Microtubule Elasticity: Connecting All-Atom Simulations with Continuum Mechanics

The mechanical properties of microtubules have been extensively studied using a wide range of biophysical techniques, seeking to understand the mechanics of these cylindrical polymers. Here we develop a method for connecting all-atom molecular dynamics simulations with continuum mechanics and show how this can be applied to understand microtubule mechanics. Our coarse-graining technique applied to the microscopic simulation system yields consistent predictions for the Young's modulus and persistence length of microtubules, while clearly demonstrating how binding of the drug Taxol decreases the stiffness of microtubules. The techniques we develop should be widely applicable to other macromolecular systems. © 2010 The American Physical Society

Effects of distance dependence of exciton hopping on the Davydov soliton

The Davydov model of energy transfer in molecular chains is reconsidered assuming the distance dependence of the exciton hopping term. New equations of motion for phonons and excitons are derived within the coherent state approximation. Solving these nonlinear equations result in the existence of Davydov-like solitons. In the case of a dilatational soliton, the amplitude and width is decreased as a results of the mechanism introduced here and above a critical coupling strength our equations do not allow for localized solutions. For compressional solitons, stability is increased.Comment: RevTeX 13 pages, 3 Postscript figure

Elastic properties of grafted microtubules

We use single-particle tracking to study the elastic properties of single microtubules grafted to a substrate. Thermal fluctuations of the free microtubule's end are recorded, in order to measure position distribution functions from which we calculate the persistence length of microtubules with contour lengths between 2.6 and 48 micrometers. We find the persistence length to vary by more than a factor of 20 over the total range of contour lengths. Our results support the hypothesis that shearing between protofilaments contributes significantly to the mechanics of microtubules.Comment: 9 pages, 3 figure

Ectopic A-lattice seams destabilize microtubules

Natural microtubules typically include one A-lattice seam within an otherwise helically symmetric B-lattice tube. It is currently unclear how A-lattice seams influence microtubule dynamic instability. Here we find that including extra A-lattice seams in GMPCPP microtubules, structural analogues of the GTP caps of dynamic microtubules, destabilizes them, enhancing their median shrinkage rate by >20-fold. Dynamic microtubules nucleated by seeds containing extra A-lattice seams have growth rates similar to microtubules nucleated by B-lattice seeds, yet have increased catastrophe frequencies at both ends. Furthermore, binding B-lattice GDP microtubules to a rigor kinesin surface stabilizes them against shrinkage, whereas microtubules with extra A-lattice seams are stabilized only slightly. Our data suggest that introducing extra A-lattice seams into dynamic microtubules destabilizes them by destabilizing their GTP caps. On this basis, we propose that the single A-lattice seam of natural B-lattice MTs may act as a trigger point, and potentially a regulation point, for catastrophe

Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

Thermopower of the Correlated Narrow Gap Semiconductor FeSi and Comparison to RuSi

Iron based narrow gap semiconductors such as FeSi, FeSb2, or FeGa3 have received a lot of attention because they exhibit a large thermopower, as well as striking similarities to heavy fermion Kondo insulators. Many proposals have been advanced, however, lacking quantitative methodologies applied to this problem, a consensus remained elusive to date. Here, we employ realistic many-body calculations to elucidate the impact of electronic correlation effects on FeSi. Our methodology accounts for all substantial anomalies observed in FeSi: the metallization, the lack of conservation of spectral weight in optical spectroscopy, and the Curie susceptibility. In particular we find a very good agreement for the anomalous thermoelectric power. Validated by this congruence with experiment, we further discuss a new physical picture of the microscopic nature of the insulator-to-metal crossover. Indeed, we find the suppression of the Seebeck coefficient to be driven by correlation induced incoherence. Finally, we compare FeSi to its iso-structural and iso-electronic homologue RuSi, and predict that partially substituted Fe(1-x)Ru(x)Si will exhibit an increased thermopower at intermediate temperatures.Comment: 14 pages. Proceedings of the Hvar 2011 Workshop on 'New materials for thermoelectric applications: theory and experiment

