Search bioRxiv⌕ Search

Biology subjects

Mittag, T.

Publications and source records attributed to Mittag, T..

At least 19 recordsLinked to original sources

BRD4 recruitment desilences transcription without erasure or depletion of repressive chromatin

How genes are desilenced within mesoscale repressive chromatin is a crucial yet poorly understood phenomenon. Prevailing models posit that methylation of lysine-9 of histone H3 (H3K9me3) engages heterochromatin protein 1 (HP1) to drive chromatin compaction and transcriptional silencing. The erasure of this repressive mark and its replacement with acetyl/acyl groups recruits positive factors such as BRD4/BET to elicit gene transcription. We report that in Friedreichs ataxia, a synthetic gene regulator (SynGR1) drives transcription across repressive chromatin without removal or replacement of H3K9me3 or HP1. By selectively recruiting BRD4/BET into repressive GAA-repeats in frataxin (FXN), SynGR1 creates a paradoxical state where gene transcription and repressive chromatin co-exist. Contrary to convention, we find that BRD4 readily partitions into phase separated HP1 condensates in vitro and into HP1 puncta in patient-derived cells, thus presenting a mechanistic explanation for desilencing transcription without the dispersal of mesoscale repressive chromatin. Epigenetic drugs that gate sequential steps in transcription, synergistically stimulate FXN expression while concomitantly increasing, rather than eliminating, repressive H3K9me3 and HP1 levels. More broadly, this study highlights the dynamic nature of repressive chromatin and the context-dependence of epigenetic marks in regulating gene expression.

cell biology↗

Viscoelasticity and interface properties of multi-component condensates govern protein sequestration and suppression of amyloid formation

Stress granules (SGs) are multi-component biomolecular condensates widely implicated as sites of protein aggregation by virtue of the high concentrations of amyloidogenic RNA-binding proteins they contain. This model, in which SGs are viewed as crucibles for amyloid formation, has not been rigorously tested. Here, we employed twelve multi-component protein-nucleic acid condensate systems as SG-mimics with diverse physicochemical features. Utilizing three fibril-forming proteins, hnRNPA1, Tau, and FUS, which are concentrated more than 50-fold in condensates, we report that multi-component biomolecular condensates robustly suppress, rather than promote, amyloid formation. Multiscale experimental analyses, including quantitative kinetic measurements, rheology, and microscopy, combined with computational modelling, reveal that condensates serve as sinks for soluble protein, and fibrils form in the dilute phase, although interfaces can promote nucleation. Three key physicochemical properties of condensates govern suppression of fibril formation: First, condensate-mediated sequestration lowers the concentration of fibril-forming proteins in the dilute phase. Second, condensate viscoelasticity constrains efflux-driven fibril growth in the dilute phase. And third, dilution of fibril-forming proteins at condensate interfaces mitigates fibril nucleation. The sink potential of SG-mimics is recapitulated in G3BP1-RNA condensates and SGs reconstituted in mammalian cell lysate, suggesting that SGs may have evolved to suppress stress-induced protein aggregation.

biophysics↗

The equilibrium between two quaternary assembly states determines the activity of SPOP and its cancer mutants

Proteostasis is critical for preventing oncogenesis. Both activating and inactivating mutations in the ubiquitin ligase subunit SPOP result in oncogenesis in different tissues. SPOP assembles into filaments that are multivalent for substrates, and substrates have multiple weak motifs for SPOP that are not activated via post-translational modifications. It is thus unclear how regulation is achieved. Here, we show that SPOP filaments circularize into rings that dimerize into up to 2.5 MDa-large, auto-inhibited double donuts. The equilibrium between double donuts and linear filaments determines SPOP activity. Activating and deactivating cancer mutations shift the equilibrium towards the filament or the double donut, respectively, and this influences substrate turnover and subcellular localization. This regulatory mechanism requires long filaments that can circularize into rings, likely explaining the presence of multiple weak SPOP-binding motifs in substrates. Activating and deactivating mutations combine to give rise to intermediate activities, suggesting new levers for cancer therapies. Highlights- SPOP assemblies exist in an equilibrium between circular double donuts and linear filaments. - Double donuts occlude access to the substrate binding site and are inactive. - Mutations in different cancers shift the equilibrium towards active or inactive states. - Regulation through these structural transitions requires large filamentous assemblies.

