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Mathematical biology has emerged as a powerful approach to describe and understand biological systems. Here, we introduce an interactive teaching tool with a practical hands-on skill session plan to introduce students to the various components of a mathematical model with 4 different mathematical approaches (i.e., ordinary differential equations, partial differential equations, stochastic differential equations, and spatial stochastic differential equations) and their advantages and disadvantages. As such, we provide a didactic summary for instructors and students interested in using VCell MathModels for mathematical modeling; this work is also valuable for mathematics-savvy users who would like to exploit fully the capabilities of the VCell software.

ABSTRACT

Chemical exchange line broadening is an important phenomenon in nuclear magnetic resonance (NMR) spectroscopy, in which a nuclear spin experiences more than one magnetic environment as a result of chemical or conformational changes of a molecule. The dynamic process of chemical exchange strongly affects the sensitivity and resolution of NMR experiments and increasingly provides a powerful probe of the interconversion between chemical and conformational states of proteins, nucleic acids, and other biologic macromolecules. A simple and often used theoretic description of chemical exchange in NMR spectroscopy is based on an idealized 2-state jump model (the random phase or telegraph signal). However, chemical exchange can also be represented as a barrier crossing event that can be modeled by using chemical reaction rate theory. The timescale of crossing is determined by the barrier height, the temperature, and the dissipation modeled as collisional or frictional damping. This tutorial explores the connection between the NMR theory of chemical exchange line broadening and strong collision models for chemical kinetics in statistical mechanics. Theoretic modeling and numeric simulation are used to map the rate of barrier crossing dynamics of a particle on a potential energy surface to the chemical exchange relaxation rate constant. By developing explicit models for the exchange dynamics, the tutorial aims to elucidate the underlying dynamical processes that give rise to the rich phenomenology of chemical exchange observed in NMR spectroscopy. Software for generating and analyzing the numeric simulations is provided in the form of Python and Fortran source codes.

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Before March 2020, with the outbreak of the COVID-19 pandemic, remote instruction of science was only moderately developed compared with more traditional approaches for learning science. Since the outbreak, however, all formal education systems have been carried out in remote mode, and outreach activities that take place in a research or academic setting have usually been canceled, or there has been a search for innovative approaches to shift to digital space. Therefore, the development of learning and teaching strategies has currently focused on remote activities. In this study, a design-based approach was applied to transform an existing authentic science activity using a scanning electron microscope (SEM) from face-to-face to remote learning mode. The remote mode activity included the remote operation of the SEM by the participants. The goal was to formulate a general approach to transform authentic outreach activities from face-to-face to remote operation. To evaluate the design, we compared learners' perceived authenticity in the 2 modes and reflected on the process. Data were collected with a Likert-type questionnaire regarding participants' perceived authenticity. The results suggest that items of authenticity related to the experience of learning content have a positive potential for use in remote mode. The learners' experience of connecting with the scientists is an apparent disadvantage in remote mode. However, changes in communication technology or in the pedagogy of remote teaching is a promising direction for improving social experience.

The COVID-19 pandemic impacted the biophysics community at all levels, including effects on every aspect of teaching and research at primarily undergraduate institutions (PUIs). The US National Science Foundation defines PUIs as accredited colleges and universities that award fewer than a particular threshold number of PhD degrees per year (1); a more global definition might include institutions that have little to no doctoral student presence and a central mission of teaching and training undergraduates. Biophysics faculty at PUIs are often hosted in biology, chemistry, or physics departments and teach introductory and upper-level courses, often without graduate teaching assistants.

Teaching Mathematical Modeling of Cellular Systems with the VCell MathModel

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Dynamical Models of Chemical Exchange in Nuclear Magnetic Resonance Spectroscopy

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Authentic Science Learning During COVID-19: The Adaptive Design of a SEM Outreach Activity

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Active Learning Module for Protein Structure Analysis Using Novel Enzymes

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Beyond Ticking Boxes: Holistic Assessment of Travel Award Programs Is Essential for Inclusivity

Online Assignments at Kilimanjaro Christian Medical University College during the COVID-19 Pandemic

Perspectives on How 1.5 Years of the COVID-19 Pandemic Have Impacted Biophysicists at Primarily Undergraduate Institutions

Control Theory for Physicists by John Bechhoefer

Using Published Undergraduate Biomechanics Research on Hydra Mouth Opening to Train Undergraduates

Open Microscopy in Challenge-Based Learning

An Entropy-Based Approach to Introducing Osmotic Pressure

A Homebuilt Experiment to Quantify the Mechanical Properties of Hair

Expanding the BASIL CURE

Hooking Nonscientists on Biophysics

Introductory Models of COVID-19 in the United States

Teaching Image Processing and Optical Engineering to University Biology Students

The Biophysicist: Introductory Editorial

Authentic Science Learning During COVID-19: The Adaptive Design of a SEM Outreach Activity