Covalent and non-covalent chemical engineering of actin for biotechnological applications

The cytoskeletal filaments are self-assembled protein polymers with 8–25 nm diameters and up to several tens of micrometres length. They have a range of pivotal roles in eukaryotic cells, including transportation of intracellular cargoes (primarily microtubules with dynein and kinesin motors) and cell motility (primarily actin and myosin) where muscle contraction is one example. For two decades, the cytoskeletal filaments and their associated motor systems have been explored for nanotechnological applications including miniaturized sensor systems and lab-on-a-chip devices. Several developments have also revolved around possible exploitation of the filaments alone without their motor partners. Efforts to use the cytoskeletal filaments for applications often require chemical or genetic engineering of the filaments such as specific conjugation with fluorophores, antibodies, oligonucleotides or various macromolecular complexes e.g. nanoparticles. Similar conjugation methods are also instrumental for a range of fundamental biophysical studies. Here we review methods for non-covalent and covalent chemical modifications of actin filaments with focus on critical advantages and challenges of different methods as well as critical steps in the conjugation procedures. We also review potential uses of the engineered actin filaments in nanotechnological applications and in some key fundamental studies of actin and myosin function. Finally, we consider possible future lines of investigation that may be addressed by applying chemical conjugation of actin in new ways.     

Membrane-associated nanomotors for macromolecular transport

Nature has endowed cells with powerful nanomotors to accomplish intricate mechanical tasks, such as the macromolecular transport across membranes occurring in cell division, bacterial conjugation, and in a wide variety of secretion systems. These biological motors couple the chemical energy provided by ATP hydrolysis to the mechanical work needed to transport DNA and/or protein effectors. Here, we review what is known about the molecular mechanisms of these membrane-associated machines. Sequence and structural comparison between these ATPases reveal that they share a similar motor domain, suggesting a common evolutionary ancestor. Learning how these machines operate will lead the design of nanotechnology devices with unique applications in medicine and engineering.     

In vitro studies of skeletal muscle membranes. Effects of denervation on the macromolecular components of cation transport in red and white skeletal muscle.

The effects of denervation on the macromolecular components of active monovalent cation transport in skeletal muscle have been studied using purified sarcolemma membranes. A comparison of membrane activities of fast-twitch, slow-twitch, and mixed-fiber muscles was made to determine what role, if any, the motor nerve has in regulating this important aspect of muscle metabolism. A dramatic increase in the basal sarcolemmal Mg++ ATPase activity (three- to fourfold) was found for both major muscle types. An increase in the ouabain-inhibitable (Na+ + K+)-stimulated enzyme was also found, but the effect was substantially less (1.5- to twofold). [3H]-ouabain binding, as an index of glycoside receptor sites, also increased (two- to threefold) midway in the course of denervation. On the other hand, the phosphorylated intermediate activity, a functional component of the transport system, clearly decreased over the same time course and remained below control values for the remainder of the course. This resulted in a two- to threefold increase in the turnover number, suggesting that active transport of cations should increase dramatically with denervation. The membrane protein patterns on SDS gels were less obvious than the changes observed in the functional components. The major effects appeared after only one week and seemed to be restricted to high molecular weight membrane proteins, especially in the 100,000 to 250,000 daltons range. This effect was more prominent in slow-twitch membranes with an apparent semiquantitative decrease in stain at 240,000 daltons. In gels of membranes from fast-twitch muscles a decreased stain in the range of 100,000 to 110,000 daltons occurred, and this became more obvious with longer periods of denervation. The results suggest that considerable influence on the macromolecular components of active cation transport in skeletal muscle is exerted by the motor nerve. No appreciable difference was found in this effect when the two major types of skeletal muscle, fast-twitch and slow-twitch, were compared, suggesting that motor nerve regulation of this membrane property is qualitatively the same.     

