Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model

Dynamic Monte Carlo simulation of a bead-spring model of flexible macromolecules threading through a very narrow pore in a very thin rigid membrane are presented, assuming at the cis side of the membrane a purely repulsive monomer-wall interaction, while the trans side is attractive. Two choices of monomer-wall attraction epsilon are considered, one choice is slightly below and the other slightly above the "mushroom to pancake" adsorption threshold epsilon(c) for an infinitely long chain. Studying chain lengths N=32, 64, 128, and 256 and varying the number of monomers N(trans) (time t=0) that have already passed the pore when the simulation started, over a wide range, we find for epsilonepsilon(c) a finite number N(trans)(t=0) suffices that the translocation probability is close to unity. In the case epsilonepsilon(c), we find that the translocation time scales as tau proportional, variant N(1.65+/-0.08). We suggest a tentative scaling explanation for this result. Also the distribution of translocation times is obtained and discussed.     

RATE OF INTRAMOLECULAR CONTACT FORMATION IN PROTEINS

In this paper, we estimate the rate of contact formation between two residues in the interior of the proteins using the Szabo, Schulten, and Schulten formula with the probability distribution P(r) based on 375 proteins from PDB (Protein Data Bank). The probability distribution for residue pair in proteins is different from the Gaussian distribution, especially for short distance between two residues in proteins. The rate of contact formation in the interior of protein is discussed as a function of distance n (=|j-i|) between two residues, and it decreases monotonically with n and follows the scaling relationship of k∞n-γwithγ= 1.43 for the contact radius a= 0.40 nm andγ= 1.05 for a = 0.50 nm. The diffusion coefficient for the relative diffusion of two residues in the interior of proteins is estimated as D = 6.4×10-6 cm2/s, which is close to the result that is found for monomer diffusion.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

The intrinsic stiffness of polyglutamine peptides

We have used the method of Trp/Cys contact quenching to measure the rate of contact formation in polyglutamine and find it to be a very stiff peptide. Separation of observed rates into reaction-limited and diffusion-limited rates show that the reaction-limited rates increase (rather than decrease) slightly with length between 4 and 16 amino acids. Using Szabo, Schulten, and Schulten theory, we have modeled the results with a wormlike chain with excluded volume and find the persistence length to be about 13.0 A, much longer than has been observed for other random peptides and unfolded proteins. The preferred extended conformation of polyglutamine could account for a propensity for expanded glutamine stretches to unfold the Huntington's protein and the high propensity to aggregate from a disordered monomer.     

Synthesis and characterization of aluminum- and gallium-bridged [1.1]chromarenophanes and [1.1]molybdarenophanes

