 30 experts in education, accessibility, and life sciences came together from 10 countries to develop recommendations that can help strengthen SFT globally. Participants, including representation from some of the largest life science training programs globally, assembled findings in the educational sciences and encompassed the experiences of several of the largest life science SFT programs. The 14 recommendations were derived through a Delphi method, where consensus was achieved in real time as the group completed a series of meetings and tasks designed to elicit specific recommendations. Recommendations cover the breadth of SFT contexts and stakeholder groups and include actions for instructors (e.g., make equity and inclusion an ethical obligation), programs (e.g., centralize infrastructure for assessment and evaluation), as well as organizations and funders (e.g., professionalize training SFT instructors; deploy SFT to counter inequity). Recommendations are aligned with a purpose-built framework-"The Bicycle Principles"-that prioritizes evidenced-based teaching, inclusiveness, and equity, as well as the ability to scale, share, and sustain SFT. We also describe how the Bicycle Principles and recommendations are consistent with educational change theories and can overcome systemic barriers to delivering consistently effective, inclusive, and career-spanning SFT.

Bioinformatics education dissemination with an evolutionary problem solving perspective.

Bioinformatics is central to biology education in the 21st century. With the generation of terabytes of data per day, the application of computer-based tools to stored and distributed data is fundamentally changing research and its application to problems in medicine, agriculture, conservation and forensics. In light of this 'information revolution,' undergraduate biology curricula must be redesigned to prepare the next generation of informed citizens as well as those who will pursue careers in the life sciences. The BEDROCK initiative (Bioinformatics Education Dissemination: Reaching Out, Connecting and Knitting together) has fostered an international community of bioinformatics educators. The initiative's goals are to: (i) Identify and support faculty who can take leadership roles in bioinformatics education; (ii) Highlight and distribute innovative approaches to incorporating evolutionary bioinformatics data and techniques throughout undergraduate education; (iii) Establish mechanisms for the broad dissemination of bioinformatics resource materials and teaching models; (iv) Emphasize phylogenetic thinking and problem solving; and (v) Develop and publish new software tools to help students develop and test evolutionary hypotheses. Since 2002, BEDROCK has offered more than 50 faculty workshops around the world, published many resources and supported an environment for developing and sharing bioinformatics education approaches. The BEDROCK initiative builds on the established pedagogical philosophy and academic community of the BioQUEST Curriculum Consortium to assemble the diverse intellectual and human resources required to sustain an international reform effort in undergraduate bioinformatics education.

Mathematics make microbes beautiful, beneficial, and bountiful.

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning.

Wenxiang 3.0: Evolutionary Visualization of α, π, and 3/10 Helices.

Wenxiang diagrams illustrate protein helices as spirals on a plane and thus have the advantage over helical wheels of being planar graphs. Wenxiang 3.0 extends the original version by adding 3 major features: (1) individual amino acid residues can be colored according to their evolutionary conservation in comparative multiple sequence alignments using CONSURF encoding; (2) α, π, and 3/10 helices can be illustrated by overlaying arcs representative of the pitches of these helices; and, (3) the physico-chemical properties of amino acids residues in the protein sequence can be re-presented by colored geometric shapes.

Self-Assembly, Self-Folding, and Origami: Comparative Design Principles.

Self-assembly is usually considered a parallel process while self-folding and origami are usually considered to be serial processes. We believe that these distinctions do not hold in actual experiments. Based upon our experience with 4D printing, we have developed three additional hybrid classes: (1) templated-assisted (tethered) self-assembly: e.g., when RNA is bound to viral capsomeres, the subunits are constricted in their interactions to have aspects of self-folding as well; (2) self-folding can depend upon interactions with the environment; for example, a protein synthesized on a ribosome will fold as soon as peptides enter the intracellular environment in a serial process whereas if denatured complete proteins are put into solution, parallel folding can occur simultaneously; and, (3) in turbulent environments, chaotic conditions continuously alternate processes. We have examined the 43,380 Dürer nets of dodecahedra and 43,380 Dürer nets of icosahedra and their corresponding duals: Schlegel diagrams. In order to better understand models of self-assembly of viral capsids, we have used both geometric (radius of gyration, convex hulls, angles) and topological (vertex connections, leaves, spanning trees, cutting trees, and degree distributions) perspectives to develop design principles for 4D printing experiments. Which configurations fold most rapidly? Which configurations lead to complete polyhedra most of the time? By using Hamiltonian circuits of the vertices of Dürer nets and Eulerian paths of cutting trees of polyhedra unto Schlegel diagrams, we have been able to develop a systematic sampling procedure to explore the 86,760 configurations, models of a T1 viral capsid with 60 subunits and to test alternatives with 4D printing experiments, use of MagformsTM, and origami models to demonstrate via movies the five processes described above.