Mechanical properties of organelles driven by microtubule-dependent molecular motors in living cells

The organization of the cytoplasm is regulated by molecular motors which transport organelles and other cargoes along cytoskeleton tracks. Melanophores have pigment organelles or melanosomes that move along microtubules toward their minus and plus end by the action of cytoplasmic dynein and kinesin-2, respectively. In this work, we used single particle tracking to characterize the mechanical properties of motor-driven organelles during transport along microtubules. We tracked organelles with high temporal and spatial resolutions and characterized their dynamics perpendicular to the cytoskeleton track. The quantitative analysis of these data showed that the dynamics is due to a spring-like interaction between melanosomes and microtubules in a viscoelastic microenvironment. A model based on a generalized Langevin equation explained these observations and predicted that the stiffness measured for the motor complex acting as a linker between organelles and microtubules is ～ one order smaller than that determined for motor proteins in vitro. This result suggests that other biomolecules involved in the interaction between motors and organelles contribute to the mechanical properties of the motor complex. We hypothesise that the high flexibility observed for the motor linker may be required to improve the efficiency of the transport driven by multiple copies of motor molecules.     

Thermodynamics and kinetics of a molecular motor ensemble

If, contrary to conventional models of muscle, it is assumed that molecular forces equilibrate among rather than within molecular motors, an equation of state and an expression for energy output can be obtained for a near-equilibrium, coworking ensemble of molecular motors. These equations predict clear, testable relationships between motor structure, motor biochemistry, and ensemble motor function, and we discuss these relationships in the context of various experimental studies. In this model, net work by molecular motors is performed with the relaxation of a near-equilibrium intermediate step in a motor-catalyzed reaction. The free energy available for work is localized to this step, and the rate at which this free energy is transferred to work is accelerated by the free energy of a motor-catalyzed reaction. This thermodynamic model implicitly deals with a motile cell system as a dynamic network (not a rigid lattice) of molecular motors within which the mechanochemistry of one motor influences and is influenced by the mechanochemistry of other motors in the ensemble.     

Influence of the membrane potential on the free energy of an intrinsic protein

A modified Poisson-Boltzmann equation is developed from statistical mechanical considerations to describe the influence of the transmembrane potential on macromolecular systems. Using a Green's function formalism, the electrostatic free energy of a protein associated with the membrane is expressed as the sum of three terms: a contribution from the energy required to charge the system's capacitance, a contribution corresponding to the interaction of the protein charges with the membrane potential, and a contribution corresponding to a voltage-independent reaction field free energy. The membrane potential, which is due to the polarization interface, is calculated in the absence of the protein charges, whereas the reaction field is calculated in the absence of transmembrane potential. Variations in the capacitive energy associated with typical molecular processes are negligible under physiological conditions. The formulation of the theory is closely related to standard algorithms used to solve the Poisson-Boltzmann equation and only small modifications to current source codes are required for its implementation. The theory is illustrated by examining the voltage-dependent membrane insertion of a simple polyalanine alpha-helix and by computing the electrostatic potential across a 60-A-diameter sphere meant to represent a large intrinsic protein.     

Some Fundamental Molecular Mechanisms of Contractility in Fibrous Macromolecules

The fundamental molecular mechanisms of contractility and tension development in fibrous macromolecules are developed from the point of view of the principles of polymer physical chemistry. The problem is treated in a general manner to encompass the behavior of all macromolecular systems irrespective of their detailed chemical structure and particular function, if any. Primary attention is given to the contractile process which accompanies the crystal-liquid transition in axially oriented macromolecular systems. The theoretical nature of the process is discussed, and many experimental examples are given from the literature which demonstrate the expected behavior. Experimental attention is focused on the contraction of fibrous proteins, and the same underlying molecular mechanism is shown to be operative for a variety of different systems.     

