Learning protein folding and evolution with a snake puzzle

We propose here a working unit for teaching basic concepts of protein folding and evolution centred around the example of a wooden snake puzzle, strikingly similar to toy models widely used in the literature of protein folding. In our experience, developed at a Master course at the Universidad Autónoma de Madrid (Spain), the concreteness of this example helps to overcome difficulties caused by the interdisciplinary nature of this field and its high level of abstraction, in particular for students coming from traditional disciplines. The puzzle will allow us discussing a simple algorithm for finding folded solutions, through which we will introduce the concept of the configuration space and the contact matrix representation. This is a central tool for comparing protein structures, for studying simple models of protein energetics, and even for a qualitative discussion of folding kinetics, through the concept of the Contact Overlap. It also allows a simple representation of misfolded conformations and their free energy. These concepts, in particular protein structure comparison and the stability of the native state with respect to unfolded and misfolded conformations, will motivate evolutionary questions. We address these questions by simulating a structurally constrained model of protein evolution, again modelled on the snake puzzle. In this way, we can discuss the analogy between evolutionary concepts and statistical mechanics that facilitates the understanding of both concepts. The proposed examples and literature are accessible, and we provide supplementary material to reproduce the numerical experiments. We also suggest possible directions to expand the unit. We hope that this work will further stimulate the adoption of games in teaching practice.