Intracellular Electric Field and pH Optimize Protein Localization and Movement

Mammalian cell function requires timely and accurate transmission of information from the cell membrane (CM) to the nucleus (N). These pathways have been intensively investigated and many critical components and interactions have been identified. However, the physical forces that control movement of these proteins have received scant attention. Thus, transduction pathways are typically presented schematically with little regard to spatial constraints that might affect the underlying dynamics necessary for protein-protein interactions and molecular movement from the CM to the N. We propose messenger protein localization and movements are highly regulated and governed by Coulomb interactions between: 1. A recently discovered, radially directed E-field from the NM into the CM and 2. Net protein charge determined by its isoelectric point, phosphorylation state, and the cytosolic pH. These interactions, which are widely applied in elecrophoresis, provide a previously unknown mechanism for localization of messenger proteins within the cytoplasm as well as rapid shuttling between the CM and N. Here we show these dynamics optimize the speed, accuracy and efficiency of transduction pathways even allowing measurement of the location and timing of ligand binding at the CM –previously unknown components of intracellular information flow that are, nevertheless, likely necessary for detecting spatial gradients and temporal fluctuations in ligand concentrations within the environment. The model has been applied to the RAF-MEK-ERK pathway and scaffolding protein KSR1 using computer simulations and in-vitro experiments. The computer simulations predicted distinct distributions of phosphorylated and unphosphorylated components of this transduction pathway which were experimentally confirmed in normal breast epithelial cells (HMEC)

Structure–property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body

Accessing a Hidden Conformation of the Maltose Binding Protein Using Accelerated Molecular Dynamics

Periplasmic binding proteins (PBPs) are a large family of molecular transporters that play a key role in nutrient uptake and chemotaxis in Gram-negative bacteria. All PBPs have characteristic two-domain architecture with a central interdomain ligand-binding cleft. Upon binding to their respective ligands, PBPs undergo a large conformational change that effectively closes the binding cleft. This conformational change is traditionally viewed as a ligand induced-fit process; however, the intrinsic dynamics of the protein may also be crucial for ligand recognition. Recent NMR paramagnetic relaxation enhancement (PRE) experiments have shown that the maltose binding protein (MBP) - a prototypical member of the PBP superfamily - exists in a rapidly exchanging (ns to µs regime) mixture comprising an open state (approx 95%), and a minor partially closed state (approx 5%). Here we describe accelerated MD simulations that provide a detailed picture of the transition between the open and partially closed states, and confirm the existence of a dynamical equilibrium between these two states in apo MBP. We find that a flexible part of the protein called the balancing interface motif (residues 175–184) is displaced during the transformation. Continuum electrostatic calculations indicate that the repacking of non-polar residues near the hinge region plays an important role in driving the conformational change. Oscillations between open and partially closed states create variations in the shape and size of the binding site. The study provides a detailed description of the conformational space available to ligand-free MBP, and has implications for understanding ligand recognition and allostery in related proteins

Ghosts of Yellowstone: Multi-Decadal Histories of Wildlife Populations Captured by Bones on a Modern Landscape

Natural accumulations of skeletal material (death assemblages) have the potential to provide historical data on species diversity and population structure for regions lacking decades of wildlife monitoring, thereby contributing valuable baseline data for conservation and management strategies. Previous studies of the ecological and temporal resolutions of death assemblages from terrestrial large-mammal communities, however, have largely focused on broad patterns of community composition in tropical settings. Here, I expand the environmental sampling of large-mammal death assemblages into a temperate biome and explore more demanding assessments of ecological fidelity by testing their capacity to record past population fluctuations of individual species in the well-studied ungulate community of Yellowstone National Park (Yellowstone). Despite dramatic ecological changes following the 1988 wildfires and 1995 wolf re-introduction, the Yellowstone death assemblage is highly faithful to the living community in species richness and community structure. These results agree with studies of tropical death assemblages and establish the broad capability of vertebrate remains to provide high-quality ecological data from disparate ecosystems and biomes. Importantly, the Yellowstone death assemblage also correctly identifies species that changed significantly in abundance over the last 20 to ∼80 years and the directions of those shifts (including local invasions and extinctions). The relative frequency of fresh versus weathered bones for individual species is also consistent with documented trends in living population sizes. Radiocarbon dating verifies the historical source of bones from Equus caballus (horse): a functionally extinct species. Bone surveys are a broadly valuable tool for obtaining population trends and baseline shifts over decadal-to-centennial timescales