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153
Molecular Modeling Of Proteins And Mathematical Prediction Of Protein Structure
 SIAM Review
, 1997
"... . This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possib ..."
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Cited by 61 (5 self)
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. This paper discusses the mathematical formulation of and solution attempts for the socalled protein folding problem. The static aspect is concerned with how to predict the folded (native, tertiary) structure of a protein, given its sequence of amino acids. The dynamic aspect asks about the possible pathways to folding and unfolding, including the stability of the folded protein. From a mathematical point of view, there are several main sides to the static problem:  the selection of an appropriate potential energy function;  the parameter identification by fitting to experimental data; and  the global optimization of the potential. The dynamic problem entails, in addition, the solution of (because of multiple time scales very stiff) ordinary or stochastic differential equations (molecular dynamics simulation), or (in case of constrained molecular dynamics) of differentialalgebraic equations. A theme connecting the static and dynamic aspect is the determination and formation of...
Metastable Walking Machines
, 2008
"... Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Due to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with highgain feedback. Minimallyactuated walkin ..."
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Cited by 42 (11 self)
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Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Due to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with highgain feedback. Minimallyactuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limitcycle stability; however, they can still demonstrate impressively longliving periods of continuous walking. Here, we employ tools from stochastic processes to examine the “stochastic stability” of idealized rimlesswheel and compassgait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability the mean firstpassagetime and compare its performance to a deterministic counterpart. Our results demonstrate that walking is wellcharacterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.
Artificial Brownian motors: Controlling transport on the nanoscale
 REV MOD. PHYS
, 2009
"... In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of “Brownian motors. ” In this review the constructive r ..."
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Cited by 31 (4 self)
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In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic and random alike, can assist directed motion of particles at submicron scales. In such cases, one speaks of “Brownian motors. ” In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cellular molecular machinery: the working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e., nonbiological, nanopores, lithographic tracks, and optical traps, where singleparticle currents were first measured. Much emphasis is given to two and threedimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented here. The field has recently been enriched with impressive experimental achievements in building artificial Brownian motor devices that even operate within the quantum domain by harvesting quantum Brownian motion. Sundry akin topics include activities aimed at noiseassisted shuttling other degrees of freedom such as charge, spin, or even heat and the assembly of chemical synthetic molecular motors. This review ends with a perspective for future pathways and potential new applications.
A microcantilever device to assess the effect of force on the lifetime of selectincarbohydrate bonds
 Biophys. J
, 2001
"... A microcantilever technique was used to apply force to receptorligand molecules involved in leukocyte rolling on blood vessel walls. Eselectin was adsorbed onto 3μmdiameter, 4mmlong glass fibers, and the selectin ligand, sialyl Lewisx, was coupled to latex microspheres. After binding, the micr ..."
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Cited by 22 (1 self)
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A microcantilever technique was used to apply force to receptorligand molecules involved in leukocyte rolling on blood vessel walls. Eselectin was adsorbed onto 3μmdiameter, 4mmlong glass fibers, and the selectin ligand, sialyl Lewisx, was coupled to latex microspheres. After binding, the microsphere and bound fiber were retracted using a computerized loading protocol that combines hydrodynamic and Hookean forces on the fiber to produce a range of force loading rates (force/time), rf. From the distribution of forces at failure, the average force was determined and plotted as a function of ln rf. The slope and intercept of the plot yield the unstressed reverse reaction rate, kro, and a parameter that describes the force dependence of reverse reaction rates, ro. The ligand was titrated so adhesion occurred in ~30 % of tests, implying that>80 % of adhesive events involve single bonds. Monte Carlo simulations show that this level of multiple bonding has little effect on parameter estimation. The estimates are ro = 0.048 and 0.016 nm and kro = 0.72 and 2.2 s1 for loading rates in the ranges 200–1000 and 1000–5000 pN s1, respectively. LevenbergMarquardt fitting across all values of rf gives ro = 0.034 nm and kro = 0.82 s1. The values of these parameters are in the range required for rolling, as
Simple Physical Models Connect Theory and Experiment in Protein Folding Kinetics
 J. Mol. Biol
, 2002
"... s, provide predictions of folding rates and mechanisms for a comprehensive set of over 400 small protein domains of known structure. q 2002 Elsevier Science Ltd. All rights reserved Keywords: protein folding; transition state; kinetics; fvalues; master equation *Corresponding author Introduction ..."
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Cited by 21 (0 self)
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s, provide predictions of folding rates and mechanisms for a comprehensive set of over 400 small protein domains of known structure. q 2002 Elsevier Science Ltd. All rights reserved Keywords: protein folding; transition state; kinetics; fvalues; master equation *Corresponding author Introduction Recent theoretical models by Alm & Baker, Galzitskaya & Finkelstein, and Munoz & Eaton have focused on the importance of topology in determining proteinfolding mechanisms, using simple free energy functions to make predictions about folding rates and transition state (TS) structures. All three groups used a simplified approach in which each residue is considered to be either ordered as in the native state or completely disordered, with ordered residues occurring in one or more contiguous segments of the protein chain (the multiple sequence approximation) . The models balance the entropic cost of ordering residues against the free energy decrease associated with making native inte
Nonequilibrium fluctuations in small systems: From physics to biology
 Advances in Chemical Physics
, 2006
"... In this paper I am presenting an overview on several topics related to nonequilibrium fluctuations in small systems. I start with a general discussion about fluctuation theorems and applications to physical examples extracted from physics and biology: a bead in an optical trap and single molecule fo ..."
