Monte Carlo Simulation on Coordinated Movement of Kinesin and Dynein Motors

Kinesin and dynein are two important classes of molecular motors which are responsible for active organelle trafficking and cell division. They can work together to carry a cargo, moving along the microtubule in a coordinated way. We use Monte Carlo method to simulate the dynamics of this coordinated movement. Based on four essential assumptions, our simulations reproduce some features of the recent in vivo experiments. The fast moving speed of the cargo is simulated and the speed distribution is presented.     

On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability

In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.     

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity VN and effective diffusion coefficient DN of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient Deff of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient Deff from the moments of the particle's coordinate.     

A general two-cycle network model of molecular motors

Molecular motors are single macromolecules that generate forces at the piconewton range and nanometer scale. They convert chemical energy into mechanical work by moving along filamentous structures. In this paper, we study the velocity of two-head molecular motors in the framework of a mechanochemical network theory. The network model, a generalization of the recently work of Liepelt and Lipowsky [Steffen Liepelt, Reinhard Lipowsky, Kinesins network of chemomechanical motor cycles, Physical Review Letters 98 (25) (2007) 258102], is based on the discrete mechanochemical states of a molecular motor with multiple cycles. By generalizing the mathematical method developed by Fisher and Kolomeisky for a single cycle motor [Michael E. Fisher, Anatoly B. Kolomeisky, Simple mechanochemistry describes the dynamics of kinesin molecules, Proceedings of the National Academy of Sciences 98 (14) (2001) 7748-7753], we are able to obtain an explicit formula for the velocity of a molecular motor.     

Electrostatic theory of viral self-assembly

Viruses self-assemble from identical capsid proteins and their genome consisting, for example, of a long single stranded (ss) RNA. For a big class of T=3 viruses, capsid proteins have long positive N-terminal tails. We explore the role played by the Coulomb interaction between the brush of positive N-terminal tails rooted at the inner surface of the capsid and the negative ss RNA molecule. We show that viruses are most stable when the total contour length of ss RNA is close to the total length of the tails. For such a structure the absolute value of the total RNA charge is approximately twice as large as the charge of the capsid. This conclusion agrees with structural data.     

Global analysis of the immune response

The immune system may be seen as a complex system, characterized using tools developed in the study of such systems, for example, surface roughness and its associated Hurst exponent. We analyze densitometric (Panama blot) profiles of immune reactivity, to classify individuals into groups with similar roughness statistics. We focus on a population of individuals living in a region in which malaria endemic, as well as a control group from a disease-free region. Our analysis groups individuals according to the presence, or absence, of malaria symptoms and number of malaria manifestations. Applied to the Panama blot data, our method proves more effective at discriminating between groups than principal-components analysis or super-paramagnetic clustering. Our findings provide evidence that some phenomena observed in the immune system can be only understood from a global point of view. We observe similar tendencies between experimental immune profiles and those of artificial profiles, obtained from an immune network model. The statistical entropy of the experimental profiles is found to exhibit variations similar to those observed in the Hurst exponent.     

Elementary excitations of biomembranes: Differential geometry of undulations in elastic surfaces

Biomembrane undulations are elementary excitations in the elastic surfaces of cells and vesicles. As such they can provide surprising insights into the mechanical processes that shape and stabilize biomembranes. We explain how naturally these undulations can be described by classical differential geometry. In particular, we apply the analytical formalism of differential-geometric calculus to the surfaces generated by a cell membrane and underlying cytoskeleton. After a short derivation of the energy due to a membrane's elasticity, we show how undulations arise as elementary excitations originating from the second derivative of an energy functional. Furthermore, we expound the efficiency of classical differential-geometric formalism to understand the effect of differential operators that characterize processes involved in membrane physics. As an introduction to concepts the paper is self-contained and rarely exceeds calculus level.     

ncRNA-mediated bistability in the synthesis of hundreds of distinct mRNAs and proteins

The kinetics of gene expression can be bistable due to the feedback between the mRNA and protein formation. In eukaryotic cells, the interplay between mRNAs and proteins can be influenced by non-coding RNAs. Some of these RNAs, e.g., microRNAs, may target hundreds of distinct mRNAs. The model presented here shows how a non-coding RNA can be used as a mediator in order to involve numerous mRNAs and proteins into a bistable network.     

Rectification Efficiency of Two Harmonically Coupled Particles

Transportation properties of two harmonically coupled particles moving in a flashing or rocking ratchet potential are investigated in terms of Langevin simulation. The efficiency for rectification of non-equilibrium fluctuation is calculated by using a new definition. The results show that both the average current and efficiency of two coupled particles in the flashing ratchet are larger than that of a single particle and these quantities are non-monotonous functions of the potential remaining time.     

The dynamics of cargo driven by molecular motors in the context of asymmetric simple exclusion processes

We consider the dynamics of cargo driven by a collection of interacting molecular motors in the context of an asymmetric simple exclusion process (ASEP). The model is formulated to account for (i) excluded-volume interactions, (ii) the observed asymmetry of the stochastic movement of individual motors and (iii) interactions between motors and cargo. Items (i) and (ii) form the basis of ASEP models and have already been considered to study the behavior of motor density profile [A. Parmeggiani, T. Franosch, E. Frey, Phase Coexistence in driven one-dimensional transport, Phys. Rev. Lett. 90 (2003) 086601-1-086601-4]. Item (iii) is new. It is introduced here as an attempt to describe explicitly the dependence of cargo movement on the dynamics of motors in this context. The steady-state solutions of the model indicate that the system undergoes a phase transition of condensation type as the motor density varies. We study the consequences of this transition to the behavior of the average cargo velocity.     