The synthesis and structural characterization of the first [1.1]chromarenophanes and the first [1.1]molybdarenophanes are described. A salt-metathesis reaction of [2-(Me 2NCH 2)C 6H 4]AlCl 2 with freshly prepared [Cr(LiC 6H 5) 2].TMEDA (TMEDA = N, N, N', N'-tetramethylethylenediamine) resulted in the dialumina[1.1]chromarenophane [{2-(Me 2NCH 2)C 6H 4}Al(eta (6)-C 6H 5) 2Cr] 2 ( 2a). The poor solubility of 2a in organic solvents prompted us to synthesize the new intramolecularly coordinated aluminum- and gallium dichlorides [5- tBu-2-(Me 2NCH 2)C 6H 3]ECl 2 [E = Al ( 3a), Ga ( 3b)] in which the phenyl group was equipped with a tert-butyl group. Salt-metathesis reactions of 3a and 3b, respectively, with freshly prepared [M(LiC 6H 5) 2].TMEDA (M = Cr, Mo) resulted in four new [1.1]metallarenophanes of the general type [{5- tBu-2-(Me 2NCH 2)C 6H 3}E(eta (6)-C 6H 5) 2M] 2 [E = Al, M = Cr ( 4a); E = Ga, M = Cr ( 4b); E = Al, M = Mo ( 5a); E = Ga, M = Mo ( 5b)]. 2a, 4a, b, and 5a, b have been structurally characterized by single-crystal analysis [ 2a.1/2C 6H 12: C 48H 56Al 2Cr 2N 2, monoclinic, P2 1/ c, a = 9.9117(9) A, b = 19.9361(16) A, c = 10.638(2) A, alpha = 90 degrees , beta = 112.322(5) degrees , gamma = 90 degrees , Z = 2; 4a.2C 6H 6: C 62H 72Al 2Cr 2N 2, monoclinic, P2 1/ c, a = 10.9626(9) A, b = 19.3350(18) A, c = 12.4626(9) A, alpha = 90 degrees , beta = 100.756(5) degrees , gamma = 90 degrees , Z = 2; 4b.2C 6H 6: C 62H 72Cr 2Ga 2N 2, monoclinic, P2 1/ c, a = 10.8428(2) A, b = 19.4844(4) A, c = 12.4958(2) A, alpha = 90 degrees , beta = 100.6187 degrees , gamma = 90 degrees , Z = 2; 5a.2C 6H 6: C 62H 72Al 2Mo 2N 2, triclinic, P1, a = 10.4377(4) A, b = 11.6510(4) A, c = 11.6514(4) A, alpha = 73.545(3) degrees , beta = 89.318(2) degrees , gamma = 76.120(2) degrees , Z = 1; 5b.2C 6H 6: C 62H 72Ga 2Mo 2N 2, triclinic, P1, a = 10.3451(5) A, b = 11.6752(6) A, c = 11.6900(5) A, alpha = 73.917(3) degrees , beta = 89.550(3) degrees , gamma = 76.774(2) degrees , Z = 1]. All five [1.1]metallarenophanes 2a, 4a, b, and 5a, b crystallize as anti isomers with both Me 2N donor groups in exo positions ( C i point group symmetry). The new [1.1]metallarenophanes show NMR spectra that can be interpreted as being caused by time-averaged C 2 h symmetrical species, which is consistent with the findings of their molecular structures in the solid state. Variable-temperature (1)H NMR measurements for 4a, b and 5a, b (500 MHz; -90 to 90 degrees C) revealed only peak broadening in the lower temperature range of -70 to -90 degrees C. (1)H NMR saturation transfer difference experiments did not show an expected anti-to-anti isomerization, rendering the new [1.1]metallacyclophanes rigid on the NMR time scale. Electrochemical measurements were performed for 4a, b and 5a, b. However, reproducible cyclic voltammograms could only be obtained for the two gallium species 4b and 5b, revealing the expected weak communication between the two transition-metal atoms in both compounds (class II).     

Determination of ionic liquids solvent properties using an unusual probe: the electron donor-acceptor complex between 4,4'-bis(dimethylamino)-benzophenone and tetracyanoethene

Michler's ketone (MK) and tetracyanoethene (TCNE) may be used as a UV-vis probe to investigate the solvent properties of ionic liquids (ILs). In molecular solvents, MK and TCNE give an electron donor-acceptor (EDA) complex, a zwitterionic species or a radical ion pair, depending on the aprotic or protic nature of the solvent and on its ionizing power. In agreement with the behavior observed in aprotic solvents, only the EDA complex was detected in ILs bearing low donor anions (beta < 0.7). The formation constant determined in [bmim][Tf(2)N] (K(c) = 5.6 (0.5) M(-1)) is similar to that measured in 1,2-dichloroethane at 25 degrees C. The visible absorption maximum (nu(max,CTC)) of the EDA complex is quantitatively described by a multiple correlation using the Kamlet-Taft pi, beta, and alpha parameters of the solvents. The H-bond donating capacity of ILs is not sufficient to determine the transformation of the EDA complex into the zwitterionic species, but the Kamlet-Taft alpha parameter seems to affect the position of the absorption band. The high ionization power of ILs, moreover, favors the slow dissociation of the EDA complex into its corresponding radical ion pair; this behavior generally characterizes highly polar and highly ionizing protic solvents, such as TFE and HFI. Finally, since the formation of the EDA complex is strongly affected by the presence of impurities, traces of nucleophiles (chloride or amines) or water may be easily detected through the change of the solution color.     

Coherent Dynamic Structure Factor of a Polymer Chain Confined Into a Harmonic Radial Potential

The coherent dynamic structure factor of a single polymer chain is calculated based on the model of a Rouse polymer chain constrained (confined) by a harmonic radial potential and its behavior in different limiting cases is analyzed. The strength of confinement is characterized using an effective diameter of the harmonic radial potential as a model parameter. The method provides a reliable model to study the crossover between unconstrained (Rouse) and constrained dynamics.

