Calculating Structure Factors of Protein Solutions by Atomistic Modeling of Protein-Protein Interactions.

We present a method, FMAPS(q), for calculating the structure factor, S(q), of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function gC(R). At low protein concentrations, gC(R) can be approximated as e-ßW(R), where W(R) is the potential of mean force along the center-center distance R. We calculate W(R) using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203-8215]. For higher protein concentrations, we obtain S(q) by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.

Adenosine Triphosphate Mediates Phase Separation of Disordered Basic Proteins by Bridging Intermolecular Interaction Networks.

Adenosine triphosphate (ATP) is an abundant molecule with crucial cellular roles as the energy currency and a building block of nucleic acids and for protein phosphorylation. Here we show that ATP mediates the phase separation of basic intrinsically disordered proteins (bIDPs). In the resulting condensates, ATP is highly concentrated (apparent partition coefficients up to 7700) and serves as bridges between bIDP chains. These liquid-like droplets have some of the lowest interfacial tension (∼25 pN/µm) but high zero-shear viscosities (1-15 Pa s) due to the bridged protein networks, and yet their fusion has some of the highest speeds (∼1 µm/ms). The rapid fusion manifests extreme shear thinning, where the apparent viscosity is lower than zero-shear viscosity by over 100-fold, made possible by fast reformation of the ATP bridges. At still higher concentrations, ATP does not dissolve bIDP droplets but results in aggregates and fibrils.

Surface Charge Can Modulate Phase Separation of Multidomain Proteins.

Phase separation has emerged as an important mechanism explaining the formation of certain biomolecular condensates. Biological phase separation is often driven by the multivalent interactions of modular protein domains. Beyond valency, the physical features of folded domains that promote phase separation are poorly understood. We used a model system─the small ubiquitin modifier (SUMO) and its peptide ligand, the SUMO interaction motif (SIM)─to examine how domain surface charge influences multivalency-driven phase separation. Phase separation of polySUMO and polySIM was altered by pH via a change in the protonation state of SUMO surface histidines. These effects were recapitulated by histidine mutations, which modulated SUMO solubility and polySUMO-polySIM phase separation in parallel and were quantitatively explained by atomistic modeling of weak interactions among proteins in the system. Thus, surface charge can tune the phase separation of multivalent proteins, suggesting a means of controlling phase separation biologically, evolutionarily, and therapeutically.

Multiple modes of DNA compaction by protamine.

In sperm cells, protamine replaces histones to compact DNA 10-20 times more than in somatic cells. To characterize the extreme compaction, we employed confocal microscopy and optical tweezers to determine the conformations and stability of protamine-bound λ-DNA. Confocal images show increasing compaction of λ-DNA at increasing protamine concentration. In the presence of protamine, single λ-DNA molecules form bends and loops that unravel at 10-40 pN forces as well as coils that shorten the contour length by up to 40% and withstand forces strong enough (~55 pN) for strand separation. Strand separation nucleates coils, indicating protamine insertion into DNA bases. Protamine may participate in both local and higher-order chromatin organization, leading to extreme compaction and global transcription silencing.

A common pathway for detergent-assisted oligomerization of Aß42.

Amyloid beta (Aß) aggregation is a slow process without seeding or assisted nucleation. Sodium dodecyl sulfate (SDS) micelles stabilize Aß42 small oligomers (in the dimer to tetramer range); subsequent SDS removal leads to a 150-kD Aß42 oligomer. Dodecylphosphorylcholine (DPC) micelles also stabilize an Aß42 tetramer. Here we investigate the detergent-assisted oligomerization pathway by solid-state NMR spectroscopy and molecular dynamics simulations. SDS- and DPC-induced oligomers have the same structure, implying a common oligomerization pathway. An antiparallel ß-sheet formed by the C-terminal region, the only stable structure in SDS and DPC micelles, is directly incorporated into the 150-kD oligomer. Three Gly residues (at positions 33, 37, and 38) create holes that are filled by the SDS and DPC hydrocarbon tails, thereby turning a potentially destabilizing feature into a stabilizing factor. These observations have implications for endogenous Aß aggregation at cellular interfaces.

Dimeric Transmembrane Structure of the SARS-CoV-2 E Protein.

The SARS-CoV-2 E protein is a transmembrane (TM) protein with its N-terminus exposed on the external surface of the virus. At debate is its oligomeric state, let alone its function. Here, the TM structure of the E protein is characterized by oriented sample and magic angle spinning solid-state NMR in lipid bilayers and refined by molecular dynamics simulations. This protein was previously found to be a pentamer, with a hydrophobic pore that appears to function as an ion channel. We identify only a front-to-front, symmetric helix-helix interface, leading to a dimeric structure that does not support channel activity. The two helices have a tilt angle of only 6°, resulting in an extended interface dominated by Leu and Val sidechains. While residues Val14-Thr35 are almost all buried in the hydrophobic region of the membrane, Asn15 lines a water-filled pocket that potentially serves as a drug-binding site. The E and other viral proteins may adopt different oligomeric states to help perform multiple functions.