biophysics↗

Reconciling competing models on the roles of condensates and soluble complexes in transcription factor function

Phase separation explains the exquisite spatial and temporal regulation of many biological processes, but the role of transcription factor-mediated condensates in gene regulation is contentious, requiring head-to-head comparison of competing models. Here, we focused on the prototypical yeast transcription factor Gcn4 and assessed two models for gene transcription activation, i.e., mediated via soluble complexes or transcriptional condensates. Both models rely on the ability of transcription factors and coactivators to engage in multivalent interactions. Unexpectedly, we found that propensity to form homotypic Gcn4 condensates does not correlate well with transcriptional activity. Contrary to prevailing models, binding to DNA suppresses Gcn4 phase separation. Notably, the ability of Gcn4 to form soluble complexes with coactivator subunit Med15 closely mirrored the propensity to recruit Med15 into condensates, indicating that these properties are intertwined and cautioning against interpretation of mutational data without head-to-head comparisons. However, Gcn4 variants with the highest affinity for Med15 do not function as well as expected and instead have activities that reflect their abilities to phase separate with Med15. These variants therefore indeed form cellular condensates, and those attenuate activity. Our results show that transcription factors can function as soluble complexes as well as condensates, reconciling two seemingly opposing models, and have implications for other phase-separating systems. Highlights- Homotypic phase separation propensities of Gcn4 variants do not predict in vivo activities well. - DNA binding leads to solubilization of GCN4 condensates, which is reversed by Med15 association. - The abilities to co-phase separate and form soluble complexes with Med15 are highly intertwined. - Variants with high affinities for Med15 form condensates that attenuate function.

biophysics↗

Biomolecular condensates are characterized by interphase electric potentials

Biomolecular condensates form via processes that combine phase separation and reversible associations of multivalent macromolecules. Condensates can be two- or multi-phase systems defined by coexisting dense and dilute phases. Here, we show that solution ions can partition asymmetrically across coexisting phases defined by condensates formed by intrinsically disordered proteins or homopolymeric RNA molecules. Our findings were enabled by direct measurements of the activities of cations and anions within coexisting phases of protein and RNA condensates. Asymmetries in ion partitioning between coexisting phases vary with protein sequence, condensate type, salt concentration, and ion type. The Donnan equilibrium set up by asymmetrical partitioning of solution ions generates interphase electric potentials known as Donnan and Nernst potentials. Our measurements show that the interphase potentials of condensates are of the same order of magnitude as membrane potentials of membrane-bound organelles. Interphase potentials quantify the degree to which microenvironments of coexisting phases are different from one another. Importantly, and based on condensate-specific interphase electric potentials, which are membrane-like potentials of membraneless bodies, we reason that condensates are mesoscale capacitors that store charge. Interphase potentials lead to electric double layers at condensate interfaces. This helps explain recent observations of condensate interfaces being electrochemically active.

biophysics↗

Optical quantification of molecular interaction strength in protein condensates

Biomolecular condensates have been identified as a ubiquitous means of intracellular organization, exhibiting very diverse material properties. However, techniques to characterize these material properties and their underlying molecular interactions are scarce. Here, we introduce two optical techniques - Brillouin microscopy and quantitative phase imaging (QPI) - to address this scarcity. We establish Brillouin shift and linewidth as measures for average molecular interaction and dissipation strength, respectively, and we used QPI to obtain the protein concentration within the condensates. We monitored the response of condensates formed by FUS and by the low-complexity domain of hnRNPA1 (A1-LCD) to altering temperature and ion concentration. Conditions favoring phase separation increased Brillouin shift, linewidth, and protein concentration. In comparison to solidification by chemical crosslinking, the ion-dependent aging of FUS condensates had a small effect on the molecular interaction strength inside. Finally, we investigated how sequence variations of A1-LCD, that change the driving force for phase separation, alter the physical properties of the respective condensates. Our results provide a new experimental perspective on the material properties of protein condensates. Robust and quantitative experimental approaches such as the presented ones will be crucial for understanding how the physical properties of biological condensates determine their function and dysfunction.

