Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.

Unlike proteins, the RNA backbone has numerous degrees of freedom (eight, if one counts the sugar pucker), making RNA modeling, structure building and prediction a multidimensional problem of exceptionally high complexity. And yet RNA tertiary structures are not infinite in their structural morphology; rather, they are built from a limited set of discrete units. In order to reduce the dimensionality of the RNA backbone in a physically reasonable way, a shorthand notation was created that reduced the RNA backbone torsion angles to two (η and θ, analogous to φ and ψ in proteins). When these torsion angles are calculated for nucleotides in a crystallographic database and plotted against one another, one obtains a plot analogous to a Ramachandran plot (the η/θ plot), with highly populated and unpopulated regions. Nucleotides that occupy proximal positions on the plot have identical structures and are found in the same units of tertiary structure. In this review, we describe the statistical validation of the η/θ formalism and the exploration of features within the η/θ plot. We also describe the application of the η/θ formalism in RNA motif discovery, structural comparison, RNA structure building and tertiary structure prediction. More than a tool, however, the η/θ formalism has provided new insights into RNA structure itself, revealing its fundamental components and the factors underlying RNA architectural form.

Proteins provide much of the scaffolding for life, as well as undertaking a variety of essential catalytic reactions. These characteristic functions have led us to presuppose that proteins are in general functional only when well structured and correctly folded. As we begin to explore the repertoire of possible protein sequences inherent in the human and other genomes, two stark facts that belie this supposition become clear: firstly, the number of apparent open reading frames in the human genome is significantly smaller than appears to be necessary to code for all of the diverse proteins in higher organisms, and secondly that a significant proportion of the protein sequences that would be coded by the genome would not be expected to form stable three-dimensional (3D) structures. Clearly the genome must include coding for a multitude of alternative forms of proteins, some of which may be partly or fully disordered or incompletely structured in their functional states. At the same time as this likelihood was recognized, experimental studies also began to uncover examples of important protein molecules and domains that were incompletely structured or completely disordered in solution, yet remained perfectly functional. In the ensuing years, we have seen an explosion of experimental and genome-annotation studies that have mapped the extent of the intrinsic disorder phenomenon and explored the possible biological rationales for its widespread occurrence. Answers to the question ‘why would a particular domain need to be unstructured?’ are as varied as the systems where such domains are found. This review provides a survey of recent new directions in this field, and includes an evaluation of the role not only of intrinsically disordered proteins but also of partially structured and highly dynamic members of the disorder–order continuum.