Elina Bengtsson

Parallel computation with molecular-motor-propelled agents in nanofabricated networks

Significance Electronic computers are extremely powerful at performing a high number of operations at very high speeds, sequentially. However, they struggle with combinatorial tasks that can be solved faster if many operations are performed in parallel. Here, we present proof-of-concept of a parallel computer by solving the specific instance {2, 5, 9} of a classical nondeterministic-polynomial-time complete (“NP-complete”) problem, the subset sum problem. The computer consists of a specifically designed, nanostructured network explored by a large number of molecular-motor-driven, protein filaments. This system is highly energy efficient, thus avoiding the heating issues limiting electronic computers. We discuss the technical advances necessary to solve larger combinatorial problems than existing computation devices, potentially leading to a new way to tackle difficult mathematical problems. The combinatorial nature of many important mathematical problems, including nondeterministic-polynomial-time (NP)-complete problems, places a severe limitation on the problem size that can be solved with conventional, sequentially operating electronic computers. There have been significant efforts in conceiving parallel-computation approaches in the past, for example: DNA computation, quantum computation, and microfluidics-based computation. However, these approaches have not proven, so far, to be scalable and practical from a fabrication and operational perspective. Here, we report the foundations of an alternative parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. Exploring the network in a parallel fashion using a large number of independent, molecular-motor-propelled agents then solves the mathematical problem. This approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power consumption and heat dissipation. We provide a proof-of-concept demonstration of such a device by solving, in a parallel fashion, the small instance {2, 5, 9} of the subset sum problem, which is a benchmark NP-complete problem. Finally, we discuss the technical advances necessary to make our system scalable with presently available technology.

The α-defensin salt-bridge induces backbone stability to facilitate folding and confer proteolytic resistance.

Salt-bridge interactions between acidic and basic amino acids contribute to the structural stability of proteins and to protein–protein interactions. A conserved salt-bridge is a canonical feature of the α-defensin antimicrobial peptide family, but the role of this common structural element has not been fully elucidated. We have investigated mouse Paneth cell α-defensin cryptdin-4 (Crp4) and peptide variants with mutations at Arg7 or Glu15 residue positions to disrupt the salt-bridge and assess the consequences on Crp4 structure, function, and stability. NMR analyses showed that both (R7G)-Crp4 and (E15G)-Crp4 adopt native-like structures, evidence of fold plasticity that allows peptides to reshuffle side chains and stabilize the structure in the absence of the salt-bridge. In contrast, introduction of a large hydrophobic side chain at position 15, as in (E15L)-Crp4 cannot be accommodated in the context of the Crp4 primary structure. Regardless of which side of the salt-bridge was mutated, salt-bridge variants retained bactericidal peptide activity with differential microbicidal effects against certain bacterial cell targets, confirming that the salt-bridge does not determine bactericidal activity per se. The increased structural flexibility induced by salt-bridge disruption enhanced peptide sensitivity to proteolysis. Although sensitivity to proteolysis by MMP7 was unaffected by most Arg7 and Glu15 substitutions, every salt-bridge variant was degraded extensively by trypsin. Moreover, the salt-bridge facilitates adoption of the characteristic α-defensin fold as shown by the impaired in vitro refolding of (E15D)-proCrp4, the most conservative salt-bridge disrupting replacement. In Crp4, therefore, the canonical α-defensin salt-bridge facilitates adoption of the characteristic α-defensin fold, which decreases structural flexibility and confers resistance to degradation by proteinases.

Nonlinear Cross-Bridge Elasticity and Post-Power-Stroke Events in Fast Skeletal Muscle Actomyosin

Generation of force and movement by actomyosin cross-bridges is the molecular basis of muscle contraction, but generally accepted ideas about cross-bridge properties have recently been questioned. Of the utmost significance, evidence for nonlinear cross-bridge elasticity has been presented. We here investigate how this and other newly discovered or postulated phenomena would modify cross-bridge operation, with focus on post-power-stroke events. First, as an experimental basis, we present evidence for a hyperbolic [MgATP]-velocity relationship of heavy-meromyosin-propelled actin filaments in the in vitro motility assay using fast rabbit skeletal muscle myosin (28-29°C). As the hyperbolic [MgATP]-velocity relationship was not consistent with interhead cooperativity, we developed a cross-bridge model with independent myosin heads and strain-dependent interstate transition rates. The model, implemented with inclusion of MgATP-independent detachment from the rigor state, as suggested by previous single-molecule mechanics experiments, accounts well for the [MgATP]-velocity relationship if nonlinear cross-bridge elasticity is assumed, but not if linear cross-bridge elasticity is assumed. In addition, a better fit is obtained with load-independent than with load-dependent MgATP-induced detachment rate. We discuss our results in relation to previous data showing a nonhyperbolic [MgATP]-velocity relationship when actin filaments are propelled by myosin subfragment 1 or full-length myosin. We also consider the implications of our results for characterization of the cross-bridge elasticity in the filament lattice of muscle.

