The application of the "inverse problem" method for constructing confining potentials that make N-soliton waveforms exact solutions in the Gross-Pitaevskii equation.

In this work, we discuss an application of the "inverse problem" method to find the external trapping potential, which has particular N trapped soliton-like solutions of the Gross-Pitaevskii equation (GPE) also known as the cubic nonlinear Schrödinger equation (NLSE). This inverse method assumes particular forms for the trapped soliton wave function, which then determines the (unique) external (confining) potential. The latter renders these assumed waveforms exact solutions of the GPE (NLSE) for both attractive (g<0) and repulsive (g>0) self-interactions. For both signs of g, we discuss the stability with respect to self-similar deformations and translations. For g<0, a critical mass Mc or equivalently the number of particles for instabilities to arise can often be found analytically. On the other hand, for the case with g>0 corresponding to repulsive self-interactions which is often discussed in the atomic physics realm of Bose-Einstein condensates, the bound solutions are found to be always stable. For g<0, we also determine the critical mass numerically by using linear stability or Bogoliubov-de Gennes analysis, and compare these results with our analytic estimates. Various analytic forms for the trapped N-soliton solutions in one, two, and three spatial dimensions are discussed, including sums of Gaussians or higher-order eigenfunctions of the harmonic oscillator Hamiltonian.

Increasing the calcium sensitivity of muscle using trifluoperazine-induced manipulations in silico, in vitro and in vivo systems.

Many therapeutics for cardiomyopathy treat the symptoms of the disease rather than the underlying mechanism. The mechanism of cardiomyopathy onset is believed to include two means: calcium sensitivity changes and myosin activity alteration. Trifluoperazine is a compound that binds troponin, and other components of the calcium pathway, which impacts calcium regulation of contraction. Here, the ability of TFP to shift calcium sensitivity was examined in vitro with purified proteins and the impact of TFP on heart function was assessed in vivo using embryonic zebrafish. The binding of TFP to troponin was modeled in silico and a model of zebrafish troponin was generated. TFP increased regulated cardiac actomyosin activity in vitro and elevated embryonic zebrafish heart rates at effective drug concentrations. Troponin structural changes predicted in silico suggest altered protein interactions within thin filaments that would affect the regulation of heart function.

The Dark Side of Actin: Cardiac actin variants highlight the role of allostery in disease development.

Mutations in the α-cardiac actin ACTC1 gene cause dilated or hypertrophic cardiomyopathy. These diseases are the result of changes in protein interactions between ACTC protein and force-generating ß-myosin or the calcium-dependent cardiac-tropomyosin (cTm) and cardiac troponin (cTn) regulatory complex, altering the overall contractile force. The T126I and S271F ACTC variants possess amino acid substitutions on the other side of actin relative to the myosin or regulatory protein binding sites on what we call the "dark side" of actin. The T126I change results in hyposensitivity to calcium, in accordance with the calcium sensitivity pathway of cardiomyopathy development while the S271F change alters the maximum in vitro motility sliding speed, reflecting a change in maximum force. These results demonstrate the role of actin allostery in the cardiac disease development.

Assembly and Maintenance of Sarcomere Thin Filaments and Associated Diseases.

Sarcomere assembly and maintenance are essential physiological processes required for cardiac and skeletal muscle function and organism mobility. Over decades of research, components of the sarcomere and factors involved in the formation and maintenance of this contractile unit have been identified. Although we have a general understanding of sarcomere assembly and maintenance, much less is known about the development of the thin filaments and associated factors within the sarcomere. In the last decade, advancements in medical intervention and genome sequencing have uncovered patients with novel mutations in sarcomere thin filaments. Pairing this sequencing with reverse genetics and the ability to generate patient avatars in model organisms has begun to deepen our understanding of sarcomere thin filament development. In this review, we provide a summary of recent findings regarding sarcomere assembly, maintenance, and disease with respect to thin filaments, building on the previous knowledge in the field. We highlight debated and unknown areas within these processes to clearly define open research questions.