biophysics↗

Metastable condensates suppress conversion to amyloid fibrils

Stress granules form via co-condensation of RNA-binding proteins containing prion-like low complexity domains (PLCDs) with RNA molecules. Homotypic interactions among PLCDs can drive amyloid fibril formation that is enhanced by ALS-associated mutations. We report that condensation-versus fibril-driving homotypic interactions are separable for A1-LCD, the PLCD of hnRNPA1. Separable interactions lead to thermodynamically metastable condensates and globally stable fibrils. Interiors of condensates suppress fibril formation whereas interfaces have the opposite effect. ALS-associated mutations enhance the stability of fibrils and weaken condensate metastability, thus enhancing the rate of fibril formation. We designed mutations to enhance A1-LCD condensate metastability and discovered that stress granule disassembly in cells can be restored even when the designed variants carry ALS-causing mutations. Therefore, fibril formation can be suppressed by condensate interiors that function as sinks. Condensate sink potentials are influenced by their metastability, which is tunable through separable interactions even among minority components of stress granules.

biophysics↗

Design of intrinsically disordered protein variants with diverse structural properties

Intrinsically disordered proteins (IDPs) perform a wide range of functions in biology, suggesting that the ability to design IDPs could help expand the repertoire of proteins with novel functions. Designing IDPs with specific structural or functional properties has, however, been diffcult, in part because determining accurate conformational ensembles of IDPs generally requires a combination of computational modelling and experiments. Motivated by recent advancements in effcient physics-based models for simulations of IDPs, we have developed a general algorithm for designing IDPs with specific structural properties. We demonstrate the power of the algorithm by generating variants of naturally occurring IDPs with different levels of compaction and that vary more than 100 fold in their propensity to undergo phase separation, even while keeping a fixed amino acid composition. We experimentally tested designs of variants of the low-complexity domain of hnRNPA1 and find high accuracy in our computational predictions, both in terms of single-chain compaction and propensity to undergo phase separation. We analyze the sequence features that determine changes in compaction and propensity to phase separate and find an overall good agreement with previous findings for naturally occurring sequences. Our general, physics-based method enables the design of disordered sequences with specified conformational properties. Our algorithm thus expands the toolbox for protein design to include also the most flexible proteins and will enable the design of proteins whose functions exploit the many properties afforded by protein disorder.

biophysics↗

Crowder titrations enable the quantification of driving forces for macromolecular phase separation

Macromolecular solubility is an important contributor to the driving forces for phase separation. Formally, the driving forces in a binary mixture comprising a macromolecule dissolved in a solvent can be quantified in terms of the saturation concentration, which is the threshold macromolecular concentration above which the mixture separates into coexisting dense and dilute phases. Additionally, the second virial coefficient, which measures the effective strength of solvent-mediated intermolecular interactions provides direct assessments of solvent quality. The sign and magnitude of second virial coefficients will be governed by a combination of solution conditions and the nature of the macromolecule of interest. Here, we show, using a combination of theory, simulation, and in vitro experiments, that titrations of crowders, providing they are true depletants, can be used to extract the intrinsic driving forces for macromolecular phase separation. This refers to saturation concentrations in the absence of crowders and the second virial coefficients that quantify the magnitude of the incompatibility between macromolecules and the solvent. Our results show how the depletion-mediated attractions afforded by crowders can be leveraged to obtain comparative assessments of macromolecule-specific, intrinsic driving forces for phase separation. SIGNIFICANCEPhase separation has emerged as a process of significant relevance to sorting macromolecules into distinct compartments, thereby enabling spatial and temporal control over cellular matter. Considerable effort is being invested into uncovering the driving forces that enable the separation of macromolecular solutions into coexisting phases. At its heart, this process is governed by the balance of macromolecule-solvent, inter-macromolecule, and solvent-solvent interactions. We show that the driving forces for phase separation, including the coefficients that measure interaction strengths between macromolecules, can be extracted by titrating the concentrations of crowders that enable macromolecules to phase separate at lower concentrations. Our work paves the way to leverage specific categories of measurements for quantitative characterizations of driving forces for phase separation.

biophysics↗

Sequence-encoded grammars determine material properties and physical aging of protein condensates