Atomistic modeling of liquid-liquid phase equilibrium explains dependence of critical temperature on γ-crystallin sequence.

Liquid-liquid phase separation of protein solutions has regained heightened attention for its biological importance and pathogenic relevance. Coarse-grained models are limited when explaining residue-level effects on phase equilibrium. Here we report phase diagrams for γ-crystallins using atomistic modeling. The calculations were made possible by combining our FMAP method for computing chemical potentials and Brownian dynamics simulations for configurational sampling of dense protein solutions, yielding the binodal and critic temperature (Tc). We obtain a higher Tc for a known high-Tc γ-crystallin, γF, than for a low-Tc paralog, γB. The difference in Tc is corroborated by a gap in second virial coefficient. Decomposition of inter-protein interactions reveals one amino-acid substitution between γB and γF, from Ser to Trp at position 130, as the major contributor to the difference in Tc. This type of analysis enables us to link phase equilibrium to amino-acid sequence and to design mutations for altering phase equilibrium.

ATP Mediates Phase Separation of Disordered Basic Proteins by Bridging Intermolecular Interaction Networks.

ATP is an abundant molecule with crucial cellular roles as the energy currency and a building block of nucleic acids and for protein phosphorylation. Here we show that ATP mediates the phase separation of basic intrinsically disordered proteins (bIDPs). In the resulting condensates, ATP is highly concentrated (apparent partition coefficients at 200-5000) and serves as bridges between bIDP chains. These liquid-like droplets have some of the lowest interfacial tension (~25 pN/µm) but high zero-shear viscosities (1-15 Pa s) due to the bridged protein networks, and yet their fusion has some of the highest speeds (~1 µm/ms). The rapid fusion manifests extreme shear thinning, where the apparent viscosity is lower than zero-shear viscosity by over 100-fold, made possible by fast reformation of the ATP bridges. At still higher concentrations, ATP does not dissolve bIDP droplets but results in aggregates and fibrils.

Magnesium ions mediate ligand binding and conformational transition of the SAM/SAH riboswitch.

The SAM/SAH riboswitch binds S-adenosylmethionine (SAM) and S-adenosylhomocysteine (SAH) with similar affinities. Mg2+ is generally known to stabilize RNA structures by neutralizing phosphates, but how it contributes to ligand binding and conformational transition is understudied. Here, extensive molecular dynamics simulations (totaling 120 µs) predicted over 10 inner-shell Mg2+ ions in the SAM/SAH riboswitch. Six of them line the two sides of a groove to widen it and thereby pre-organize the riboswitch for ligand entry. They also form outer-shell coordination with the ligands and stabilize an RNA-ligand hydrogen bond, which effectively diminishes the selectivity between SAM and SAH. One Mg2+ ion unique to the apo form maintains the Shine-Dalgarno sequence in an autonomous mode and thereby facilitates its release for ribosome binding. Mg2+ thus plays vital roles in SAM/SAH riboswitch function.

Atomistic Modeling of Liquid-Liquid Phase Equilibrium Explains Dependence of Critical Temperature on γ-Crystallin Sequence.

Liquid-liquid phase separation of protein solutions has regained heightened attention for its biological importance and pathogenic relevance. Coarse-grained models are limited when explaining residue-level effects on phase equilibrium. Here we report phase diagrams for γ-crystallins using atomistic modeling. The calculations were made possible by combining our FMAP method for computing chemical potentials and Brownian dynamics simulations for configurational sampling of dense protein solutions, yielding the binodal and critic temperature ( T c ). We obtain a higher T c for a known high- T c γ-crystallin, γF, than for a low- T c paralog, γB. The difference in T c is corroborated by a gap in second virial coefficient. Decomposition of inter-protein interactions reveals one amino-acid substitution between γB and γF, from Ser to Trp at position 130, as the major contributor to the difference in T c . This type of analysis enables us to link phase equilibrium to amino-acid sequence and to design mutations for altering phase equilibrium.

Power law in a bounded range: Estimating the lower and upper bounds from sample data.

