Dynamics of driven translocation of semiflexible polymers.

We study translocation of semiflexible polymers driven by force f_{d} inside a nanometer-scale pore using our three-dimensional Langevin dynamics model. We show that the translocation time τ increases with increasing bending rigidity κ. Similarly, the exponent ß for the scaling of τ with polymer length N,τ∼N^{ß}, increases with increasing κ as well as with increasing f_{d}. By comparing waiting times between semiflexible and fully flexible polymers we show that for realistic f_{d} translocation dynamics is to a large extent, but not completely, determined by the polymer's elastic length measured in number of Kuhn segments N_{Kuhn}. Unlike in driven translocation of flexible polymers, friction related to the polymer segment on the trans side has a considerable effect on the resulting dynamics. This friction is intermittently reduced by buckling of the polymer segment in the vicinity of the pore opening on the trans side. We show that in the experimentally relevant regime where viscosity is higher than in computer simulation models, the probability for this buckling increases with increasing f_{d}, giving rise to a larger contribution to the trans side friction at small f_{d}. Similarly to flexible polymers, we find significant center-of-mass diffusion of the cis side polymer segment which speeds up translocation. This effect is larger for smaller f_{d}. However, this speedup is smaller than the slowing down due to the trans side friction. At large enough N_{Kuhn}, the roles can be seen to be reversed, and the dynamics of flexible polymers can be reached. However, for example, polymers used in translocation experiments of DNA are elastically so short that the finite-length dynamics outlined here applies.

Uniform description of polymer ejection dynamics from capsid with and without hydrodynamics.

We use stochastic rotation dynamics (SRD) to examine the dynamics of the ejection of an initially strongly confined flexible polymer from a spherical capsid with and without hydrodynamics. The results obtained using stochastic rotation dynamics (SRD) are compared to similar Langevin simulations. Inclusion of hydrodynamic modes speeds up the ejection but also allows the part of the polymer outside the capsid to expand closer to equilibrium. This shows as higher values of radius of gyration when hydrodynamics are enabled. By examining the waiting times of individual polymer beads, we find that the waiting time t_{w} grows with the number of ejected monomers s as a sum of two exponents. When ≈63% of the polymer has ejected, the ejection enters the regime of slower dynamics. The functional form of t_{w} versus s is universal for all ejection processes starting from the same initial monomer densities. Inclusion of hydrodynamics only reduces its magnitude. Consequently, we define a universal scaling function h such that the cumulative waiting time t=N_{0}h(s/N_{0}) for large N_{0}. Our unprecedentedly precise measurements of force indicate that this form for t_{w}(s) originates from the corresponding force toward the pore decreasing superexponentially at the end of the ejection. Our measured t_{w}(s) explains the apparent superlinear scaling of the ejection time with the polymer length for short polymers. However, for asymptotically long polymers, t_{w}(s) predicts linear scaling.

Quantification of tension to explain bias dependence of driven polymer translocation dynamics.

Motivated by identifying the origin of the bias dependence of tension propagation, we investigate methods for measuring tension propagation quantitatively in computer simulations of driven polymer translocation. Here, the motion of flexible polymer chains through a narrow pore is simulated using Langevin dynamics. We measure tension forces, bead velocities, bead distances, and bond angles along the polymer at all stages of translocation with unprecedented precision. Measurements are done at a standard temperature used in simulations and at zero temperature to pin down the effect of fluctuations. The measured quantities were found to give qualitatively similar characteristics, but the bias dependence could be determined only using tension force. We find that in the scaling relation τ∼N^{ß}f_{d}^{α} for translocation time τ, the polymer length N, and the bias force f_{d}, the increase of the exponent ß with bias is caused by center-of-mass diffusion of the polymer toward the pore on the cis side. We find that this diffusion also causes the exponent α to deviate from the ideal value -1. The bias dependence of ß was found to result from combination of diffusion and pore friction and so be relevant for polymers that are too short to be considered asymptotically long. The effect is relevant in experiments all of which are made using polymers whose lengths are far below the asymptotic limit. Thereby, our results also corroborate the theoretical prediction by Sakaue's theory [Polymers 8, 424 (2016)2073-436010.3390/polym8120424] that there should not be bias dependence of ß for asymptotically long polymers. By excluding fluctuations we also show that monomer crowding at the pore exit cannot have a measurable effect on translocation dynamics under realistic conditions.

Rigidity-induced scale invariance in polymer ejection from capsid.