     

Confinement and viscoelastic effects on chain closure dynamics

Chemical reactions inside cells are typically subject to the effects both of the cell's confining surfaces and of the viscoelastic behavior of its contents. In this paper, we show how the outcome of one particular reaction of relevance to cellular biochemistry--the diffusion-limited cyclization of long chain polymers--is influenced by such confinement and crowding effects. More specifically, starting from the Rouse model of polymer dynamics, and invoking the Wilemski-Fixman approximation, we determine the scaling relationship between the mean closure time t(c) of a flexible chain (no excluded volume or hydrodynamic interactions) and the length N of its contour under the following separate conditions: (a) confinement of the chain to a sphere of radius d and (b) modulation of its dynamics by colored Gaussian noise. Among other results, we find that in case (a) when d is much smaller than the size of the chain, t(c) ~ Nd(2), and that in case (b), t(c) ~ N(2/(2-2H)), H being a number between 1/2 and 1 that characterizes the decay of the noise correlations. H is not known a priori, but values of about 0.7 have been used in the successful characterization of protein conformational dynamics. At this value of H (selected for purposes of illustration), t(c) ~ N(3.4), the high scaling exponent reflecting the slow relaxation of the chain in a viscoelastic medium.     

Chromatographie von Carbamat- und Phenylharnstoff-Pesticiden auf Dünnschichten von basischem Zinkcarbonat

Thin layers of basic zinc carbonate can be used with good results for separation and multiple identification of carbamate and phenylurea pesticides. Five important substances could be separated by one-dimension TLC. The best results were obtained by the following developing solvents: a) benzene, b) a mixture of benzene/petroleum ether/chloroform (6∶1∶1). The substances are either recognisable in short-wave UV-light, when a fluorescence indicator (F 254 nm) is added, or in day-light, after spraying a solution of 0.1 N AgNO₃ in 3 N HNO₃, followed by an UV-exposure for about 4 min.     

EFFECTS OF SECONDARY STRUCTURE ON ELASTIC BEHAVIOR OF PROTEIN-LIKE CHAINS

The elastic behavior of protein-like chains was investigated by using the Pruned-Enriched-Rosenbluth Method (PERM).Three typical protein-like chains such as all-α,all-β,and α+β(α/β) proteins were studied in our modified orientation dependent monomer-monomer interaction (ODI) model.We calculated the ratio of /N and shape factor <δ*> of protein-like chains in the process of elongation.In the meantime,we discussed the average energy per bond ＜U＞/N,average contact energy per bond ＜U＞c/N,average helical energy per bond ＜U＞h/N and average sheet energy per bond ＜U＞b/N.Three maps of contact formation,α-helix formation,β-sheet formation were depicted.All the results educe a view that the helix structure is the most stable structure,while the other two structures are easy to be destroyed.Besides,the average Helmholtz free energy per bond ＜A＞/Nis was presented.The force f obtained from the free energy was also discussed.It was shown that the chain extended itself spontaneously first.The force was studied in the process of elongation.Lastly,the energy contribution to elastic force fu was calculated too.It was noted that fu for all-β chains increased first,and then decreased with x0 increasing.     

Fluorescence properties of (R)- and (S)-[1,1′-binaphthalene]-2,2′-diols solutions and their complexes with cyclodextrins in aqueous medium

Steady-state and time-resolved fluorescence techniques were used to study (R)- and (S)-[1,1′-binaphthalene]-2,2′-diol (1,1′-binaphthol or BINOL) dilute solutions of different polarity solvents, as well as their inclusion complexes with α- and βcyclodextrins (CDs) in water. BINOLs in dilute water solutions exhibited a surprisingly high fluorescence anisotropy that was explained as being due to the formation of fairly large order π–π stacking aggregates in aqueous polar media. Stoichiometries, formation constants and the changes of enthalpy and entropy upon inclusion were also obtained by measuring the variation of the fluorescence intensity with [CD] and temperature. Results agree with the formation of 1:1 stoichiometry complexes, but the association constants are rather low and very similar for both enantiomers. Molecular mechanic calculations in the presence of water were employed to study the formation of BINOL complexes with both α- and βCDs. For the most stable structures of any of the complexes only a small portion of the guests, in agreement with thermodynamics parameters and quenching experiments, penetrates inside the CD cavities. Driving forces for 1:1 inclusion processes may be dominated by non-bonded van der Waals host:guest interactions. The low guest:host binding constants and poor enantioselectivity of α- and βCDs for BINOLS may be a consequence of the BINOL aggregation in water.     

