Dynamical Models of Chemical Exchange in Nuclear Magnetic Resonance Spectroscopy

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.

Teaching Mathematical Modeling of Cellular Systems with the VCell MathModel

ABSTRACT 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.

Introductory Models of COVID-19 in the United States

ABSTRACT Students develop and test simple kinetic models of the spread of coronavirus disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Microsoft Excel is used as the modeling platform because it is nonthreatening to students and it is widely available. Students develop finite difference models and implement them in the cells of preformatted spreadsheets following a guided inquiry pedagogy that introduces new model parameters in a scaffolded step-by-step manner. That approach allows students to investigate the implications of new model parameters in a systematic way. Students fit the resulting models to reported cases per day data for the United States using least squares techniques with Excel's Solver. Using their own spreadsheets, students discover for themselves that the initial exponential growth of COVID-19 can be explained by a simplified unlimited growth model and by the susceptible-infected-recovered (SIR) model. They also discover that the effects of social distancing can be modeled using a Gaussian transition function for the infection rate coefficient and that the summer surge was caused by prematurely relaxing social distancing and then reimposing stricter social distancing. Students then model the effect of vaccinations and validate the resulting susceptible-infected-recovered-vaccinated (SIRV) model by showing that it successfully predicts the reported cases per day data from Thanksgiving through the holiday period up to 14 February 2021. The same SIRV model is then extended and successfully fits the fourth peak up to 1 June 2021, caused by further relaxation of social distancing measures. Finally, students extend the model up to the present day (27 August 2021) and successfully account for the appearance of the delta variant of the SARS-CoV-2 virus. The fitted model also predicts that the delta variant peak will be comparatively short, and the cases per day data should begin to fall off in early September 2021, counter to current expectations. This case study makes an excellent capstone experience for students interested in scientific modeling.

Instructional Design for an Undergraduate Laboratory Course in Molecular Biophysics

ABSTRACT In this article, an approach to teaching molecular biophysics is described. The organization and course content has been carefully chosen and curated so that fundamental ideas in molecular biophysics can be taught effectively to upper classmen in higher education. Three general topic areas are introduced along with accompanying experiments that illustrate major principles related to each topic area. This article outlines an approach to organizing chosen course material and suggests multiple teaching activities within each major topic area: thermodynamics, kinetics, and structural biology. Subtopics are presented along with suggested laboratory experiments. The experiments are outlined in a way that they can be readily adopted by educators teaching a biophysical chemistry lab. The accompaniment of workshop exercises as an additional teaching modality is a component of the course intended to enhance the development of important problem-solving skills and comprehension of new content. Finally, a reflection on student feedback and course outcomes along with targeted learning goals is discussed.

Microscope in Action: An Interdisciplinary Fluorescence Microscopy Hands-on Resource for Schools

ABSTRACT Fluorescence microscopy is a ubiquitous technique in the life sciences that uses fluorescent molecules to visualize specific components of biological specimens. This powerful tool has revolutionized biology, and it represents a perfect example of the advancements enabled by biophysical research and technology development. However, despite its central role in contemporary research, fluorescence is hardly covered in typical secondary school curricula, with few hands-on “entry-level” materials available for secondary school teachers to introduce this important method to their students. Furthermore, most commercially available fluorescence microscopes are prohibitively costly and often appear as “black boxes.” To address this gap, we introduce here an experimental, research-grade fluorescence microscopy kit and educational resource targeted at secondary school students and teachers. Microscope in Action is an interdisciplinary resource based on active learning that combines concepts from both optics and biology. The students assemble a functional microscope from basic optical, mechanical, and electronic parts, thereby testing and understanding the function of each component “hands-on.” We also present sample preparation and imaging activities that can be incorporated to enable an exploration of biological topics with the assembled microscope and exercises in which students actively learn and practice scientific thinking by collecting and analyzing data. Although the resource was developed with secondary schools in mind, the variety of available protocols and the adjustable module lengths make it suitable for different age groups and topics, from middle school to PhD level, from short workshops to courses spanning several days.