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and, in many cases, also an upper bound. Estimating these bounds from sample data is notoriously difficult, with a recent method involving O(N3) operations, where N denotes sample size. Here I develop an approach for estimating the lower and upper bounds that involve O(N) operations. The approach centers on calculating the mean values, x̂min and x̂max, of the smallest x and the largest x in N-point samples. A fit of x̂min or x̂max as a function of N yields the estimate for the lower or upper bound. Application to synthetic data demonstrates the accuracy and reliability of this approach.

Dimeric Transmembrane Structure of the SARS-CoV-2 E Protein.

The SARS-CoV-2 E protein is a transmembrane (TM) protein with its N-terminus exposed on the external surface of the virus. Here, the TM structure of the E protein is characterized by oriented sample and magic angle spinning solid-state NMR in lipid bilayers and refined by molecular dynamics simulations. This protein has been found to be a pentamer, with a hydrophobic pore that appears to function as an ion channel. We identified only a symmetric helix-helix interface, leading to a dimeric structure that does not support channel activity. The two helices have a tilt angle of only 6°, resulting in an extended interface dominated by Leu and Val sidechains. While residues Val14-Thr35 are almost all buried in the hydrophobic region of the membrane, Asn15 lines a water-filled pocket that potentially serves as a drug-binding site. The E and other viral proteins may adopt different oligomeric states to help perform multiple functions.

N-WASP is competent for downstream signaling before full release from autoinhibition.

Allosteric regulation of intrinsically disordered proteins (IDPs) is still vastly understudied compared to the counterpart of structured proteins. Here, we used molecular dynamics simulations to characterize the regulation of the IDP N-WASP by the binding of its basic region with inter- and intramolecular ligands (PIP2 and an acidic motif, respectively). The intramolecular interactions keep N-WASP in an autoinhibited state; PIP2 binding frees the acidic motif for interacting with Arp2/3 and thereby initiating actin polymerization. We show that PIP2 and the acidic motif compete in binding with the basic region. However, even when PIP2 is present at 30% in the membrane, the acidic motif is free of contact with the basic region ("open" state) in only 8.5% of the population. The very C-terminal three residues of the A motif are crucial for Arp2/3 binding; conformations where only the A tail is free are present at a much higher population than the open state (40- to 6-fold, depending on the PIP2 level). Thus, N-WASP is competent for Arp2/3 binding before it is fully freed from autoinhibition.

Why Does Synergistic Activation of WASP, but Not N-WASP, by Cdc42 and PIP2 Require Cdc42 Prenylation?

Human WASP and N-WASP are homologous proteins that require the binding of multiple regulators, including the acidic lipid PIP2 and the small GTPase Cdc42, to relieve autoinhibition before they can stimulate the initiation of actin polymerization. Autoinhibition involves intramolecular binding of the C-terminal acidic and central motifs to an upstream basic region and GTPase binding domain. Little is known about how a single intrinsically disordered protein, WASP or N-WASP, binds multiple regulators to achieve full activation. Here we used molecular dynamics simulations to characterize the binding of WASP and N-WASP with PIP2 and Cdc42. In the absence of Cdc42, both WASP and N-WASP strongly associate with PIP2-containing membranes, through their basic region and also possibly through a tail portion of the N-terminal WH1 domain. The basic region also participates in Cdc42 binding, especially for WASP; consequently Cdc42 binding significantly compromises the ability of the basic region in WASP, but not N-WASP, to bind PIP2. PIP2 binding to the WASP basic region is restored only when Cdc42 is prenylated at the C-terminus and tethered to the membrane. This distinction in the activation of WASP and N-WASP may contribute to their different functional roles.

Power Law in a Bounded Range: Estimating the Lower and Upper Bounds from Sample Data.

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds from sample data is notoriously difficult, with a recent method involving O(N^3) operations, where N denotes sample size. Here I develop an approach for estimating the lower and upper bounds that involves O(N) operations. The approach centers on calculating the mean values, x_min and x_max, of the smallest x and the largest x in N-point samples. A fit of x_min or x_max as a function of N yields the estimate for the lower or upper bound. Application to synthetic data demonstrates the accuracy and reliability of this approach.

Two gates mediate NMDA receptor activity and are under subunit-specific regulation.

Kinetics of NMDA receptor (NMDAR) ion channel opening and closing contribute to their unique role in synaptic signaling. Agonist binding generates free energy to open a canonical gate at the M3 helix bundle crossing. Single channel activity is characterized by clusters, or periods of rapid opening and closing, that are separated by long silent periods. A conserved glycine in the outer most transmembrane helices, the M4 helices, regulates NMDAR function. Here we find that the GluN1 glycine mainly regulates single channel events within a cluster, whereas the GluN2 glycine mainly regulates entry and exit from clusters. Molecular dynamics simulations suggest that, whereas the GluN2 M4 (along with GluN2 pre-M1) regulates the gate at the M3 helix bundle crossing, the GluN1 glycine regulates a 'gate' at the M2 loop. Subsequent functional experiments support this interpretation. Thus, the distinct kinetics of NMDARs are mediated by two gates that are under subunit-specific regulation.

