Symbiosis I ( Semester 1). Biology and Statistics. A brief description of the topics covered in the first semester.

Module 1    Introduction: The Scientific Method from the biologist’s viewpoint and the role that statistics plays in measuring variation by statistical hypotheses. The binomial distribution is introduced to test hypotheses about population proportions and the randomization test is introduced to test hypotheses about the equality of means in tow populations. Case studies of scientific hypotheses using von Helmont’s experiments, Stanley Pruissner work on the prion hypothesis, models of yellow fever as a mosquito vectored pathogen and then a class project to ask if HIV can be transmitted by mosquitoes.

Module 2     The Cell as the biological basis of life. Use of statistical graphs and descriptive statistics including correlation with data from cell size databases. The transcription from descriptive to inference through randomization tests and bootstrapping. Biological consequences of surface area/volume rations and mitosis as a consequence of growth.

Module 3.     Size and scale. Introduction to the concepts of scaling and allometry. Differences between isometric and allometric scaling. Fractal branching for surface area/volume problems. Slope as a rate of change. Log-Log plots and the Power Law. The exponential function and the normal distribution. Linear regression and transformations.

Module 4.     Mendelian genetics. The use of Mendel’s original data and how to draw conclusions based on probability. Goodness of Fit tests and independence tests are done using Mendel’s data. The use of the Punnett’s Square and probability trees to demonstrate how the probability of combination of alleles is a representation of the meiosis process. Conditional probability, Bayes rule, Poisson and normal approximation to the binomial distribution and an introduction to sampling methods are the main statistical topics of the module.

Module 5.     DNA Molecular Biology and the Genome. DNA replication and sequence analysis. Revisiting mitosis at the molecular level. Goodness of Fit test and independence tests to study nucleotide and di-nucleotide frequencies in sequence data. Matrices and graphs in the context of transitional (conditional) probabilities. Repeats and palindromes (related to restriction enzyme sites) using probability, random walks in the context of sequence comparisons. Examination of genomes and genome sequences for defined elements.

Module 6.    Evolution. Using probability functions to demonstrate changes in gene frequency over generational times. Evolution concepts including a Walk through DEEP TIME, protein structure, genetic code and mutations. Changes in gene frequency in populations and an introduction to the Wright-Fisher model. Hardy-Weinberg equilibrium, steady state conditions and the t-test.

Symbiosis II ( Semester 2):  Biology and Calculus. A brief description of the topics covered in the second semester. One of the goals of the SYMBIOSIS project is to cover the topics in a first semester calculus course by the end of Symbiosis II. Thus, the calculus in Symbiosis II is actually a continuation of calculus concepts begun in Symbiosis I.

Module  7.     Population Ecology. Introduction to population ecology that uses an increasingly complex sequence of models to explore the annual salmon smolt migration from the headwaters of the Columbia River to the Pacific Ocean. The module begins with a simple emigration/immigration difference equation model, thus giving an accessible context within which to introduce ecological models and rates of change. The inclusion of mortality and reproduction then motivates the development of instantaneous rates of change and the derivative, during which the rules of differentiation are also developed.

Module  8.     Ecological Interactions. Focuses on species-species interactions with an emphasis on competition, predation, symbiosis, and parasitism. This allows several different models to be introduced and the continued development of the calculus. In particular, these models serve as both a pretext and a context for the development of the chain rule, of the properties of the derivative, and of the use of derivatives in qualitative exploration of mathematical models. This includes topics such as differentiability implying continuity, monotonicity and concavity, and the Mean Value Theorem, among others. This also allows us to talk about equilibria in a meaningful way that includes specifics and quantitative results.

Module  9.     Ecological Models. The theme of ecology continues via a different set of mathematical concepts – namely, optimization, limiting processes, structural ecology and simple matrix algebra, and game theoretic concepts. The goal of this module is to show how ecological processes tend toward optimal strategies, as well as being a means of concluding the conceptual development of differential calculus.

Module  10.     Chronobiology. Circadian rhythms and other periodic biological phenomena that allows for the introduction and development of the trigonometric functions. The discussion of the trigonometric functions is delayed not only because students often struggle with trigonometry, but also because periodic processes occur frequently enough in biology so as to allow them to be the subject of an entire module.  The development of the trigonometric functions in this context includes the coverage of harmonic oscillations, derivatives of trigonometric functions, and the statistical concept of a periodogram.

Module 11.     Plant Physiology/Integrals Introduction of the concept of the definite integral using integration in the study of plant physiology. The emphasis is on cumulative processes, as such accumulations are modeled by mathematical integrals. In particular, the concept of a relative rate of change, which is important both mathematically and biologically, is introduced and developed.  Such development motivates and benefits from the concept of the definite integral as a tool for measuring areas, volumes, and masses. The fundamental theorem of calculus is developed and illustrated via several examples, as are some basic techniques for working with integrals.

Module 12.     Enzymes and Energy. Differential equation models are used to study enzymes and energy. These topics includes the Michealis-Menten equations, the use of integrals in solving differential equations, and the use of integrals in the study of cumulative processes other than those which produce changes in area or volume. This module not only wraps up the coverage of the integral calculus with arguably its most important application – the solution and study of differential equations – but it also broadens students’ perspectives to the importance of fields such as physics and chemistry to the pursuit of biology.

 The mathematics component is also assessed since the students have to take the Math Department’s Gateway exam that demonstrates competency in calculus concepts. Successful passage of this exam is required to receive credit from calculus and allows students to take Calculus II.

Symbiosis III ( Semester 3):   Biology, Math and Bioinformatics. A brief description of the topics covered in the first semester.  In Symbiosis III the quantitative components include calculus, matrices, graph theory, advanced statistical topics such as non-linear estimation, multivariate methods and an introduction to bioinformatics. The biological topics are Neurons, Membranes, Developmental Biology and BioInformatics.

Module 13.    Transport across the membrane. Fick’s Law, Danielli-Davson equation and integration to find concentrations. CFTR activity on ion transport. Diffusion, facilitative diffusion and active transport. Trans-membrane proteins. Consequences of the sodium potassium pump on these processes is developed.  

Module 14.     Neuroscience. Excitable cells and membrane potential in nerve transmission and muscle contractions. Action potential and signal propagation. Synapses. Ladder circuit approximation and Ohm’s Law. Cable equation, Hodgkin Huxley Equations. Artificial neural network. 

Module 15.     Photosynthesis. Cyclic and noncyclic electron transport, ATP generation using membrane potential. Integrals and differential equations in Bear-Lambert Law. Estimating parameters of an enzymatic pathway.   

Module 16.    Developmental Biology. A broad description of basic concepts in developmental biology. Topics include morphogenesis, determination and differentiation, morphogens and polarity gradients to establish fields for gene activation. Other topics include fertilization, cleavage, gastrulation; differential gene expression and developmental gene interactions. The approach examines gene expression in relation to development.

Module 17.    Genomics and molecular biology. A short module to introduce basic molecular tools such as cloning, vectors, nucleic acid hybridization (southerns and northerns), genomic sequencing.

Module 18.     Gene expression and BioInformatics. A longer module that uses the previous modules to further examine bioinformatics using gene expression and microarrays. Introduction to NCBI datasets, specifically microarrays from various studies. Datasets are downloaded and “cleaned up”. Log2 values of differential gene expression is introduced and used in analysis. Microarray analysis project. Use of Minitab statistic analysis program. Normalization of values in dataset. Calculation of MA plots and regression analysis of the graphs.