Factors Affecting Polymer Translocation Through a Nanopore in a Membrane

The variation of the translocation time with respect to the solvent quality was also studied. It showed that there is a transition, as the solvent quality improves from \poor to \good: when ABc, τ increases with increasing AB. When the chain length was changed, it was found that when the absorbed energy u0 was greater than uc, τ was proportional to N1:602; for u0相似文献   

A Monte Carlo algorithm to study polymer translocation through nanopores. II. Scaling laws

In the first paper of this series, we developed a new one-dimensional Monte Carlo approach for the study of flexible chains that are translocating through a small channel. We also presented a numerical scheme that can be used to obtain exact values for both the escape times and the escape probabilities given an initial pore-polymer configuration. We now present and discuss the fundamental scaling behaviors predicted by this Monte Carlo method. Our most important result is the fact that, in the presence of an external bias E, we observe a change in the scaling law for the translocation time tau as function of the polymer length N: In the general expression tau approximately N(beta)E, the exponent changes from beta=1 for moderately long chains to beta=1+nu or beta=2nu for very large values of N (for Rouse and Zimm dynamics, respectively). We also observe an increase in the effective diffusion coefficient due to the presence of entropic pulling on unbiased polymer chains.     

Solvent-dependent coordination polymers: cobalt complexes of 3,5-dinitrobenzoic acid and 3,5-dinitro-4-methylbenzoic acid with 4,4'-bipyrdine

The synthesis, structure elucidation, and analysis of the self-assembly of Co(II) complexes of 3,5-dinitrobenzoic acid and 3,5-dinitro-4-methylbenzoic acid with 4,4'-bipyridine have been reported. Formation of the complexes and the self-assembly in the three-dimensional structures have been found to be dependent on the solvents (such as acetone, dimethly sulfoxide, etc.) employed for the synthesis of the aggregates. 3,5-Dinitrobenzoic acid forms two coordination polymers, 1a and 1b, from methanol and a mixture of methanol and acetone solvents, respectively, with entirely different recognition patterns. Similarly, 3,5-dinitro-4-methylbenzoic acid also forms two coordination complexes, 2a and 2b, incorporating the solvent of the reaction medium into the crystal lattice. Complex 2a forms a solvated channel structure, whereas 2b gives a bilayered structure, with the layers being separated by solvent of crystallization (dimethyl sulfoxide) molecules. All the complexes have been characterized by single-crystal X-ray diffraction studies. Complexes 1b, 2a, and 2b crystallize in a monoclinic lattice, but 1a adopts a tetragonal lattice. The unit cell dimensions are, for 1a, a = 8.095(1) A, b = 8.095(1) A, c = 46.283 (6) A, alpha = 90 degrees, beta = 90 degrees, and gamma = 90 degrees (space group P4(3)2(1)2, Z = 4), for 1b, a = 22.774(2) A, b = 11.375 (1) A, c = 22.533(2) A, alpha = 90 degrees, beta = 104.15(1) degrees, and gamma = 90 degrees (space group P2(1)/c, Z = 4), for 2a, a = 17.657(6) A, b = 18.709(4) A, c = 21.044(6) A, alpha = 90 degrees, beta = 108.68(3) degrees, and gamma = 90 degrees (space group, C2/c, Z = 8), and, for 2b, a = 11.025(5) A, b = 15.139(4) A, c = 11.443(4) A, alpha = 90 degrees, beta = 97.48(3) degrees, and gamma = 90 degrees (space group P2/n, Z = 2). In all the complexes 1a, 1b, 2a, and 2b, the basic interaction between Co(II) and 4,4'-bipyridine remains the same with the formation of linear Co-N dative bonds, but the carboxylates display various modes of interaction with Co(II). The average Co-N and Co-O distances are 2.161 and 2.108 A, respectively.     

Kinetics of interior loop formation in semiflexible chains

Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using a mean field approach. Using the potential of mean force derived from the distance distribution function we present a simple expression for the kinetics of interior looping by adopting Kramers theory. For the parameters, that are appropriate for DNA, the theoretical predictions in comparison with the case are in excellent agreement with explicit Brownian dynamics simulations of wormlike chain (WLC) model. The interior looping times (tauIC) can be greatly altered in the cases when the stiffness of the loop differs from that of the dangling ends. If the dangling end is stiffer than the loop then tauIC increases for the case of the WLC with uniform persistence length. In contrast, attachment of flexible dangling ends enhances rate of interior loop formation. The theory also shows that if the monomers are charged and interact via screened Coulomb potential then both the cyclization (tauc) and interior looping (tauIC) times greatly increase at low ionic concentration. Because both tauc and tauIC are determined essentially by the effective persistence length [lp(R)] we computed lp(R) by varying the range of the repulsive interaction between the monomers. For short range interactions lp(R) nearly coincides with the bare persistence length which is determined largely by the backbone chain connectivity. This finding rationalizes the efficacy of describing a number of experimental observations (response of biopolymers to force and cyclization kinetics) in biomolecules using WLC model with an effective persistence length.     