While the dynamics of a fully flexible polymer ejecting a capsid through a nanopore has been extensively studied, the ejection dynamics of semiflexible polymers has not been properly characterized. Here we report results from simulations of ejection dynamics of semiflexible polymers ejecting from spherical capsids. Ejections start from strongly confined polymer conformations of constant initial monomer density. We find that, unlike for fully flexible polymers, for semiflexible polymers the force measured at the pore does not show a direct relation to the instantaneous ejection velocity. The cumulative waiting time t(s), that is, the time at which a monomer s exits the capsid the last time, shows a clear change when increasing the polymer rigidity κ. The major part of an ejecting polymer is driven out of the capsid by internal pressure. At the final stage the polymer escapes the capsid by diffusion. For the driven part there is a crossover from essentially exponential growth of t with s of the fully flexible polymers to a scale-invariant form. In addition, a clear dependence of t on polymer length N_{0} was found. These findings combined give the dependence t(s)∝N_{0}^{0.55}s^{1.33} for the strongly rigid polymers. This crossover in dynamics where κ acts as a control parameter is reminiscent of a phase transition. This analogy is further enhanced by our finding a perfect data collapse of t for polymers of different N_{0} and any constant κ.

Chaperone-assisted translocation of flexible polymers in three dimensions.

Polymer translocation through a nanometer-scale pore assisted by chaperones binding to the polymer is a process encountered in vivo for proteins. Studying the relevant models by computer simulations is computationally demanding. Accordingly, previous studies are either for stiff polymers in three dimensions or flexible polymers in two dimensions. Here, we study chaperone-assisted translocation of flexible polymers in three dimensions using Langevin dynamics. We show that differences in binding mechanisms, more specifically, whether a chaperone can bind to a single site or multiple sites on the polymer, lead to substantial differences in translocation dynamics in three dimensions. We show that the single-binding mode leads to dynamics that is very much like that in the constant-force driven translocation and accordingly mainly determined by tension propagation on the cis side. We obtain ß≈1.26 for the exponent for the scaling of the translocation time with polymer length. This fairly low value can be explained by the additional friction due to binding particles. The multiple-site binding leads to translocation the dynamics of which is mainly determined by the trans side. For this process we obtain ß≈1.36. This value can be explained by our derivation of ß=4/3 for constant-bias translocation, where translocated polymer segments form a globule on the trans side. Our results pave the way for understanding and utilizing chaperone-assisted translocation where variations in microscopic details lead to rich variations in the emerging dynamics.

Criteria for minimal model of driven polymer translocation.

While the characteristics of the driven translocation for asymptotically long polymers are well understood, this is not the case for finite-sized polymers, which are relevant for real-world experiments and simulation studies. Most notably, the behavior of the exponent α, which describes the scaling of the translocation time with polymer length, when the driving force fp in the pore is changed, is under debate. By Langevin dynamics simulations of regular and modified translocation models using the freely jointed-chain polymer model we find that a previously reported incomplete model, where the trans side and fluctuations were excluded, gives rise to characteristics that are in stark contradiction with those of the complete model, for which α increases with fp. Our results suggest that contribution due to fluctuations is important. We construct a minimal model where dynamics is completely excluded to show that close alignment with a full translocation model can be achieved. Our findings set very stringent requirements for a minimal model that is supposed to describe the driven polymer translocation correctly.

Dynamics of polymer ejection from capsid.

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the ejection times scale with polymer length, τ ∼ N(α). We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) ρ inside the capsid. For very low densities ρ ≤ 0.002 the polymer is only weakly confined by the capsid, and we measure α = 1.33, which is close to α=1.4 obtained for polymer translocation. At intermediate densities the scaling exponents α = 1.25 and 1.21 for ρ = 0.01 and 0.02, respectively. These scalings are in accord with a crude derivation for the lower limit α = 1.2. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, ρ ⪆ 0.25. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.

Culture model of human corneal epithelium for prediction of ocular drug absorption.

PURPOSE: The main purpose of this study was to develop a cell culture model of immortalized epithelium from the human cornea for drug permeability testing. METHODS: Immortalized human corneal epithelial (HCE) cells were grown on filters, with various filter materials and coating procedures. In the optimal case, HCE cells were grown on polyester filters coated with rat tail collagen gel containing fibroblast cells. Transepithelial electrical resistance (TER) was measured during the growth of the cells to evaluate the epithelial differentiation and tightness of the epithelial cell layers. Transmission electron microscopy (TEM) was used to show the formation of tight junctions, desmosomes, and microvilli. Cellular morphology was characterized by light microscopy. Permeabilities of (3)H-mannitol and 6-carboxyfluorescein were determined, to evaluate the intercellular spaces of the epithelium. Rhodamine B was used as a lipophilic marker of transcellular permeability. Permeabilities of the excised rabbit corneas were determined in side-by-side diffusion chambers. RESULTS: The TER values of the corneal epithelial cultures were 200 to 800 Omega x cm(2), depending on the culture conditions. In optimal conditions, cultured corneal epithelium consisted of five to eight cell layers, TER was at least 400 Omega x cm(2), and the most apical cells were flat, with tight junctions, microvilli, and desmosomes. The permeability coefficients (P(cell), 10(-6) cm/sec) for (3)H-mannitol, 6-carboxyfluorescein, and rhodamine B were 1.42 +/- 0.36, 0.77 +/- 0.40, and 16.3 +/- 4.0, respectively. Corresponding values (at 10(-6) cm/sec) for the isolated rabbit corneas were 0.38 +/- 0.16, 0.46 +/- 0.27, and 18.1 +/- 4.0, respectively. CONCLUSIONS: The TER, morphology, and permeability of the cultured corneal epithelial cells resemble those of the intact cornea. This cell culture model may be useful in evaluation of corneal drug permeation and its mechanisms.

