Direct computations of viscoelastic moduli of biomolecular condensates.

In vitro facsimiles of biomolecular condensates are formed by different types of intrinsically disordered proteins including prion-like low complexity domains (PLCDs). PLCD condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model and information regarding intra- and inter-chain contacts that is extracted from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations. The key ingredient of the generalized Rouse model is the Zimm matrix that we compute from equilibrium MMC simulations. We compute two flavors of Zimm matrices, one referred to as the single-chain model that accounts only for intra-chain contacts, and the other referred to as a collective model, that accounts for inter-chain interactions. The single-chain model systematically overestimates the storage and loss moduli, whereas the collective model reproduces the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two models proves to be most accurate. In line with the theory of Rouse, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic versus dominantly viscous behaviors is influenced by the totality of the relaxation modes. Hence, our analysis suggests that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain distributions of relaxation times that underlie the dynamics within condensates.

Biomolecular condensates form spatially inhomogeneous network fluids.

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Biomolecular condensates form spatially inhomogeneous network fluids.

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Biomolecular condensates form spatially inhomogeneous network fluids.

The functions of biomolecular condensates are thought to be influenced by their material properties, and these are in turn determined by the multiscale structural features within condensates. However, structural characterizations of condensates are challenging, and hence rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and bespoke coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that mimic nucleolar granular components (GCs). We show that facsimiles of GCs are network fluids featuring spatial inhomogeneities across hierarchies of length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights, extracted from a combination of approaches, suggest that condensates formed by multivalent proteins share features with network fluids formed by associative systems such as patchy or hairy colloids.

Sequence-specific interactions determine viscoelasticity and aging dynamics 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.

Phase Transitions of Associative Biomacromolecules.

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Condensates formed by prion-like low-complexity domains have small-world network structures and interfaces defined by expanded conformations.

Biomolecular condensates form via coupled associative and segregative phase transitions of multivalent associative macromolecules. Phase separation coupled to percolation is one example of such transitions. Here, we characterize molecular and mesoscale structural descriptions of condensates formed by intrinsically disordered prion-like low complexity domains (PLCDs). These systems conform to sticker-and-spacers architectures. Stickers are cohesive motifs that drive associative interactions through reversible crosslinking and spacers affect the cooperativity of crosslinking and overall macromolecular solubility. Our computations reproduce experimentally measured sequence-specific phase behaviors of PLCDs. Within simulated condensates, networks of reversible inter-sticker crosslinks organize PLCDs into small-world topologies. The overall dimensions of PLCDs vary with spatial location, being most expanded at and preferring to be oriented perpendicular to the interface. Our results demonstrate that even simple condensates with one type of macromolecule feature inhomogeneous spatial organizations of molecules and interfacial features that likely prime them for biochemical activity.

Extracting Information on Linear and Nonlinear Absorption from Two-Beam Action Spectroscopy Data.

Two-beam action (2-BA) spectroscopies are a recently developed class of techniques for determining the order(s) of absorption (one-photon, two-photon, etc.) that contribute to an observable signal. When only a single order of absorption is present, 2-BA spectroscopies allow for the determination of that order from data obtained at a single value of the observable. It has been shown previously that when two orders of absorption are present, they can be determined unambiguously from measurements made at several values of the observable. However, this latter approach cannot be used for single-valued observables, such as a polymerization threshold. Here we develop a theoretical comparison between conventional methods that determine the order(s) of absorption using logarithmic plots and 2-BA-based techniques. We also explore how 2-BA plots arising from two orders of absorption deviate from a plot with a single, noninteger exponent. We demonstrate that these deviations can usually be used to identify the two orders of absorption and their relative contributions to the signal on the basis of measurements made at a single value of the observable.

Determination of the contributions of two simultaneous absorption orders using 2-beam action spectroscopy.

The concept of a 2-beam action (2-BA) spectroscopy was recently introduced as a method for determining the order of effective nonlinear absorption in multiphoton photoresists. Here we demonstrate that the 2-BA approach can be extended to any measureable observable generated by linear and/or nonlinear absorption. As an example, 2-beam constant-amplitude photocurrent spectroscopy is used to study absorption of a tightly focused, mode-locked or continuous-wave, 800 nm laser by a GaAsP photodiode. The effective order of the absorption process can be measured at any desired value of the photocurrent or photovoltage. A self-consistent framework is presented for using non-integral 2-BA exponents to determine the relative contributions of two absorption mechanisms of different order. The dependence of the ratio of the quadratic and linear contributions on the average excitation power is used to verify that these are the dominant orders of absorption in the photodiode with 800 nm excitation.

Toward in Situ Measurement of the Density of Liquid Benzene Using Optical Kerr Effect Spectroscopy.

The high-frequency portion of the optical Kerr effect (OKE) spectrum of benzene shifts to higher frequency with decreasing temperature at constant pressure. This behavior has been interpreted previously in terms of an increase in librational frequencies due to the decrease in free volume with liquid densification. However, decreasing temperature also provides less access to the more repulsive portion of the intermolecular potential, which would cause the blue edge of the spectrum to red-shift. To explore the relative importance of these phenomena, molecular dynamics simulations of benzene are used to isolate the effects of temperature and density on the spectrum. The simulations show that, at constant density, the high-frequency portion of the spectrum shifts to lower frequency with decreasing temperature. In contrast, at constant temperature, the high-frequency portion of the spectrum shifts to higher frequency with increasing density. These results indicate that density plays a greater role in determining the position of the blue edge of the low-frequency Raman spectrum of benzene than does temperature. Empirical fits show that the effects of changing density or temperature are similar in experimental and simulated OKE spectra. Furthermore, line-shape analysis of simulated spectra under isochoric and isothermal conditions shows that the effects of density and temperature are separable, suggesting that OKE spectroscopy is a viable technique for in situ measurement of the density of van der Waals liquids.

Chronic oxidative stress after irradiation: An unproven hypothesis.

Injury and organ failure after irradiation of late-responding tissues is a substantial problem in radiation oncology and a major threat after accidental or belligerent exposures. The mechanisms of injury may include death of clonogens, vascular injury, activation of cytokine networks, and/or chronic oxidative stress. Knowledge of mechanisms may guide optimal use of mitigators. The hypothesis of chronic oxidative stress as a mechanism for late radiation injury has received much attention. We review herein the published evidence for chronic oxidative stress in vivo, and for use of antioxidants as mitigators of normal tissue radiation injury. We conclude that there is only indirect evidence for chronic oxidative stress after irradiation, and there are only limited published reports of mitigation by antioxidants. We did not find a differentiation of persistent markers of oxidative stress from an ongoing production of oxygen radicals. It is thus unproven that chronic oxidative stress plays a major role in causing radiation injury and organ failure in late-responding tissues. Further investigation is justified, to identify chronic oxidative stress and to identify optimal mitigators of radiation injury.