Biomolecular condensates are viscoelastic materials. Here, we report results from investigations into molecular-scale determinants of sequence-encoded and age-dependent viscoelasticity of condensates formed by prion-like low-complexity domains (PLCDs). The terminally viscous forms of PLCD condensates are Maxwell fluids. Measured viscoelastic moduli of these condensates are reproducible using a Rouse-Zimm model that accounts for the network-like organization engendered by reversible physical crosslinks among PLCDs in the dense phase. Measurements and computations show that the strengths of aromatic inter-sticker interactions determine the sequence-specific amplitudes of elastic and viscous moduli as well as the timescales over which elastic properties dominate. PLCD condensates also undergo physical aging on sequence-specific timescales. This is driven by mutations to spacer residues that weaken the metastability of terminally viscous phases. The aging of PLCD condensates is accompanied by disorder-to-order transitions, leading to the formation of non-fibrillar, beta-sheet-containing, semi-crystalline, terminally elastic, Kelvin-Voigt solids. Our results suggest that sequence grammars, which refer to the identities of stickers versus spacers in PLCDs, have evolved to afford control over the metastabilities of terminally viscous fluid phases of condensates. This selection can, in some cases, render barriers for conversion from metastable fluids to globally stable solids to be insurmountable on functionally relevant timescales.

biophysics↗

Phase Separation in Mixtures of Prion-Like Low Complexity Domains is Driven by the Interplay of Homotypic and Heterotypic Interactions

Prion-like low-complexity domains (PLCDs) are involved in the formation and regulation of distinct biomolecular condensates that form via coupled associative and segregative phase transitions. We previously deciphered how evolutionarily conserved sequence features drive phase separation of PLCDs through homotypic interactions. However, condensates typically encompass a diverse mixture of proteins with PLCDs. Here, we combine simulations and experiments to study mixtures of PLCDs from two RNA binding proteins namely, hnRNPA1 and FUS. We find that 1:1 mixtures of the A1-LCD and FUS-LCD undergo phase separation more readily than either of the PLCDs on their own. The enhanced driving forces for phase separation of mixtures of A1-LCD and FUS-LCD arise partly from complementary electrostatic interactions between the two proteins. This complex coacervation-like mechanism adds to complementary interactions among aromatic residues. Further, tie line analysis shows that stoichiometric ratios of different components and their sequence-encoded interactions jointly contribute to the driving forces for condensate formation. These results highlight how expression levels might be tuned to regulate the driving forces for condensate formation in vivo. Simulations also show that the organization of PLCDs within condensates deviates from expectations based on random mixture models. Instead, spatial organization within condensates will reflect the relative strengths of homotypic versus heterotypic interactions. We also uncover rules for how interaction strengths and sequence lengths modulate conformational preferences of molecules at interfaces of condensates formed by mixtures of proteins. Overall, our findings emphasize the network-like organization of molecules within multicomponent condensates, and the distinctive, composition-specific conformational features of condensate interfaces. Significance StatementBiomolecular condensates are mixtures of different protein and nucleic acid molecules that organize biochemical reactions in cells. Much of what we know about how condensates form comes from studies of phase transitions of individual components of condensates. Here, we report results from studies of phase transitions of mixtures of archetypal protein domains that feature in distinct condensates. Our investigations, aided by a blend of computations and experiments, show that the phase transitions of mixtures are governed by a complex interplay of homotypic and heterotypic interactions. The results point to how expression levels of different protein components can be tuned in cells to modulate internal structures, compositions, and interfaces of condensates, thus affording distinct ways to control the functions of condensates.

biophysics↗

Reduction of oligomer size modulates the competition between cluster formation and phase separation of the tumor suppressor SPOP

Phase separation is a ubiquitous process that compartmentalizes many cellular pathways. Given that the same interactions that drive phase separation mediate the formation of complexes below the saturation concentration, the contribution of condensates vs complexes to function is not always clear. Here, we characterized several new cancer-associated mutations of the tumor suppressor Speckle-type POZ protein (SPOP), a substrate recognition subunit of the Cullin3-RING ubiquitin ligase (CRL3), which pointed to a strategy for generating separation-of-function mutations. SPOP self-associates into linear oligomers and interacts with multivalent substrates, and this mediates the formation of condensates. These condensates bear the hallmarks of enzymatic ubiquitination activity. We characterized the effect of mutations in the dimerization domains of SPOP on its linear oligomerization, binding to the substrate DAXX, and phase separation with DAXX. We showed that the mutations reduce SPOP oligomerization and shift the size distribution of SPOP oligomers to smaller sizes. The mutations therefore reduce the binding affinity to DAXX, but enhance the poly-ubiquitination activity of SPOP towards DAXX. This unexpectedly enhanced activity may be explained by enhanced phase separation of DAXX with the SPOP mutants. Our results provide a comparative assessment of the functional role of clusters versus condensates and support a model in which phase separation is an important factor in SPOP function. Our findings also suggest that tuning of linear SPOP self-association could be used by the cell to modulate its activity, and provide insights into the mechanisms underlying hypermorphic SPOP mutations. The characteristics of these cancer-associated SPOP mutations suggest a route for designing separation-of-function mutations in other phase-separating systems.