Different effects of pH on the permeation of pilocarpine and pilocarpine prodrugs across the isolated rabbit cornea.

Ocular absorption of pilocarpine and many other ophthalmic drugs can be improved by prodrug derivatization. For stability and solubility reasons basic prodrugs must be formulated at acidic pH, which may affect the corneal drug permeability. We studied the effects of pH on in vitro permeation of pilocarpine, pilocarpic acid benzyl diester prodrugs [O-propionyl (I) and O-valeryl (II)] and O,O'-(1, 4-xylylene) bispilocarpic acid diester prodrugs [O,O'-diacetyl (III), O,O'-dipropionyl (IV) and O,O'-divaleryl (V)] through albino rabbit cornea. Reversed-phase high-performance liquid chromatography was used to assay pilocarpine and its prodrugs. The permeability coefficient for pilocarpine decreased more than three times, from 2. 8x10-6 cm/s to 0.9x10-6 cm/s, when the pH was decreased from 7.65 to 5.5. At pH 7.65 permeability of pilocarpine improved several fold with delivery as prodrugs. Acidic pH (5.5, 6.0) affected to a different extent the corneal permeability of pilocarpine given as prodrugs. Consequently, the rank order of the corneal permeabilities among the compounds was different at various pH values. The effect of pH was greatest (an order of magnitude) for prodrugs with intermediate lipophilicity (I, III, IV), while pH had only minor or no effect on permeability of the most lipophilic prodrugs (II, V). In conclusion, the effect of pH on pilocarpine delivery as prodrug is dependent on prodrug structure and the advantage gained with prodrugs relative to pilocarpine is dependent on formulation pH.

Comparison of enzymatic hydrolysis of pilocarpine prodrugs in human plasma, rabbit cornea, and butyrylcholinesterase solutions.

Various bispilocarpic acid diesters (double prodrugs of pilocarpine) were synthesized, and their in vitro esterase catalyzed hydrolysis was evaluated in diluted human plasma, rabbit cornea homogenate, and specific butyrylcholinesterase solution. The structural changes greatly affected the rate of enzymatic hydrolysis of the prodrugs. Bispilocarpic acid with 2 cyclopropane substituents was the most stable derivative, whereas bispilocarpic acid with 2 cyclobutane substituents was the most labile derivative. The charged bispilocarpic acid diester hydrolyzed more slowly than the unchanged form. Comparison of the results obtained from different plasma and cornea homogenate batches is difficult because of the variety of the enzyme systems involved. This variety also makes comparing the results between different laboratories difficult.

Ocular absorption and irritation of pilocarpine prodrug is modified with buffer, polymer, and cyclodextrin in the eyedrop.

The influence of buffer, viscosity and cyclodextrin on the ocular absorption and irritation of a pilocarpine prodrug, O,O'-dipropionyl-(1,4-xylylene) bispilocarpic acid diester, was studied in albino rabbits. The prodrug solutions, equivalent to 0.5% pilocarpine, were prepared in 0, 10, 20, 50, or 75 mM citrate buffer at pH 5.0. Viscosity of the solutions (20, 50 or 115 cP) was modified with hydroxypropyl methylcellulose. 2-hydroxypropyl-beta-cyclodextrin (HPCD) was included at concentrations 5, 10 and 15% (w/v). The formulations were compared to a commercial pilocarpine eyedrop (1.7%). Ocular irritation was graded in a double-masked experiment and miosis was used as a bioassay for pilocarpine delivery to the iris. The prodrug showed decreased peak and prolonged duration of miosis compared to pilocarpine, but it caused ocular irritation. Increasing buffer strength decreased and elevated viscosity intensified the miotic response and irritation by the pilocarpine prodrug. HPCD decreased both the ocular delivery of pilocarpine and the irritation by the prodrug, but the net effect was positive. Thus, administering 1.0% of pilocarpine as a prodrug with 15% (w/v) HPCD, the irritation was at the same level with the commercial pilocarpine eyedrop, but the ocular delivery was substantially improved. In conclusion, the ocular delivery of the pilocarpine prodrug may be enhanced in relation to its local irritation by properly combining buffer, viscosity and HPCD.