Persistence length of fascin-cross-linked actin filament bundles in solution and the in vitro motility assay

BACKGROUND Bundles of unipolar actin filaments (F-actin), cross-linked via the actin-binding protein fascin, are important in filopodia of motile cells and stereocilia of inner ear sensory cells. However, such bundles are also useful as shuttles in myosin-driven nanotechnological applications. Therefore, and for elucidating aspects of biological function, we investigate if the bundle tendency to follow straight paths (quantified by path persistence length) when propelled by myosin motors is directly determined by material properties quantified by persistence length of thermally fluctuating bundles. METHODS Fluorescent bundles, labeled with rhodamine-phalloidin, were studied at fascin:actin molar ratios: 0:1 (F-actin), 1:7, 1:4 and 1:2. Persistence lengths (Lp) were obtained by fitting the cosine correlation function (CCF) to a single exponential function: =exp(-s/(2Lp)) where θ(s) is tangent angle; s: path or contour lengths. < > denotes averaging over filaments. RESULTS Bundle-Lp (bundles<15μm long) increased from ~10 to 150μm with increased fascin:actin ratio. The increase was similar for path-Lp (path<15μm), with highly linear correlation. For longer bundle paths, the CCF-decay deviated from a single exponential, consistent with superimposition of the random path with a circular path as suggested by theoretical analysis. CONCLUSIONS Fascin-actin bundles have similar path-Lp and bundle-Lp, both increasing with fascin:actin ratio. Path-Lp is determined by the flexural rigidity of the bundle. GENERAL SIGNIFICANCE The findings give general insight into mechanics of cytoskeletal polymers that interact with molecular motors, aid rational development of nanotechnological applications and have implications for structure and in vivo functions of fascin-actin bundles.

Myosin-Induced Gliding Patterns at Varied [MgATP] Unveil a Dynamic Actin Filament

Actin filaments have key roles in cell motility but are generally claimed to be passive interaction partners in actin-myosin-based motion generation. Here, we present evidence against this static view based on an altered myosin-induced actin filament gliding pattern in an in vitro motility assay at varied [MgATP]. The statistics that characterize the degree of meandering of the actin filament paths suggest that for [MgATP] ≥ 0.25 mM, the flexural rigidity of heavy meromyosin (HMM)-propelled actin filaments is similar (without phalloidin) or slightly lower (with phalloidin) than that of HMM-free filaments observed in solution without surface tethering. When [MgATP] was reduced to ≤0.1 mM, the actin filament paths in the in vitro motility assay became appreciably more winding in both the presence and absence of phalloidin. This effect of lowered [MgATP] was qualitatively different from that seen when HMM was mixed with ATP-insensitive, N-ethylmaleimide-treated HMM (NEM-HMM; 25–30%). In particular, the addition of NEM-HMM increased a non-Gaussian tail in the path curvature distribution as well as the number of events in which different parts of an actin filament followed different paths. These effects were the opposite of those observed with reduced [MgATP]. Theoretical modeling suggests a 30–40% lowered flexural rigidity of the actin filaments at [MgATP] ≤ 0.1 mM and local bending of the filament front upon each myosin head attachment. Overall, the results fit with appreciable structural changes in the actin filament during actomyosin-based motion generation, and modulation of the actin filament mechanical properties by the dominating chemomechanical actomyosin state.

Analysis of flexural rigidity of actin filaments propelled by surface adsorbed myosin motors

Actin filaments are central components of the cytoskeleton and the contractile machinery of muscle. The filaments are known to exist in a range of conformational states presumably with different flexural rigidity and thereby different persistence lengths. Our results analyze the approaches proposed previously to measure the persistence length from the statistics of the winding paths of actin filaments that are propelled by surface‐adsorbed myosin motor fragments in the in vitro motility assay. Our results suggest that the persistence length of heavy meromyosin propelled actin filaments can be estimated with high accuracy and reproducibility using this approach provided that: (1) the in vitro motility assay experiments are designed to prevent bias in filament sliding directions, (2) at least 200 independent filament paths are studied, (3) the ratio between the sliding distance between measurements and the camera pixel‐size is between 4 and 12, (4) the sliding distances between measurements is less than 50% of the expected persistence length, and (5) an appropriate cut‐off value is chosen to exclude abrupt large angular changes in sliding direction that are complications, e.g., due to the presence of rigor heads. If the above precautions are taken the described method should be a useful routine part of in vitro motility assays thus expanding the amount of information to be gained from these.

Reply to Einarsson: The computational power of parallel network exploration with many bioagents

REPLY TO EINARSSON : The computational power of parallel network exploration with many bioagents

In Vitro Motility Assay Studies at Low [MgATP] - Evidence For Inter-Head Cooperativity in Fast Skeletal Myosin II

The idea that fast skeletal myosin II exhibits processivity with sequential actions of the two myosin heads during muscle contraction has long been a topic of discussion but with appreciable difficulties to obtain conclusive experimental results. The difficulties may be related to a limited processivity (few sequential head actions) that is of greatest importance at low velocity (e.g. high resistive load), difficult to study accurately in vitro. In order to aid the investigations we here make use of recent evidence that the bipyridine drug amrinone inhibits the strain-dependent ADP-release step of myosin II with expected enhancement of processivity (Albet-Torres et al., J Biol Chem., 2009); Mansson, Biophys J., 2010). For accurate velocity measurements, the recombinant expressed capping protein CapZ (Soeno et. al., J Muscle Res Cell Motil., 1998) was fluorescence labeled. Nanometer tracking was achieved by two-dimensional Gaussian fits to single molecule fluorescence intensity profiles representing CapZ attached to the trailing actin filament end. Importantly, the heavy meromyosin (HMM) propelled actin filament sliding velocity (1mM MgATP) for CapZ-capped filaments was comparable to that of uncapped filaments at different ionic strengths and HMM surface densities. Studies at low [MgATP] (5-30μM) suggests a non-linearity in the [MgATP]-velocity plot that was enhanced by 1mM amrinone. The result is in contrast to the linearity expected for independent myosin heads and could be interpreted as an apparent velocity dependence of the myosin step length. This is in accordance with the idea of limited processivity of myosin II if it is assumed that a doubled apparent step length corresponds to sequential action of the two heads. Further insight into the mechanism will be obtained using proteolytically prepared one-headed HMM and e.g. studies with external loads on actin.