A crosslinked and ribosylated actin trimer does not interact productively with myosin.

A purified F-actin-derived actin trimer that interacts with end-binding proteins did not activate or bind the side-binding protein myosin under rigor conditions. Remodeling of the actin trimer by the binding of gelsolin did not rescue myosin binding, nor did the use of different means of inhibiting the polymerization of the trimer. Our results demonstrate that ADP-ribosylation on all actin subunits of an F-actin-derived trimer inhibits myosin binding and that the binding of DNase-I to the pointed end subunits of a crosslinked trimer also remodels the myosin binding site. Taken together, this work highlights the need for a careful balance between modification of actin subunits and maintaining protein-protein interactions to produce a physiologically relevant short F-actin complex.

M-class hypertrophic cardiomyopathy cardiac actin mutations increase calcium sensitivity of regulated thin filaments.

Hypertrophic cardiomyopathy is a commonly occurring cardiovascular disease resulting primarily from changes in proteins participating in muscle contraction in the heart, including the cardiac actin protein. Changes in cardiac actin located exclusively in the myosin binding site are called M-class variants and include the H88Y, R95C, and E99K substitutions and F90Δ deletion. The prevailing hypothesis for these mutations is that hypertrophic cardiomyopathy is the result of increased calcium sensitivity of contraction in the myocardium. To test this hypothesis, we studied the activity of myosin at varying calcium concentrations in the presence of regulated thin filaments containing M-class cardiac actin variants. We found that all M-class cardiac actin variants exhibit increased calcium sensitivity, with the R95C variant also displaying significant decreases in maximal myosin activity. This work represents the first characterization of all M-class variant proteins and suggests that drugs targeting contraction specifically to treat hypertrophic cardiomyopathy must consider the impact on both calcium sensitivity and maximal myosin activity on overall heart health.

Cardiac actin changes in the actomyosin interface have different effects on myosin duty ratio.

Hypertrophic cardiomyopathy (HCM) is an inherited cardiovascular disease (CD) that commonly causes an increased size of cardiomyocytes in the left ventricle. The proteins myosin and actin interact in the myocardium to produce contraction through the actomyosin ATPase cycle. The duty ratio (r) of myosin is the proportion of the actomyosin ATPase cycle that myosin is bound to actin and does work. A common hypothesis is that HCM mutations increase contraction in cardiac sarcomeres; however, the available data are not clear on this connection. Based on previous work with human α-cardiac actin (ACTC), we hypothesize that HCM-linked ACTC variants with alterations near the myosin binding site have an increased r, producing more force. Myosin duty ratios using human ACTC variant proteins were calculated with myosin ATPase activity and in-vitro motility data. We found no consistent changes in the duty ratio of the ACTC variants, suggesting that other factors are involved in the development of HCM when ACTC variants are present.

The immediate effect of HCM causing actin mutants E99K and A230V on actin-Tm-myosin interaction in thin-filament reconstituted myocardium.

Human cardiac actin mutants E99K and A230V were expressed with baculovirus/insect cells and used to reconstitute the thin-filament of bovine cardiac (BVC) muscle fibers, together with tropomyosin (Tm) and troponin (Tn) purified from bovine ventricles. Effects of [Ca(2+)], [ATP], and [phosphate] on tension and its transients were studied at 25°C. In the absence of Tm/Tn, both mutants significantly decreased the tension of actin filament reconstituted fibers (WT: 0.75±0.06 T0, E99K: 0.58±0.04 T0, A230V: 0.58±0.03 T0), where T0 is active tension of native fibers (T0=26.9±1.1kPa, N=41), indicating diminished actin-myosin interactions. However, in the presence of Tm and Tn, WT, E99K, and A230V recovered tension (0.85±0.06 T0, 0.89±0.06 T0, and 0.85±0.05 T0, respectively), demonstrating the compensatory effect of Tm/Tn. Ca(2+) sensitivity (pCa50) increased (5.59±0.02, 5.80±0.03, 5.77±0.03, respectively) and cooperativity (nH) decreased (2.6±0.3, 1.87±0.21, 1.60±0.11, respectively). The kinetic constants of the cross-bridge cycle were deduced using sinusoidal analysis. E99K did not show any significant changes in any of the kinetic constants compared to those of WT. A230V caused a decrease in K1 (ATP association constant), k2 and k-2 (rate constants of the cross-bridge detachment step). The cross-bridge distribution was similar among WT, E99K, and A230V. In conclusion, our experiments demonstrate that the first step of HCM pathogenesis with E99K is increased pCa50 and decreased nH, which result in larger tension during partial activation to cause a diastolic problem. The effect on nH is more severe with A230V. In addition, A230V has a problem of decreased cross-bridge kinetics, which affects the normal functions of the cross-bridge cycle and may contribute to the first step of the HCM pathogenesis.