Synthesis and analysis of O,O'-dicarboxylate (dibenzyl) bispilocarpates as possible prodrugs of pilocarpine.

As a part of a series of studies to develop prodrug derivatives of pilocarpine, the O,O'-succinyl (dibenzyl), O,O-adipoyl (dibenzyl), O,O-fumaryl (dibenzyl), and O,O-terephthaloyl (dibenzyl) bispilocarpate fumarates were synthesized as a new class of pilocarpine prodrugs. The compounds were prepared from pilocarpic acid benzyl monoester by coupling two pilocarpic acid benzyl monoesters together with spacer chains by usual esterification methods. Liquid chromatography, thermospray liquid chromatography-mass spectrometry, high-resolution mass spectrometry, and NMR spectroscopy were applied to the identification and the purity evaluation of the synthetic products.

Improved corneal pilocarpine permeability with O,O'-(1,4-xylylene) bispilocarpic acid ester double prodrugs.

O,O'-(1,4-Xylylene) bispilocarpic acid esters are pilocarpine prodrugs containing two pilocarpic acid monoesters linked with one pro-moiety. Each mole of prodrug forms two pilocarpine moles in the presence of esterases. Corneal uptake and permeability of various bispilocarpic acid diesters were investigated in vitro using isolated albino rabbit corneas. The permeability coefficient of pilocarpine was 2.8 x 10(-6) cm/sec, whereas for bispilocarpic acid diesters, despite their large molecular weights (between 638 and 722), permeability coefficients were 6.5-20.2 x 10(-6) cm/sec. Only pilocarpine, and no intact prodrug, was observed at the endothelial side. Corneal uptake was increased with increasing lipophilicity, but a parabolic relationship between the logarithm of the apparent partition coefficient (1-octanol-pH 7.4 phosphate buffer) (log PC) and the corneal permeability was noticed. Corneal permeability and the rate of enzymatic hydrolysis of the compounds correlated well. The corneal permeability of pilocarpine given as lipophilic bispilocarpic acid diester (log PC greater than or equal to 3) prodrugs seems to be controlled by the formation of pilocarpine in the corneal epithelium rather than by the absorption of prodrugs into the epithelium or their epithelium-stroma transport rate.

Determination of physicochemical properties, stability in aqueous solutions and serum hydrolysis of pilocarpic acid diesters.

New alkyl and aralkyl pilocarpic acid diesters, prodrugs of pilocarpine, were synthesized with the aim of improving the bioavailability of pilocarpine by increasing its corneal permeability. These esters were several orders of magnitude more lipophilic than pilocarpine as determined by their apparent partition coefficients between 1-octanol and phosphate buffer (pH 7.40) (log P). Good correlation between log P and HPLC capacity factors of the compounds was observed. All the compounds are stable in acidic aqueous solution; in serum, however, pilocarpic acid diesters are hydrolysed enzymatically to pilocarpic acid monoester, which undergoes spontaneous cyclization to active pilocarpine and inactive isopilocarpine. The half-lives of the diesters in serum varied from 6-232 min. In addition to the direct effects of the R2, R1 moiety had a remarkable effect on the rate of enzyme-catalysed hydrolysis taking place in moiety R2. The formed pilocarpine was analysed with a new HPLC method which allowed good resolution of pilocarpine, isopilocarpine, pilocarpic acid and isopilocarpic acid. Rates for pilocarpine formation were both determined by experiment and calculated using the STELLA simulation programme with known degradation rate constants of pilocarpic acid diesters and monoesters. Since the simulations were in good agreement with the experimental results, it is concluded that STELLA simulation programme is useful in predicting pilocarpine formation.

Synthesis and identification of pilocarpic acid diesters, prodrugs of pilocarpine.

A series of new pilocarpic acid diesters were synthesized to obtain prodrugs for pilocarpine with varying physico-chemical properties. Thermospray liquid chromatography-mass spectrometry (TSP-LC-MS), liquid chromatography with UV-detection (LC-UV) and NMR-spectroscopy were used for the identification of the synthetic products and for evaluation of their purity including typical impurities (pilocarpic acid monoester, pilocarpine). TSP-LC-MS-analysis was performed in the reversed-phase mode using acetonitrile (60%)-0.2 M ammonium acetate (40%) as mobile phase. In LC-UV-analysis chromatographic separation was carried out on a reversed-phase column and the mobile phase consisted of methanol (71%) and 0.02 M potassium dihydrogen phosphate, pH 4.5 (29%). Electron ionization-mass spectrometry (EI-MS) was used for elucidation of structures. Elemental compositions of the substances were verified with high resolution-mass spectrometry (HR-MS). The complete establishment of structures presented was based on 1H-, and COSY-NMR-spectroscopy joined to TSP-LC-MS-analysis.