Cooperativity of multiple kinesin-1 motors mechanically coupled through a shared load

Recent experiments using single-molecule techniques have characterized the mechanical properties of single kinesin molecules in vitro at a range of loads and ATP concentrations. These experiments have shown that kinesin moves processively along microtubules by alternately advancing each of its motor domains in a hand-over-hand fashion, using Brownian motion and the energy from ATP hydrolysis. We have extended the theoretical analysis of kinesin through a mechanistic model that is capable of describing transient and steady-state behavior. Transient dynamics are needed to describe the effect of external perturbations (e.g. interactions with other kinesin molecules). Quantitative metrics are tailored to characterize the synchronization of nonlinear, nonsmooth systems such as kinesin. These metrics are employed to analyze the simulation results and to quantify the effect of the cargo linker stiffness, the load, and the difference in intrinsic velocity on the synchronization of two coupled motor proteins. Herein, the mechanistic model and the new analysis techniques are demonstrated for the case of two coupled kinesin motors.     

Water in the Neck-Zipper Region of Kinesin

Neck linker （NL） is one of the most important mechanical elements of kinesin motors. The zipping up process of the neck-zipper （NZ） formed by NL and the related secondary structure elements is one of the major parts of kinesin＇s power stroke. All the weak interactions that are responsible for the formation of NZ are sensitive to or dependent on water. To investigate the role of water in the NZ region, a molecular dynamics （MD） model is set up with a crystal structure of kinesin 2KIN surrounded by a 10 A water layer, and minimization is performed to determine the positions of hydrogen atoms and other atoms. It is revealed that water molecules can assist the docking process of NL by forming hydrogen bonds at those positions where direct hydrogen bonding between the two sides of NZ is hindered and then acts as a constructive component of NZ at the docked state of NL. This result may improve the understanding of the mechanism for the docking of NL of kinesin wherein the function of water has not been comprehended sufficiently.     

Properties of Hydrated Alkali Metals Aimed at the Ion Channel Selectivity

The hydration structure properties of different alkali metal ions with eight water molecules and potassium ions with different numbers of water molecules are studied using the mixed density functional theory, B3LYP, with 6-3110 basis set. The hydration structures are obtained from structure optimization and the optimum numbers of water molecules in the innermost hydration shell for the alkali metal ions are found. Some useful information about the ion channel selectivity is presented.     

Optical tweezers for confocal microscopy

In confocal laser scanning microscopes (CLSMs), lasers can be used for image formation as well as tools for the manipulation of microscopic objects. In the latter case, in addition to the imaging lasers, the light of an extra laser has to be focused into the object plane of the CLSM, for example as optical tweezers. Imaging as well as trapping by optical tweezers can be done using the same objective lens. In this case, z-sectioning for 3D imaging shifts the optical tweezers with the focal plane of the objective along the optical axis, so that a trapped object remains positioned in the focal plane. Consequently, 3D imaging of trapped objects is impossible without further measures. We present an experimental set-up keeping the axial trapping position of the optical tweezers at its intended position whilst the focal plane can be axially shifted over a distance of about 15 μm. It is based on fast-moving correctional optics synchronized with the objective movement. First examples of application are the 3D imaging of chloroplasts of Elodea densa (Canadian waterweed) in a vigorous cytoplasmic streaming and the displacement of zymogen granules in pancreatic cancer cells (AR42 J). Received: 24 March 2000 / Revised version: 23 June 2000 / Published online: 11 October 2000     

Force generation by polymerizing microtubules

Polymerization ratchets formed by the assembly of actin filaments and microtubules are possibly the simplest realizations of biological thermal ratchets. A variety of experimental evidence exists that significant forces are generated by these processes, but quantitative studies lag far behind similar studies for molecular motors such as kinesin and myosin. Here we present a discussion of the theory of polymerization ratchets as well as experimental techniques used in our laboratory for the study of forces generated by single growing microtubules. Data obtained with these techniques provide us with valuable information that may eventually allow us to distinguish between different models for the growth of microtubules. Received: 15 January 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Vesicle self-reproduction: The involvement of membrane hydraulic and solute permeabilities

Conditions for self-reproduction are sought for a growing vesicle with its growth defined by an exponential increase of vesicle membrane area and by adequate flow of the solution across the membrane. In the first step of the presumed vesicle self-reproduction process, the initially spherical vesicle must double its volume in the doubling time of the membrane area and, through the appropriate shape transformations, attain the shape of two equal spheres connected by an infinitesimally thin neck. The second step involves separation of the two spheres and relies on conditions that cause the neck to be broken. In this paper we consider the first step of this self-reproduction process for a vesicle suspended in a solution whose solute can permeate the vesicle membrane. It is shown that vesicle self-reproduction occurs only for certain combinations of the values of membrane hydraulic and solute permeabilities and the external solute concentration, these quantities being related to the mechanical properties of the membrane and the membrane area doubling time. The analysis includes also the relaxation of a perturbed system towards stationary self-reproduction behavior and the case where the final shape consists of two connected spheres of different radii.     

Numerical Simulations of Calcium Ions Spiral Wave in Single Cardiac Myocyte

The calcium ions （Ca^2＋） spark is an elementary Ca^2＋ release event in cardiac myocytes. It is believed to buildup cell-wide Ca^2＋ signals, such as Ca^2＋ transient and Ca^2＋ wave, through a Ca^2＋-induced Ca^2＋ release （CICR） mechanism. Here the excitability of the Ca^2＋ wave in a single cardiac myoeyte is simulated by employing the fire-diffuse-fire model. By modulating the dynamic parameters of Ca^2＋ release and re-uptake channels, we find three Ca^2＋ signaling states in a single cardiac myoeyte： no wave, plane wave, and spiral wave. The period of a spiral wave is variable in the different regimes. This study indicates that the spiral wave or the excitability of the system can be controlled through micro-modulation in a living excitable medium.