Do cardiac actin mutations lead to altered actomyosin interactions?

It is currently hypothesized that increased heart muscle contractility leads to hypertrophic cardiomyopathy (HCM), and reduced contractility leads to dilated cardiomyopathy (DCM). To determine if changes in the core interaction between actin and myosin occur due to mutations in the cardiac actin gene (ACTC), we measured the interactions between myosin and 8 ACTC mutant proteins found in patients with HCM or DCM. R312H showed a decreased actin-activated myosin S1 ATPase rate (13.1 ± 0.63 µmol/L/min) compared to WT (15.3 ± 1.6 µmol/L/min), whereas the rate with E99K was significantly higher (20.1 ± 1.5 µmol/L/min). In vitro motility assays with varying ATP concentrations showed that the KM for E99K remains unchanged with a significantly decreased Vmax (1.90 ± 0.37 µm/sec) compared to WT (3.33 ± 0.46 µm/sec). Based on a 5 nm myosin step size, we calculated a duty ratio of approximately 0.04 for WT and the majority of mutant actins; however, the duty ratio for E99K was twice as high. Based on our analysis of 8 ACTC mutants, we infer that mutations in ACTC lead to disease through various molecular mechanisms. While changes in actomyosin interactions with the E99K mutation might cause increased ATP usage and tension leading to HCM, measurable changes in the basic interaction between actin and myosin do not appear to be involved in the mechanisms of disease development for the other ACTC mutants tested.

Using baculovirus/insect cell expressed recombinant actin to study the molecular pathogenesis of HCM caused by actin mutation A331P.

Recombinant WT human cardiac actin (WT actin) was expressed using the baculovirus/insect cell expression system, purified, and used to reconstitute the thin-filament of bovine cardiac muscle fibers, together with bovine cardiac tropomyosin (Tm) and troponin (Tn). Effects of [Ca(2+)], [ATP], [phosphate] and [ADP] on tension and tension transients were studied at 25°C by using sinusoidal analysis, and the results were compared with those of native fibers and fibers reconstituted with purified bovine cardiac actin (BVC actin). In actin filament reconstituted fibers (without Tm/Tn), those reconstituted with WT actin showed exactly the same active tension as those reconstituted with purified BVC actin (WT: 0.75±0.06 T0, N=11; BVC: 0.73±0.07 T0, N=12, where T0 is the tension of original fibers before extraction). After Tm/Tn reconstitution, fibers reconstituted with WT actin generated 0.85±0.06 T0 (N=11) compared to 0.98±0.04 T0 (N=12) recovered by those reconstituted with BVC actin. In the presence of Tm/Tn, WT actin reconstituted fibers showed exactly the same Ca(2+) sensitivity as those of the native fibers and BVC actin reconstituted fibers (pCa50: native fibers: 5.69±0.01, N=10; WT: 5.69±0.02, N=11; BVC: 5.68±0.02, N=12). Sinusoidal analysis showed that the cross-bridge kinetics were the same among native fibers, BVC actin reconstituted fibers and WT actin reconstituted fibers, followed by reconstitution of Tm/Tn. These results demonstrate that baculovirus/insect cell expressed actin has no significant differences from tissue purified actin and can be used for thin-filament reconstitution assays. One hypertrophic cardiomyopathy (HCM) causing actin mutant A331P actin was also expressed and studied similarly, and the results were compared to those of the WT actin. In the reconstituted fibers, A331P significantly decreased the tension both in the absence of Tm/Tn (0.55±0.03 T0, N=13) and in their presence (0.65±0.02 T0, N=13) compared to those of the WT (0.75±0.06 T0 and 0.85±0.06 T0, respectively, N=11). A331P also showed decreased pCa50 (5.57±0.03, N=13) compared to that of WT (5.69±0.02, N=11). The cross-bridge kinetics and its distribution were similar between WT and A331P actin reconstituted fibers, indicating that force/cross-bridge was decreased by A331P. In conclusion, A331P causes a weakened cross-bridge force, which leads to a decreased active tension, reduces left-ventricular ejection fraction, and eventually results in the HCM phenotype.