Integral equation theories for predicting water structure around molecules

Water plays a crucial role in the structure and function of proteins and other biological macromolecules; thus, theories of aqueous solvation for these molecules are of great importance. However, water is a complex solvent whose properties are still not completely understood. Statistical mechanical integral equation theories predict the density distribution of water molecules around a solute so that all particles are fully represented and thus potentially both molecular and macroscopic properties are included. Here we discuss how several theoretical tools we have developed have been integrated into an integral equation theory designed for globular macromolecular solutes such as proteins. Our approach predicts the three-dimensional spatial and orientational distribution of water molecules around a solute. Beginning with a three-dimensional Ornstein-Zernike equation, a separation is made between a reference part dependent only on the spatial distribution of solvent and a perturbation part dependent also on the orientational distribution of solvent. The spatial part is treated at a molecular level by a modified hypernetted chain closure whereas the orientational part is treated as a Boltzmann prefactor using a quasi-continuum theory we developed for solvation of simple ions. A potential energy function for water molecules is also needed and the sticky dipole models of water, such as our recently developed soft-sticky dipole (SSD) model, are ideal for the proposed separation. Moreover, SSD water is as good as or better than three point models typically used for simulations of biological macromolecules in structural, dielectric and dynamics properties and yet is seven times faster in Monte Carlo and four times faster in molecular dynamics simulations. Since our integral equation theory accurately predicts results from Monte Carlo simulations for solvation of a variety of test cases from a single water or ion to ice-like clusters and ion pairs, the application of this theory to biological macromolecules is promising.     

Diffusion of the Reaction Boundary of Rapidly Interacting Macromolecules in Sedimentation Velocity

Sedimentation velocity analytical ultracentrifugation combines relatively high hydrodynamic resolution of macromolecular species with the ability to study macromolecular interactions, which has great potential for studying dynamically assembled multiprotein complexes. Complicated sedimentation boundary shapes appear in multicomponent mixtures when the timescale of the chemical reaction is short relative to the timescale of sedimentation. Although the Lamm partial differential equation rigorously predicts the evolution of concentration profiles for given reaction schemes and parameter sets, this approach is often not directly applicable to data analysis due to experimental and sample imperfections, and/or due to unknown reaction pathways. Recently, we have introduced the effective particle theory, which explains quantitatively and in a simple physical picture the sedimentation boundary patterns arising in the sedimentation of rapidly interacting systems. However, it does not address the diffusional spread of the reaction boundary from the cosedimentation of interacting macromolecules, which also has been of long-standing interest in the theory of sedimentation velocity analytical ultracentrifugation. Here, effective particle theory is exploited to approximate the concentration gradients during the sedimentation process, and to predict the overall, gradient-average diffusion coefficient of the reaction boundary. The analysis of the heterogeneity of the sedimentation and diffusion coefficients across the reaction boundary shows that both are relatively uniform. These results support the application of diffusion-deconvoluting sedimentation coefficient distributions c(s) to the analysis of rapidly interacting systems, and provide a framework for the quantitative interpretation of the diffusional broadening and the apparent molar mass values of the effective sedimenting particle in dynamically associating systems.     

Duration time of a one-dimensional random walk as a function of the energies of the intermediate states: application for dissociation and relaxation processes in DNA hybrids.

Kinetic parameters of macromolecular systems are important for their function in vitro and in vivo. These parameters describe how fast the system dissociates (the characteristic dissociation time), and how fast the system reaches equilibrium (characteristic relaxation time). For many macromolecular systems, the transitions within the systems are described as a random walk through a number of states with various free energies. The rate of transition between two given states within the system is characterized by the average time which passes between starting the movement from one state, and reaching the other state. This time is referred to as the mean first-passage time between two given states. The characteristic dissociation and relaxation times of the system depend on the first-passages times between the states within the system. Here, for a one-dimensional random walk we derived an equation, which connects the mean first-passage time between two states with the free energies of the states within the system. We also derived the general equation, which is not restricted to one-dimensional systems, connecting the relaxation time of the system with the first-passage times between states. The application of these equations to DNA branch migration, DNA structural transitions and other processes is discussed.     

Sedimentation-equilibrium studies on the heterogeneity of two β-lactamases

Solutions of crystalline beta-lactamase I and beta-lactamase II, prepared by Kuwabara (1970), were examined in the ultracentrifuge and their sedimentation coefficients, diffusion coefficients, molecular weights and heterogeneity determined. Each sample was shown to consist of a major component comprising at least 97% of the material and a minor component of much higher molecular weight. The molecular weights of the major components were 27800 for beta-lactamase I and 35600 for beta-lactamase II. Emphasis is placed on a straightforward practical way of analysing the sedimentation-equilibrium results on mixtures of two macromolecular components rather than on a strict theoretical solution. Appendices describe the theory of systems at both chemical and sedimentation equilibrium and the procedure for calculating the combined distribution of two components.     