biophysics↗

Conformational and oligomeric states of SPOP from small-angle X-ray scattering and molecular dynamics simulations

Speckle-type POZ protein (SPOP) is a substrate adaptor in the ubiquitin proteasome system, and plays important roles in cell-cycle control, development, and cancer. SPOP forms linear higher-order oligomers following an isodesmic self-association model. Oligomerization is essential for SPOPs multivalent interactions with substrates, which facilitate phase separation and localization to biomolecular condensates. Structural characterization of SPOP in its oligomeric state and in solution is, however, challenging due to the inherent conformational and compositional heterogeneity of the oligomeric species. Here, we develop an approach to simultaneously and self-consistently characterize the conformational ensemble and the distribution of oligomeric states of SPOP by combining small-angle X-ray scattering (SAXS) and molecular dynamics simulations. We build initial conformational ensembles of SPOP oligomers using coarse-grained molecular dynamics simulations, and use a Bayesian/maximum entropy approach to refine the ensembles, along with the distribution of oligomeric states, against a concentration series of SAXS experiments. Our results suggest that SPOP oligomers behave as rigid, helical structures in solution, and that a flexible linker region allows SPOPs substrate binding domains to extend away from the core of the oligomers. Additionally, our results are in good agreement with previous characterization of the isodesmic self-association of SPOP. In the future, the approach presented here can be extended to other systems to simultaneously characterize structural heterogeneity and self-assembly.

biophysics↗

Quantifying coexistence concentrations in multi-component phase-separating systems using analytical HPLC

Over the last decade, evidence has accumulated to suggest that numerous instances of cellular compartmentalization can be explained by the phenomenon of phase separation. This is a process by which a macromolecular solution separates spontaneously into dense and dilute coexisting phases. Semi-quantitative, in vitro approaches for measuring phase boundaries have proven very useful in determining some key features of biomolecular condensates, but these methods often lack the precision necessary for generating quantitative models. Therefore, there is a clear need for techniques that allow quantitation of coexisting dilute and dense phase concentrations of phase-separating biomolecules, especially in systems with more than one type of macromolecule. Here we report the design and deployment of analytical High-Performance Liquid Chromatography (HPLC) for in vitro separation and quantification of distinct biomolecules that allows us to measure dilute and dense phase concentrations needed to reconstruct coexistence curves in multicomponent mixtures. This approach is label-free, detects lower amounts of material than is accessible with classic UV-spectrophotometers, is applicable to a broad range of macromolecules of interest, is a semi-high-throughput technique, and if needed, the macromolecules can be recovered for further use. The approach promises to provide quantitative insights into the balance of homotypic and heterotypic interactions in multicomponent phase-separating systems.

biophysics↗

Condensates of disordered proteins have small-world network structures and interfaces defined by expanded conformations

The formation of membraneless biomolecular condensates is driven by macromolecules with sticker-and-spacer architectures that undergo phase separation coupled to percolation (PSCP). Driving forces for PSCP are governed by the interplay between reversible inter-sticker crosslinks and solvation preferences of spacers. Here, we introduce molecular and mesoscale descriptions of structures within, outside, and at the interfaces of condensates that are formed by prion-like low complexity domains (PLCDs), which are exemplars of intrinsically disordered, linear multivalent proteins. Our studies are based on simulations that accurately describe sequence-specific phase behaviors of PLCDs. We find that networks of reversible, intermolecular, inter-sticker crosslinks organize PLCDs into small-world topologies within condensates. These topologies result from distinct conformational preferences within dense, dilute, and interfacial regions. Specifically, the degree of conformational expansion varies non-monotonically, being most expanded at the interface and most compact in the dilute phase with molecules preferring to be oriented perpendicular to condensate interfaces. This contrasts with dense and dilute phases where molecules are randomly oriented relative to one another. Our results demonstrate that even simple condensates, with only one type of macromolecule, feature inhomogeneous spatial organizations of molecules and interfacial features that likely prime them for being locations of biochemical activity.