Altered interactions between cardiac myosin binding protein-C and α-cardiac actin variants associated with cardiomyopathies.

The two genes most commonly associated with mutations linked to hypertrophic or dilated cardiomyopathies are ß-myosin and cardiac myosin binding protein-C (cMyBP-C). Both of these proteins interact with cardiac actin (ACTC). Currently there are 16 ACTC variants that have been found in patients with HCM or DCM. While some of these ACTC variants exhibit protein instability or polymerization-deficiencies that might contribute to the development of disease, other changes could cause changes in protein-protein interactions between sarcomere proteins and ACTC. To test the hypothesis that changes in ACTC disrupt interactions with cMyBP-C, we examined the interactions between seven ACTC variants and the N-terminal C0C2 fragment of cMyBP-C. We found there was a significant decrease in binding affinity (increase in Kd values) for the A331P and Y166C variants of ACTC. These results suggest that a change in the ability of cMyBP-C to bind actin filaments containing these ACTC protein variants might contribute to the development of disease. These results also provide clues regarding the binding site of the C0C2 fragment of cMyBP-C on F-actin.

Flightless I is a focal adhesion-associated actin-capping protein that regulates cell migration.

The role of adhesion-associated actin-binding proteins in cell migration is not well defined. In mouse fibroblasts we screened for focal adhesion-associated proteins that were isolated with collagen-coated beads and detected by tandem mass spectrometry. We identified flightless I (FliI) as an actin-binding protein in focal adhesion fractions, which was verified by immunoblotting. By confocal microscopy most FliI was distributed throughout the cytosol and in focal adhesions. By sedimentation assays and in vitro binding assays, we found that FliI associates with actin filaments and actin monomers. Assays using purified proteins showed that FliI inhibits actin polymerization and caps but does not sever actin filaments. Cells with FliI knockdown or cells overexpressing FliI migrated more or less rapidly, respectively, than wild-type controls. Compared with controls, cells with FliI knockdown were less adherent than wild-type cells, exhibited reduced numbers of focal adhesions containing activated ß1 integrins and vinculin, and exhibited increased incorporation of actin monomers into nascent filaments at focal adhesions. These data indicate that FliI regulates cell migration through its localization to focal adhesions and its ability to cap actin filaments, which collectively affect focal adhesion maturation.

Actin's C-terminus coordinates actin structural changes and functions.

Actin is essential to eukaryotic cellular processes. Actin's C-terminus appears to play a direct role in modulating actin's structure and properties, facilitating the binding and function of actin-binding proteins (ABPs). The structural and functional characterization of filamentous actin's C-terminus has been impeded by its inherent flexibility, as well as actin's resistance to crystallization for x-ray diffraction and the historical resolution constraints associated with electron microscopy. Many biochemical studies have established that actin's C-terminus must retain its flexibility and structural integrity to modulate actin's structure and functions. For example, C-terminal structural changes are known to affect nucleotide binding and exchange, as well as propagate actin structural changes throughout extensive allosteric networks, facilitating the binding and function of ABPs. Advances in electron microscopy have resulted in high-resolution structures of filamentous actin, providing insights into subtle structural changes that are mediated by actin's C-terminus. Here, we review existing knowledge establishing the importance of actin's C-terminus within actin structural changes and functions and discuss how modern structural characterization techniques provide the tools to understand the role of actin's C-terminus in cellular processes.