Art Forms in Nature: radiolaria from Haeckel and Blaschka to 3D nanotomography, quantitative image analysis, evolution, and contemporary art.

The illustrations of the late nineteenth-/twentieth-century scientist/artist Ernst Haeckel, as depicted in his book Art Forms in Nature (originally in German as Kunstformen der Natur, 1898-1904), have been at the intersection of art, biology, and mathematics for over a century. Haeckel's images of radiolaria (microscopic protozoans described as amoeba in glass houses) have influenced various artists for over a century (glass artists Leopold and Rudolph Blaschka; sculptor Henry Moore; architects Rene Binet, Zaha Hadid, Antoni Gaudi, Chris Bosse and Frank Gehry; and designers-filmmakers Charles and Ray Eames). We focus on this history and extend the artistic, biological, and mathematical contributions of this interdisciplinary legacy by going beyond the 3D visual, topological, and geometric analyses of radiolaria to include the nanoscale with graph theory, spatial statistics, and computational geometry. We analyze multiple visualizations of radiolaria generated through Haeckel's images, light microscopy, scanning electron microscopy, micro- and nanotomography, and three-dimensional computer rendering. Mathematical analyses are conducted using the image analysis package "Ka-me: A Voronoi Image Analyzer." Further analyses utilize three-dimensional printing, laser etched crystalline glass art, and sculpture. Open sharing of three-dimensional nanotomography of radiolaria and other protozoa through MorphoSource enables new possibilities for artists, architects, paleontologists, structural morphologists, taxonomists, museum curators, and mathematical biologists. Distinctively, newer models of radiolaria fit into a larger context of productive interdisciplinary collaboration that continues Haeckel's legacy that lay a foundation for new work in biomimetic design and additive manufacturing where artistic and scientific models mutually and robustly generate wonder, beauty, utility, curiosity, insight, environmentalism, theory, and questions.

Barriers to integration of bioinformatics into undergraduate life sciences education: A national study of US life sciences faculty uncover significant barriers to integrating bioinformatics into undergraduate instruction.

Bioinformatics, a discipline that combines aspects of biology, statistics, mathematics, and computer science, is becoming increasingly important for biological research. However, bioinformatics instruction is not yet generally integrated into undergraduate life sciences curricula. To understand why we studied how bioinformatics is being included in biology education in the US by conducting a nationwide survey of faculty at two- and four-year institutions. The survey asked several open-ended questions that probed barriers to integration, the answers to which were analyzed using a mixed-methods approach. The barrier most frequently reported by the 1,260 respondents was lack of faculty expertise/training, but other deterrents-lack of student interest, overly-full curricula, and lack of student preparation-were also common. Interestingly, the barriers faculty face depended strongly on whether they are members of an underrepresented group and on the Carnegie Classification of their home institution. We were surprised to discover that the cohort of faculty who were awarded their terminal degree most recently reported the most preparation in bioinformatics but teach it at the lowest rate.

Bioinformatics core competencies for undergraduate life sciences education.

Although bioinformatics is becoming increasingly central to research in the life sciences, bioinformatics skills and knowledge are not well integrated into undergraduate biology education. This curricular gap prevents biology students from harnessing the full potential of their education, limiting their career opportunities and slowing research innovation. To advance the integration of bioinformatics into life sciences education, a framework of core bioinformatics competencies is needed. To that end, we here report the results of a survey of biology faculty in the United States about teaching bioinformatics to undergraduate life scientists. Responses were received from 1,260 faculty representing institutions in all fifty states with a combined capacity to educate hundreds of thousands of students every year. Results indicate strong, widespread agreement that bioinformatics knowledge and skills are critical for undergraduate life scientists as well as considerable agreement about which skills are necessary. Perceptions of the importance of some skills varied with the respondent's degree of training, time since degree earned, and/or the Carnegie Classification of the respondent's institution. To assess which skills are currently being taught, we analyzed syllabi of courses with bioinformatics content submitted by survey respondents. Finally, we used the survey results, the analysis of the syllabi, and our collective research and teaching expertise to develop a set of bioinformatics core competencies for undergraduate biology students. These core competencies are intended to serve as a guide for institutions as they work to integrate bioinformatics into their life sciences curricula.

Mathematical manipulative models: in defense of "beanbag biology".

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.