An Arg/Ala-rich helix in the N-terminal region of M. tuberculosis FtsQ is a potential membrane anchor of the Z-ring.

Mtb infects a quarter of the worldwide population. Most drugs for treating tuberculosis target cell growth and division. With rising drug resistance, it becomes ever more urgent to better understand Mtb cell division. This process begins with the formation of the Z-ring via polymerization of FtsZ and anchoring of the Z-ring to the inner membrane. Here we show that the transmembrane protein FtsQ is a potential membrane anchor of the Mtb Z-ring. In the otherwise disordered cytoplasmic region of FtsQ, a 29-residue, Arg/Ala-rich α-helix is formed that interacts with upstream acidic residues in solution and with acidic lipids at the membrane surface. This helix also binds to the GTPase domain of FtsZ, with implications for drug binding and Z-ring formation.

Magnesium ions mediate ligand binding and conformational transition of the SAM/SAH riboswitch.

The SAM/SAH riboswitch binds S-adenosylmethionine (SAM) and S-adenosylhomocysteine (SAH) with similar affinities. Mg 2+ is generally known to stabilize RNA structures by neutralizing phosphates, but how it contributes to ligand binding and conformational transition is understudied. Here, extensive molecular dynamics simulations (totaling 120 µs) identified over 10 inner-shell Mg 2+ ions in the SAM/SAH riboswitch. Six of them line the two sides of a groove to widen it and thereby pre-organize the riboswitch for ligand entry. They also form outer-shell coordination with the ligands and stabilize an RNA-ligand hydrogen bond, which effectively diminish the selectivity between SAM and SAH. One Mg 2+ ion unique to the apo form maintains the Shine-Dalgarno sequence in an autonomous mode and thereby facilitates its release for ribosome binding. Mg 2+ thus plays vital roles in SAM/SAH riboswitch function.

Predicting the Sequence-Dependent Backbone Dynamics of Intrinsically Disordered Proteins.

Dynamics is a crucial link between sequence and function for intrinsically disordered proteins (IDPs). NMR spin relaxation is a powerful technique for characterizing the sequence-dependent backbone dynamics of IDPs. Of particular interest is the 15N transverse relaxation rate (R2), which reports on slower dynamics (10s of ns up to 1 µs and beyond). NMR and molecular dynamics (MD) simulations have shown that local interactions and secondary structure formation slow down backbone dynamics and raise R2. Elevated R2 has been suggested to be indicators of propensities of membrane association, liquid-liquid phase separation, and other functional processes. Here we present a sequence-based method, SeqDYN, for predicting R2 of IDPs. The R2 value of a residue is expressed as the product of contributing factors from all residues, which attenuate with increasing sequence distance from the central residue. The mathematical model has 21 parameters, representing the correlation length (where the attenuation is at 50%) and the amplitudes of the contributing factors of the 20 types of amino acids. Training on a set of 45 IDPs reveals a correlation length of 5.6 residues, aromatic and long branched aliphatic amino acids and Arg as R2 promotors whereas Gly and short polar amino acids as R2 suppressors. The prediction accuracy of SeqDYN is competitive against that of recent MD simulations using IDP-specific force fields. For a structured protein, SeqDYN prediction represents R2 in the unfolded state. SeqDYN is available as a web server at https://zhougroup-uic.github.io/SeqDYNidp/ for rapid R2 prediction.

Partial mimicry of the microtubule binding of tau by its membrane binding.

Tau, as typical of intrinsically disordered proteins (IDPs), binds to multiple targets including microtubules and acidic membranes. The latter two surfaces are both highly negatively charged, raising the prospect of mimicry in their binding by tau. The tau-microtubule complex was recently determined by cryo-electron microscopy. Here, we used molecular dynamics simulations to characterize the dynamic binding of tau K19 to an acidic membrane. This IDP can be divided into three repeats, each containing an amphipathic helix. The three amphipathic helices, along with flanking residues, tether the protein to the membrane interface. The separation between and membrane positioning of the amphipathic helices in the simulations are validated by published EPR data. The membrane contact probabilities of individual residues in tau show both similarities to and distinctions from native contacts with microtubules. In particular, a Lys that is conserved among the repeats forms similar interactions with membranes and with microtubules, as does a conserved Val. This partial mimicry facilitates both the membrane anchoring of microtubules by tau and the transfer of tau from membranes to microtubules.