Muscular contraction

A molecular theory of muscular contraction, based on the trigger action of the cross bridge between actin and myosin, is postulated. The formation of the cross bridge is followed by a transconformation in contractile protein producing work and liberating heat. The process possesses a mechanochemical character and utilizes the energy liberated by dephosphorylation of ATP. The equation of for tension dependence of muscle power is derived from the theory of reaction rates. The equation of is meaningful after elementary treatment; the physical meaning of the constants in these equations is explained. Quantitative analyses are corroborated by the experimental data.     

Multivariate analysis of simultaneously active motor units in human skeletal muscle

The joint activity of simultaneously active motor units was analyzed, using several methods including interunit interval and expectation density functions. The results show that there is no significant interaction between any motor units and, except for a slight coupling, the units fire independently of one another. The coupling is weak but pervasive and affects motor units overlapping and disjoint territories. Synchronous action potentions were recorded at sites whose distance is greater than the acknowledged diameter of motor unit territories. It is proposed that these expansive motor units and the viscoelastic properties of muscle are responsible for smooth contractions in human muscle.This work was supported in part by the Social Rehabilitation Service through the Krusen Research Center, Temple University, Philadelphia, Pennsylvania, while Dr. Shiavi was with the Biomedical Engineering and Science Program, Drexel University, Philadelphia, Pennsylvania, and the Krusen Research Center.     

肌球蛋白工作循环的一个新模型

分析总结关于分子马达肌球蛋白的最新研究结果,给出一个新的肌球蛋白工作循环的机械化学偶联模型.从新模型出发,用一组化学动力学方程描述肌肉中大量肌球蛋白的集体工作行为.利用动力学方程的非平衡定态解,并结合Pate和Cooke的实验结果得到了力作为变量的肌肉态方程.理论结果同热力学原理一致,与传统的肌肉收缩理论有一定区别.根据肌肉的特殊结构,对肌肉态方程做了进一步讨论.     

A theory of contraction and a mathematical model of striated muscle

A theory of contraction and an associated model of striated muscle are presented, based on the assumption that chemical energy is being converted into electrical energy which, in turn, is being converted into mechanical energy and heat.The model, set up for the frog sartorius muscle, is able to predict the “rowing” motion of the cross-bridges, the force-velocity relation, the tension-length curve, the isometric force, all energy rates (heat and work rates), the metabolic rates and all known features of the stretched, stimulated muscle (no ATP-splitting, stretching tension higher than isometric tension, etc.). It also offers an alternative explanation for Hill's thermoelastic effect. The significance of Hill's force-velocity equation in the context of this theory is also discussed in detail.     

The basic mechanism of ATP powered motor proteins

The ability of ATP powered motor proteins to convert chemical free energy into the mechanical work required to move intra-cellular organelles is discussed in terms of the molecular and dynamic fundamentals involved in producing such movements. This is carried out in detail for muscle contraction with the result that in order for a myosin head to act as a motor protein, it is necessary for it to be able to impose a unique series of impacts on an actin filament. It is further shown that these impacts can be generated when a single water molecule is transiently attached to the ADP formed during one step of an ATP cycle in the myosin head. This analysis leads to the conclusion that muscle must be a type of heat machine which has the capability of attaining mechanochemical efficiencies that approach 100%. An extension of ATP powered motor proteins in general is made with the finding that they must share the same motor mechanism of the transiently attached water molecule. A possible application of these considerations to the problem of the active transport of ions is also pointed out.     

Free energy transduction in a chemical motor model

Motor enzymes catalyse chemical reactions, like the hydrolysis of ATP, and in the process they also perform work. Recent studies indicate that motor enzymes perform work with specific biochemical steps in their catalysed reactions, challenging the classical view that work can only be performed within a biochemical state. To address these studies an alternative class of models, often referred to as chemical motor models, has emerged in which motors perform work with biochemical transitions. In this paper, I develop a novel, self-consistent framework for chemical motor models, which accommodates multiple pathways for free energy transfer, predicts rich behaviors from the simplest multi-motor systems, and provides important new insights into muscle and motor function.