Reassessing the exon-foldon correspondence using frustration analysis.

Protein folding and evolution are intimately linked phenomena. Here, we revisit the concept of exons as potential protein folding modules across a set of 38 abundant and conserved protein families. Taking advantage of genomic exon-intron organization and extensive protein sequence data, we explore exon boundary conservation and assess the foldon-like behavior of exons using energy landscape theoretic measurements. We found deviations in the exon size distribution from exponential decay indicating selection in evolution. We show that when taken together there is a pronounced tendency to independent foldability for segments corresponding to the more conserved exons, supporting the idea of exon-foldon correspondence. While 45% of the families follow this general trend when analyzed individually, there are some families for which other stronger functional determinants, such as preserving frustrated active sites, may be acting. We further develop a systematic partitioning of protein domains using exon boundary hotspots, showing that minimal common exons correspond with uninterrupted alpha and/or beta elements for the majority of the families but not for all of them.

The physical and evolutionary energy landscapes of devolved protein sequences corresponding to pseudogenes.

Protein evolution is guided by structural, functional, and dynamical constraints ensuring organismal viability. Pseudogenes are genomic sequences identified in many eukaryotes that lack translational activity due to sequence degradation and thus over time have undergone "devolution." Previously pseudogenized genes sometimes regain their protein-coding function, suggesting they may still encode robust folding energy landscapes despite multiple mutations. We study both the physical folding landscapes of protein sequences corresponding to human pseudogenes using the Associative Memory, Water Mediated, Structure and Energy Model, and the evolutionary energy landscapes obtained using direct coupling analysis (DCA) on their parent protein families. We found that generally mutations that have occurred in pseudogene sequences have disrupted their native global network of stabilizing residue interactions, making it harder for them to fold if they were translated. In some cases, however, energetic frustration has apparently decreased when the functional constraints were removed. We analyzed this unexpected situation for Cyclophilin A, Profilin-1, and Small Ubiquitin-like Modifier 2 Protein. Our analysis reveals that when such mutations in the pseudogene ultimately stabilize folding, at the same time, they likely alter the pseudogenes' former biological activity, as estimated by DCA. We localize most of these stabilizing mutations generally to normally frustrated regions required for binding to other partners.

Differences in predictions of ODE models of tumor growth: a cautionary example.

BACKGROUND: While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer. METHODS: We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model. RESULTS: We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used. CONCLUSION: Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

A triazine-based BODIPY trimer as a molecular viscometer.

Photophysical behaviour of a novel trimeric BODIPY rotor with a high extinction coefficient is reported. Steady state and time resolved fluorescence measurements established that the trimer could be used as a viscometer for molecular solvents, membrane-like environments and several cancer cell lines.