Uniform-density Bose-Einstein condensates of the Gross-Pitaevskii equation found by solving the inverse problem for the confining potential.

In this work, we study the existence and stability of constant density (flat-top) solutions to the Gross-Pitaevskii equation (GPE) in confining potentials. These are constructed by using the "inverse problem" approach which corresponds to the identification of confining potentials that make flat-top waveforms exact solutions to the GPE. In the one-dimensional case, the exact solution is the sum of stationary kink and antikink solutions, and in the overlapping region, the density is constant. In higher spatial dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed-out finite square well with minima also at the edges. When self-interactions are added, terms proportional to ±gψ^{*}ψ and ±gM with M representing the mass or number of particles in Bose-Einstein condensates get added to the confining potential and total energy, respectively. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of M. Comparing the stability criteria from Derrick's theorem with Bogoliubov-de Gennes (BdG) analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass M for attractive interactions. However, the numerical analysis gives a much lower critical mass. This is due to the emergence of symmetry-breaking instabilities that were detected by the BdG analysis and violate the symmetry x→-x assumed by Derrick's theorem.

Photox, a novel actin-targeting mono-ADP-ribosyltransferase from Photorhabdus luminescens.

Photorhabdus luminescens is a pathogenic bacterium that produces many toxic proteins. The mono-ADP-ribosyltransferases (mARTs) are an enzyme class produced by numerous pathogenic bacteria and participate in disease in plants and animals, including humans. Herein we report a novel mART from P. luminescens called Photox. This 46-kDa toxin shows high homology to other actin-targeting mARTs in hallmark catalytic regions and a similar core catalytic fold. Furthermore, Photox shows in vivo cytotoxic activity against yeast, with protection occurring when catalytic residues are substituted with alanine. In vitro, enzymatic activity (k(cat), 1680 +/- 75 min(-1)) is higher than that of the related iota toxin, and diminishes by nearly 14,000-fold following substitution of the catalytic Glu (E355A). This toxin specifically ADP-ribosylates monomeric alpha-skeletal actin and nonmuscle beta- and gamma-actin at Arg(177), inhibiting regular polymerization of actin filaments. These results indicate that Photox is indeed an ADP-ribosyltransferase, making it the newest member of the actin-targeting mART family.

ADP-ribosylation of cross-linked actin generates barbed-end polymerization-deficient F-actin oligomers.

Actin filament subunit interfaces are required for the proper interaction between filamentous actin (F-actin) and actin binding proteins (ABPs). The production of small F-actin complexes mimicking such interfaces would be a significant advance toward understanding the atomic interactions between F-actin and its many binding partners. We produced actin lateral dimers and trimers derived from F-actin and rendered polymerization-deficient by ADP-ribosylation of Arg-177. The degree of modification resulted in a moderate reduction in thermal stability. Calculated hydrodynamic radii were comparable to theoretical values derived from recent models of F-actin. Filament capping capabilities were retained and yielded pointed-end dissociation constants similar those of wild-type actin, suggesting native or near-native interfaces on the oligomers. Changes in DNase I binding affinity under low and high ionic strength suggested a high degree of conformational flexibility in the dimer and trimer. Polymer nucleation activity was lost upon ADP-ribosylation and rescued upon enzyme-mediated deADP-ribosylation, or upon binding to gelsolin, suggesting that interactions with actin binding proteins can overcome the inhibiting activities of ADP-ribosylation. The combined strategy of chemical cross-linking and ADP-ribosylation provides a minimalistic and reversible approach to engineering polymerization-deficient F-actin oligomers that are able to act as F-actin binding protein scaffolds.

