Mean first-passage time calculations: comparison of the deterministic Hill’s algorithm with Monte Carlo simulations

Accurate determination of mean first-passage times (MFPTs) between any two states of a complex network still attracts considerable attention. Appropriate methods should take into account the discrepancy in MFPTs when a random walker moves first from a source to a target and then in the opposite direction. In addition, it is desirable to allow fast evaluation of mean first-passage times when transition probabilities are allowed to vary over time. For our calculations we make use of Hill’s algorithm, which enables the exact calculation of MFPTs. As we show in this work, when given a fixed distance to travel, the calculation of a particular MFPT depends on the choice of source and target points and their relative position on a lattice. We also demonstrate, when the network contains a relatively low number of cycles, that this deterministic technique provides exact results much faster in comparison to the more standard, but computationally demanding, stochastic Monte Carlo simulation method, where only approximate results can be obtained that are highly dependent on the number of walkers. Therefore, our specific implementation of Hill’s algorithm should facilitate efficient and accurate computation of MFPTs on a variety of network topologies of practical interest to the broad scientific community

Surface conductance in seamless microtubules

The cyto-architecture of eukaryotic cells contains self-assembled long cylinder-like structures called microtubules (MTs) which play an important role in a number of cellular activities such as cell division, motility, information processing and intracellular transport. In this paper we present a theoretical analysis of the surface conductance of a single seamless MT by representing each tubulin dimer as a resistor. Periodic boundary conditions were utilised both lengthwise (so the MT is pictured as a very large toroidal structure) and around its circumference. Firstly we have investigated the conductance matrix and found the eigenvalues and eigenvectors exactly. Then Wu's formula has been used to calculate the conductance in terms of them numerically. To check our results we have performed a series of computer simulations of random walks on the lattice of monomers utilising the widely known relationship between such a stochastic process and the theory of electrical networks. We obtain very good agreement between the two approaches. (c) 2008 Elsevier B.V. All rights reserved

Torsional elastic deformations of microtubules within continuous sheet model

This paper develops a rigorous analysis of the microtubule elastic deformations in terms of the torsional degrees of freedom using the helix-based cylindrical structure of this biopolymer. Methods of differential geometry and the theory of elasticity are employed in our analysis. We find equilibrium conditions and constitutive equations in the linear regime. We estimate the value of torsional rigidity for microtubules based on their structure and some experimentally known elastic properties. The paper concludes with the derivation of a bulk modulus formula for a microtubule in solution. Both the entropy change and the fluctuation of the twist angle are obtained

Excitation energy transfer and charge separation are affected in Arabidopsis thaliana mutants lacking light-harvesting chlorophyll a/b binding protein Lhcb3

The composition of LHCII trimers as well as excitation energy transfer and charge separation in grana cores of Arabidopsis thaliana mutant lacking chlorophyll a/b binding protein Lhcb3 have been investigated and compared to those in wild-type plants. In grana cores of lhcb3 plants we observed increased amounts of Lhcb1 and Lhcb2 apoproteins per PSII core. The additional copies of Lhcb1 and Lhcb2 are expected to substitute for Lhcb3 in LHCII trimers M as well as in the LHCII "extra" pool, which was found to be modestly enlarged as a result of the absence of Lhcb3. Time-resolved fluorescence measurements reveal a deceleration of the fast phase of excitation dynamics in grana cores of the mutant by ∼ 15 ps, whereas the average fluorescence lifetime is not significantly altered. Monte Carlo modeling predicts a slowing down of the mean hopping time and an increased stabilization of the primary charge separation in the mutant. Thus our data imply that absence of apoprotein Lhcb3 results in detectable differences in excitation energy transfer and charge separation

Chitosan–Collagen Coated Magnetic Nanoparticles for Lipase Immobilization—New Type of “Enzyme Friendly” Polymer Shell Crosslinking with Squaric Acid

This article presents a novel route for crosslinking a polysaccharide and polysaccharide/protein shell coated on magnetic nanoparticles (MNPs) surface via condensation reaction with squaric acid (SqA). The syntheses of four new types of collagen-, chitosan-, and chitosan–collagen coated magnetic nanoparticles as supports for enzyme immobilization have been done. Structure and morphology of prepared new materials were characterized by attenuated total reflectance Fourier-transform infrared (ATR-FTIR), XRD, and TEM analysis. Next, the immobilization of lipase from Candida rugosa was performed on the nanoparticles surface via N-(3-dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride (EDC)/N-hydroxy-succinimide (NHS) mechanism. The best results of lipase activity recovery and specific activities were observed for nanoparticles with polymer shell crosslinked via a novel procedure with squaric acid. The specific activity for lipase immobilized on materials crosslinked with SqA (52 U/mg lipase) was about 2-fold higher than for enzyme immobilized on MNPs with glutaraldehyde addition (26 U/mg lipase). Moreover, a little hyperactivation of lipase immobilized on nanoparticles with SqA was observed (104% and 112%)

Monte Carlo simulations of excitation and electron transfer in grana membranes

AbstractTime-resolved fluorescence measurements on grana membranes with instrumental response function of 3ps reveal faster excitation dynamics (120ps) than those reported previously. A possible reason for the faster decay may be a relatively low amount of “extra” LHCII trimers per reaction center of Photosystem II. Monte Carlo modeling of excitation dynamics in C2S2M2 form of PSII–LHCII supercomplexes has been performed using a coarse grained model of this complex, constituting a large majority of proteins in grana membranes. The main factor responsible for the fast fluorescence decay reported in this work was the deep trap constituted by the primary charge separated state in the reaction center (950–1090cm−1). This value is critical for a good fit, whereas typical hopping times between antenna polypeptides (from ~4.5 to ~10.5ps) and reversible primary charge separation times (from ~4 to ~1.5ps, respectively) are less critical. Consequently, respective mean migration times of excitation from anywhere in the PSII–LHCII supercomplexes to reaction center range from ~30 to ~80ps. Thus 1/4–2/3 of the ~120-ps average excitation lifetime is necessary for the diffusion of excitation to reaction center, whereas the remaining time is due to the bottle-neck effect of the trap. Removal of 27% of the Lhcb6 apoprotein pool by mutagenesis of DEG5 gene caused the acceleration of the excitation decay from ~120 to ~100ps. This effect may be due to the detachment of LHCII-M trimers from PSII–LHCII supercomplexes, accompanied by deepening of the reaction center trap