Ionizable residues can release and take up protons and this has an influence on protein structure and function. The extent of protonation is linked to the overall pH of the solution and the local environments of ionizable residues. Binding or unbinding of a single proton generates a distinct charge microstate defined by a specific pattern of charges. Accordingly, the overall partition function is a sum over all charge microstates and Boltzmann weights of all conformations associated with each of the charge microstates. This ensemble-of-ensembles description recast as a q-canonical ensemble allows us to analyze and interpret potentiometric titrations that provide information regarding net charge as a function of pH. In the q-canonical ensemble, charge microstates are grouped into mesostates where each mesostate is a collection of microstates of the same net charge. Here, we show that leveraging the structure of the q-canonical ensemble allows us to decouple contributions of net proton binding and release from proton arrangement and conformational considerations. Through application of the q-canonical formalism to analyze potentiometric measurements of net charge in proteins with repetitive patterns of Lys and Glu residues, we determine the underlying mesostate pK_a values and, more importantly, we estimate relative mesostate populations as a function of pH. This is a strength of using the q-canonical approach that cannot be replicated using purely site-specific analyses. Overall, our work shows how measurements of charge equilibria, decoupled from measurements of conformational equilibria, and analyzed using the framework of the q-canonical ensemble, provide protein-specific quantitative descriptions of pH-dependent populations of mesostates. This method is of direct relevance for measuring and understanding how different charge states contribute to conformational, binding, and phase equilibria of proteins.

Dnm1 and Fis1 are prototypical proteins that regulate yeast mitochondrial morphology by controlling fission, the dysregulation of which can result in developmental disorders and neurodegenerative diseases in humans. Loss of Dnm1 blocks the formation of fission complexes and leads to elongated mitochondria in the form of interconnected networks, while overproduction of Dnm1 results in excessive mitochondrial fragmentation. In the current model, Dnm1 is essentially a GTP hydrolysis-driven molecular motor that self-assembles into ring-like oligomeric structures that encircle and pinch the outer mitochondrial membrane at sites of fission. In this work, we use machine learning and synchrotron small-angle X-ray scattering (SAXS) to investigate whether the motor Dnm1 can synergistically facilitate mitochondrial fission by membrane remodeling. A support vector machine (SVM)-based classifier trained to detect sequences with membrane-restructuring activity identifies a helical Dnm1 domain capable of generating negative Gaussian curvature (NGC), the type of saddle-shaped local surface curvature found on scission necks during fission events. Furthermore, this domain is highly conserved in Dnm1 homologues with fission activity. Synchrotron SAXS measurements reveal that Dnm1 restructures membranes into phases rich in NGC, and is capable of inducing a fission neck with a diameter of 12.6 nm. Through in silico mutational analysis, we find that the helical Dnm1 domain is locally optimized for membrane curvature generation, and phylogenetic analysis suggests that dynamin superfamily proteins that are close relatives of human dynamin Dyn1 have evolved the capacity to restructure membranes via the induction of curvature mitochondrial fission. In addition, we observe that Fis1, an adaptor protein, is able to inhibit the pro-fission membrane activity of Dnm1, which points to the antagonistic roles of the two proteins in the regulation of mitochondrial fission.

The combination of phase separation and disorder-to-order transitions can give rise to ordered, semi-crystalline fibrillar assemblies that underlie prion phenomena namely, the non-Mendelian transfer of information across cells. Recently, a method known as Distributed Amphifluoric Förster Resonance Energy Transfer (DAmFRET) was developed to study the convolution of phase separation and disorder-to-order transitions in live cells. In this assay, a protein of interest is expressed to a broad range of concentrations and the acquisition of local density and order, measured by changes in FRET, is used to map phase transitions for different proteins. The high-throughput nature of this assay affords the promise of uncovering sequence-to-phase behavior relationships in live cells. Here, we report the development of a supervised method to obtain automated and accurate classifications of phase transitions quantified using the DAmFRET assay. Systems that we classify as undergoing two-state discontinuous transitions are consistent with prion-like behaviors, although the converse is not always true. We uncover well-established and surprising new sequence features that contribute to two-state phase behavior of prion-like domains. Additionally, our method enables quantitative, comparative assessments of sequence-specific driving forces for phase transitions in live cells. Finally, we demonstrate that a modest augmentation of DAmFRET measurements, specifically time-dependent protein expression profiles, can allow one to apply classical nucleation theory to extract sequence-specific lower bounds on the probability of nucleating ordered assemblies. Taken together, our approaches lead to a useful analysis pipeline that enables the extraction of mechanistic inferences regarding phase transitions in live cells.