Sulfonated Pyrene as a Photoregulator for Single-Stranded DNA Looping

Controlling the conformation and function of biomolecules through photoregulators holds great promise as a spatiotemporally controllable tool for disease control. In addition, introducing photoregulators into biomolecules has also found applications in constructing smart nanomaterials. In spite of the astonishing advances that have been made in the past few years, realizing highly controllable and efficient regulation over the conformation and function of biomolecules under physiological conditions is still challenging. Herein, sulfonated pyrene SPy was synthesized and used as a photoregulator to control the looping of single-stranded DNAs (ssDNAs) in aqueous solution. Due to its water solubility, SPy merits use in the study of biomolecules in aqueous solution. The looping of the doubly SPy -modified ssDNAs is stimulated by irradiation and regulated by SPy . Photoionization generates the radical cation of SPy ( SPy ^.+). The association of SPy ^{. +} with its neutral counterpart, SPy , gives rise to the dimer radical cation of SPy ( SPy₂ ^{. +} ). During the association process, the stabilization energy released to form SPy₂ ^{. +} provides a driving force for the looping of ssDNAs. Conversely, the formed loop conformations were trapped by the formation of SPy₂ ^{. +} , and this allowed the looping dynamics to be investigated. The results reported herein suggest potential of SPy as a photoregulator for controlling the conformation and function of biomolecules under physiological conditions.     

Molecular and crystal structure of 1-amino-3,5-diphenyl-2,4,4,6,6-Pentacyano-cyclohex-1-ene and 1-amino-3,5-diphenyl-2,4,4,6-tetracyanocyclohex-1-ene

Molecular and crystal structures of 1-amino-3,5-diphenyl-2,4,4,6,6-pentacyano-cyclohex-1-ene (I) and 1-amino-3,5-diphenyl-2,4,4,6-tetracyanocyclohex-1-ene (II) are studied to examine intermolecular interactions. Crystal data for (I): space group P2₁, a=11.172(3), b=6.561(2), c=16.390(4) Å, β=100.25(2)⁰, V=1182.1 ų, Z=2, R=0.046; for (II): space group P1, a=10.756(3), b=10.890(3), c=12.999(3) Å, α=62.20(2), β=70.73(2), γ=65.42(2)⁰, V=1207.2 ų, Z=2, R=0.074. Intermolecular bonds via the aminonitrile fragment in (I) lead to formation of chains along they axis: N1…N6′ (1?x, ?1/2+y, 1?z) of 3.465(8) Å, N6…N1″ (1?x, 1/2+y, 1?z), and the contact with the solvent (acetone) O1…N1 of 2.984(7) Å. In compound (II), the intermolecular contacts N1…N5′ (?x+1, ?y, ?z+1) of 3.064(7) Å link the molecules into dimeric associates.     

Is hairpin formation in single-stranded polynucleotide diffusion-controlled?

An intriguing puzzle in biopolymer science is the observation that single-stranded DNA and RNA oligomers form hairpin structures on time scales of tens of microseconds, considerably slower than the estimated time for loop formation for a semiflexible polymer of similar length. To address the origin of the slow kinetics and to determine whether hairpin dynamics are diffusion-controlled, the effect of solvent viscosity (eta) on hairpin kinetics was investigated using laser temperature-jump techniques. The viscosity was varied by addition of glycerol, which significantly destabilizes hairpins. A previous study on the viscosity dependence of hairpin dynamics, in which all the changes in the measured rates were attributed to a change in solvent viscosity, reported an apparent scaling of relaxation times (tau(r)) on eta as tau(r) approximately eta(0.8). In this study, we demonstrate that if the effect of viscosity on the measured rates is not deconvoluted from the inevitable effect of change in stability, then separation of tau(r) into opening (tau(o)) and closing (tau(c)) times yields erroneous behavior, with different values (and opposite signs) of the apparent scaling exponents, tau(o) approximately eta(-0.4) and tau(c) approximately eta(1.5). Under isostability conditions, obtained by varying the temperature to compensate for the destabilizing effect of glycerol, both tau(o) and tau(c) scale as approximately eta(1.1+/-0.1). Thus, hairpin dynamics are strongly coupled to solvent viscosity, indicating that diffusion of the polynucleotide chain through the solvent is involved in the rate-determining step.