biophysics↗

Deciphering how naturally occurring sequence features impact the phase behaviors of disordered prion-like domains

Phase separation of intrinsically disordered prion-like low-complexity domains (PLCDs) derived from RNA-binding proteins enable the formation of biomolecular condensates in cells. PLCDs have distinct amino acid compositions, and here we decipher the physicochemical impact of conserved compositional biases on the driving forces for phase separation. We find that tyrosine residues make for stronger drivers of phase separation than phenylalanine. Depending on their sequence contexts, arginine residues enhance or weaken phase separation, whereas lysine residues weaken cohesive interactions within PLCDs. Increased net charge per residue (NCPR) weakens the driving forces for phase separation of PLCDs and this effect can be modeled quantitatively. The effects of NCPR also weaken known correlations between the dimensions of single chains in dilute solution and the driving forces for phase separation. We build on experimental data to develop a coarse-grained model for accurate simulations of phase separation that yield novel insights regarding PLCD phase behavior.

biophysics↗

Microfluidic determination of liquid-liquid phase separation binodals

Liquid-liquid phase separation plays important roles in the compartmentalization of cells. Developing an understanding of how phase separation is encoded in biomacromolecules requires quantitative mapping of their phase behavior. Given that such experiments require large quantities of the biomolecule of interest, these efforts have been lagging behind the recent breadth of biological insights. Herein, we present a microfluidic phase chip that enables the measurement of saturation concentrations over at least three orders of magnitude for a broad spectrum of biomolecules and solution conditions. The phase chip consists of five units, each made of twenty individual sample chambers to allow the measurement of five sample conditions simultaneously. The analytes are slowly concentrated via evaporation of water, which is replaced by oil, until the sample undergoes phase separation into a dilute and dense phase. We show that the phase chip lowers the required sample quantity by 98% while offering six-fold better statistics in comparison to standard manual experiments that involve centrifugal separation of dilute and dense phase. We further show that the saturation concentrations measured in chip are in agreement with previously reported data for a variety of biomolecules. Concomitantly, time-dependent changes of the dense phase morphology and potential off-pathway processes, including aggregation, can be monitored microscopically. In summary, the phase chip is suited to exploring sequence-to-binodal relationships by enabling the determination of a large number of saturation concentrations at low protein cost.

biophysics↗

Connecting coil-to-globule transitions to full phase diagrams for intrinsically disordered proteins

Phase separation is thought to underlie spatial and temporal organization that is required for controlling biochemical reactions in cells. Multivalence of interaction motifs also known as stickers is a defining feature of proteins that drive phase separation. Intrinsically disordered proteins with stickers uniformly distributed along the linear sequence can serve as scaffold molecules that drive phase separation. The sequence-intrinsic contributions of disordered proteins to phase separation can be discerned by computing or measuring sequence-specific phase diagrams. These help to delineate the combinations of protein concentration and a suitable control parameter such as temperature that support phase separation. Here, we present an approach that combines detailed simulations with a numerical adaptation of an analytical Gaussian cluster theory to enable the calculation of sequence-specific phase diagrams. Our approach leverages the known equivalence between the driving forces for single chain collapse in dilute solutions and the driving forces for phase separation in concentrated solutions. We demonstrate the application of the theory-aided computations through calculation of phase diagrams for a set of archetypal intrinsically disordered low complexity domains. STATEMENT OF SIGNIFICANCEIntrinsically disordered proteins that have the requisite valence of adhesive linear motifs can drive phase separation and give rise to membraneless biomolecular condensates. Knowledge of how phase diagrams vary with amino acid sequence and changes to solution conditions is essential for understanding how proteins contribute to condensate assembly and dissolution. In this work, we introduce a new two-pronged computational approach to predict sequence-specific phase diagrams. This approach starts by extracting key parameters from simulations of single-chain coil-to-globule transitions. We use these parameters in our numerical implementation of the Gaussian cluster theory (GCT) for polymer solutions to construct sequences-specific phase diagrams. The method is efficient and demonstrably accurate and should pave the way for high-throughput assessments of phase behavior.

biophysics↗