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Cited by 19 (1 self)
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In this paper I am presenting an overview on several topics related to nonequilibrium fluctuations in small systems. I start with a general discussion about fluctuation theorems and applications to physical examples extracted from physics and biology: a bead in an optical trap and single molecule force experiments. Next I present a general discussion on path thermodynamics and consider distributions of work/heat fluctuations as large deviation functions. Then I address the topic of glassy dynamics from the perspective of nonequilibrium fluctuations due to small cooperatively rearranging regions. Finally, I
Dynamic tension spectroscopy and strength of biomembranes
 Biophys J
, 2003
"... ABSTRACT Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tensio ..."
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ABSTRACT Rupturing fluid membrane vesicles with a steady ramp of micropipette suction produces a distribution of breakage tensions governed by the kinetic process of membrane failure. When plotted as a function of log(tension loading rate), the locations of distribution peaks define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the kinetic pathway. Using tests on five types of giant phosphatidylcholine lipid vesicles over loading rates(tension/time) from 0.01–100 mN/m/s, we show that the kinetic process of membrane breakage can be modeled by a causal sequence of two thermallyactivated transitions. At fast loading rates, a steep linear regime appears in each spectrum which implies that membrane failure starts with nucleation of a rare precursor defect. The slope and projected intercept of this regime are set by defect size and frequency of spontaneous formation, respectively. But at slow loading rates, each spectrum crosses over to a shallowcurved regime where rupture tension changes weakly with rate. This regime is predicted by the classical cavitation theory for opening an unstable hole in a twodimensional film within the lifetime of the defect state. Under slow loading, membrane edge energy and the frequency scale for thermal fluctuations in hole size are the principal factors that govern the level of tension at failure. To critically test the model and obtain the parameters governing the rates of transition under stress, distributions of rupture tension were computed and matched to the measured histograms through solution of the kinetic master (Markov) equations for defect formation and annihilation or evolution to an unstable hole under a ramp of tension. As key predictors of membrane strength, the results for spontaneous frequencies of defect formation and hole edge energies were found to correlate with membrane thicknesses and elastic bending moduli, respectively.
Analysis of functional motions in brownian molecular machines with an efficient block normal mode approach: Myosinii and ca + 2atpase
 Bioph. J
, 2004
"... ABSTRACT The structural flexibilities of two molecular machines, myosin and Ca 21ATPase, have been analyzed with normal mode analysis and discussed in the context of their energy conversion functions. The normal mode analysis with physical intermolecular interactions was made possible by an improve ..."
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Cited by 16 (2 self)
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ABSTRACT The structural flexibilities of two molecular machines, myosin and Ca 21ATPase, have been analyzed with normal mode analysis and discussed in the context of their energy conversion functions. The normal mode analysis with physical intermolecular interactions was made possible by an improved implementation of the block normal mode (BNM) approach. The BNM results clearly illustrated that the largescale conformational transitions implicated in the functional cycles of the two motor systems can be largely captured with a small number of lowfrequency normal modes. Therefore, the results support the idea that structural flexibility is an essential part of the construction principle of molecular motors through evolution. Such a feature is expected to be more prevalent in motor proteins than in simpler systems (e.g., signal transduction proteins) because in the former, largescale conformational transitions often have to occur before the chemical events (e.g., ATP hydrolysis in myosin and ATP binding/phosphorylation in Ca 21ATPase). This highlights the importance of Brownian motions associated with the protein domains that are involved in the functional transitions; in this sense, Brownian molecular machines is an appropriate description of molecular motors, although the normal mode results do not address the origin of the ratchet effect. The results also suggest that it might be more appropriate to describe functional transitions in some molecular motors as intrinsic elastic motions modulating local structural changes in the active site, which in turn gets stabilized by the subsequent chemical events, in contrast with the conventional idea of local changes somehow getting amplified into largerscale motions. In the case of myosin, for example, we favor the idea that Brownian motions associated with the flexible converter propagates to the Switch I/II region, where the saltbridge
Effective dynamics using conditional expectations
"... Abstract. The question of coarsegraining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarsegrained variable ξ(x), where x describes the configuration of the system in a highdimensional space R n, and ξ is a smooth ..."
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Cited by 15 (6 self)
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Abstract. The question of coarsegraining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarsegrained variable ξ(x), where x describes the configuration of the system in a highdimensional space R n, and ξ is a smooth function with value in R (typically a reaction coordinate). It is well known that, given a BoltzmannGibbs distribution on x ∈ R n, the equilibrium properties on ξ(x) are completely determined by the free energy. On the other hand, the question of the effective dynamics on ξ(x) is much more difficult to address. Starting from an overdamped Langevin equation on x ∈ R n, we propose an effective dynamics for ξ(x) ∈ R using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarsegrained dynamics. AMS classification scheme numbers: 35B40, 82C31, 60H10Effective dynamics using conditional expectations 2 1.
Metastable LeggedRobot Locomotion
, 2008
"... A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and inte ..."
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Cited by 15 (9 self)
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A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean firstpassage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of