Nonperturbative predictions for cold atom bose gases with tunable interactions.

We derive a theoretical description for dilute Bose gases as a loop expansion in terms of composite-field propagators by rewriting the Lagrangian in terms of auxiliary fields related to the normal and anomalous densities. We demonstrate that already in leading order this nonperturbative approach describes a large interval of coupling-constant values, satisfies Goldstone's theorem, yields a Bose-Einstein transition that is second order, and is consistent with the critical temperature predicted in the weak-coupling limit by the next-to-leading-order large-N expansion.

Non-polymerizing long-pitch actin dimers that interact with myosin.

The production of a soluble actomyosin complex would be a significant step toward elucidating molecular interactions responsible for biological movement. We took a systematic approach to producing soluble long-pitch actin dimers that are polymerization-deficient yet retain biological protein-protein interactions, including myosin binding. Actin mutant proteins and chemical crosslinking were combined with different polymerization inhibition strategies, including ADP-ribosylation, or the use of a polymerization-deficient actin mutant protein. While all of the long-pitch actin dimers retained interactions reflective of F-actin activity, each displayed different interactions with myosin. Myosin did not interact productively with long-pitch actin dimers capped with DNase-I, and led to filament formation of unmodified long-pitch actin dimers or dimers possessing a polymerization-deficient actin subunit. However, ADP-ribosylated long-pitch actin dimers interacted with myosin, giving this dimer great potential for producing a soluble actomyosin complex, which could greatly improve our understanding of the molecular basis of movement in cells, tissues, and organisms.

Homology-Directed Repair in Zebrafish: Witchcraft and Wizardry?

Introducing desired mutations into the genome of model organisms is a priority for all research focusing on protein function and disease modeling. The need to create stable mutant lines has resulted in the rapid advancement of genetic techniques over the last few decades from chemical mutagenesis and zinc finger nucleases to clustered regularly interspaced short palindromic repeats (CRISPR) and homology-directed repair (HDR). However, achieving consistently high success rates for direct mutagenesis in zebrafish remains one of the most sought-after techniques in the field. Several genes have been modified using HDR in zebrafish, but published success rates range widely, suggesting that an optimal protocol is required. In this review, we compare target genes, techniques, and protocols from 50 genes that were successfully modified in zebrafish using HDR to find the statistically best variables for efficient HDR rates.

Induced secondary structure and polymorphism in an intrinsically disordered structural linker of the CNS: solid-state NMR and FTIR spectroscopy of myelin basic protein bound to actin.

The 18.5 kDa isoform of myelin basic protein (MBP) is a peripheral membrane protein that maintains the structural integrity of the myelin sheath of the central nervous system by conjoining the cytoplasmic leaflets of oligodendrocytes and by linking the myelin membrane to the underlying cytoskeleton whose assembly it strongly promotes. It is a multifunctional, intrinsically disordered protein that behaves primarily as a structural stabilizer, but with elements of a transient or induced secondary structure that represent binding sites for calmodulin or SH3-domain-containing proteins, inter alia. In this study we used solid-state NMR (SSNMR) and Fourier transform infrared (FTIR) spectroscopy to study the conformation of 18.5 kDa MBP in association with actin microfilaments and bundles. FTIR spectroscopy of fully (13)C,(15)N-labeled MBP complexed with unlabeled F-actin showed induced folding of both protein partners, viz., some increase in beta-sheet content in actin, and increases in both alpha-helix and beta-sheet content in MBP, albeit with considerable extended structure remaining. Solid-state NMR spectroscopy revealed that MBP in MBP-actin assemblies is structurally heterogeneous but gains ordered secondary structure elements (both alpha-helical and beta-sheet), particularly in the terminal fragments and in a central immunodominant epitope. The overall conformational polymorphism of MBP is consistent with its in vivo roles as both a linker (membranes and cytoskeleton) and a putative signaling hub.