Escape Kinetics Research Articles

Modeling the Kinetics of Lipid-Nanoparticle- Mediated Delivery of Multiple siRNAs to Evaluate the Effect on Competition for Ago2

Drug combinations can improve the control of diseases involving redundant and highly regulated pathways. Validating a multi-target therapy early in drug development remains difficult. Small interfering RNAs (siRNAs) are routinely used to selectively silence a target of interest. Owing to the ease of design and synthesis, siRNAs hold promise for combination therapies. Combining siRNAs against multiple targets remains an attractive approach to interrogating highly regulated pathways. Currently, questions remain regarding how broadly such an approach can be applied, since siRNAs have been shown to compete with one another for binding to Argonaute2 (Ago2), the protein responsible for initiating siRNA-mediated mRNA degradation. Mathematical modeling, coupled with in vitro and in vivo experiments, led us to conclude that endosomal escape kinetics had the highest impact on Ago2 depletion by competing lipid-nanoparticle (LNP)-formulated siRNAs. This, in turn, affected the level of competition observed between them. A future application of this model would be to optimize delivery of desired siRNA combinations in vitro to attenuate competition and maximize the combined therapeutic effect.

Regulation of Mycobacterial RNA Polymerase Promoter Escape Kinetics by Transcription Factors Card and RbpA

The process of bacterial RNA polymerase (RNAP) escaping the promoter region during transcription initiation can often be rate limiting, making kinetic regulation of escape a common strategy employed to control the rates of transcription. Using a pre-steady state ensemble fluorescence assay, we present the first in-depth kinetic analysis of initial nucleotide incorporation and promoter escape for the Mycobacterium tuberculosis (Mtb) RNAP.We show that in relation to E. coli RNAP, Mtb displays slower initial nucleotide incorporation but faster overall promoter escape kinetics on the MtbrrnAP3 promoter. Furthermore, in the context of the essential transcription factors CarD and RbpA, Mtb RNAP promoter escape is delayed, albeit through different mechanisms. We also see that these factors increase the inactive fraction, i.e. complexes that are unable to escape the promoter. Given that CarD and RbpA affect multiple kinetic intermediates during transcription initiation, we modelled hypothetical sets of rate constants derived from the initiation kinetics to suggest that CarD and RbpA can serve to both activate and repress transcription in a promoter-dependent context. For instance, on the rrnAP3 promoter, where DNA-opening is rate limiting, both CarD and RbpA activate transcription, whereas on promoters that are rate-limited at escape, the prediction is that these factors lead to transcriptional repression.

Kinetics of HIV-Specific CTL Responses Plays a Minimal Role in Determining HIV Escape Dynamics.

Cytotoxic T lymphocytes (CTLs) have been suggested to play an important role in controlling human immunodeficiency virus (HIV-1 or simply HIV) infection. HIV, due to its high mutation rate, can evade recognition of T cell responses by generating escape variants that cannot be recognized by HIV-specific CTLs. Although HIV escape from CTL responses has been well documented, factors contributing to the timing and the rate of viral escape from T cells have not been fully elucidated. Fitness costs associated with escape and magnitude of the epitope-specific T cell response are generally considered to be the key in determining timing of HIV escape. Several previous analyses generally ignored the kinetics of T cell responses in predicting viral escape by either considering constant or maximal T cell response; several studies also considered escape from different T cell responses to be independent. Here, we focus our analysis on data from two patients from a recent study with relatively frequent measurements of both virus sequences and HIV-specific T cell response to determine impact of CTL kinetics on viral escape. In contrast with our expectation, we found that including temporal dynamics of epitope-specific T cell response did not improve the quality of fit of different models to escape data. We also found that for well-sampled escape data, the estimates of the model parameters including T cell killing efficacy did not strongly depend on the underlying model for escapes: models assuming independent, sequential, or concurrent escapes from multiple CTL responses gave similar estimates for CTL killing efficacy. Interestingly, the model assuming sequential escapes (i.e., escapes occurring along a defined pathway) was unable to accurately describe data on escapes occurring rapidly within a short-time window, suggesting that some of model assumptions must be violated for such escapes. Our results thus suggest that the current sparse measurements of temporal CTL dynamics in blood bear little quantitative information to improve predictions of HIV escape kinetics. More frequent measurements using more sensitive techniques and sampling in secondary lymphoid tissues may allow to better understand whether and how CTL kinetics impacts viral escape.

Activated barrier crossing dynamics of a Janus particle carrying cargo.

We numerically study the escape kinetics of a self-propelled Janus particle, carrying a cargo, from a meta-stable state. We assume that the cargo is attached to the Janus particle by a flexible harmonic spring. We take into account the effect of the velocity field created in the fluid due to movements of the dimer's components, by considering a space-dependent diffusion tensor (Oseen tensor). Our simulation results show that the synchronization between barrier crossing events and the rotational relaxation process can enhance the escape rate to a large extent. Also, the load carrying capability of a Janus particle is largely controlled by its rotational dynamics and self-propulsion velocity. Moreover, the hydrodynamic interaction, conspicuously, enhances the escape rate of the Janus-cargo dimer. The most important features in escape kinetics have been justified based on analytic arguments.

Fluctuating bottleneck model studies on kinetics of DNA escape from α-hemolysin nanopores.

We have proposed a fluctuation bottleneck (FB) model to investigate the non-exponential kinetics of DNA escape from nanometer-scale pores. The basic idea is that the escape rate is proportional to the fluctuating cross-sectional area of DNA escape channel, the radius r of which undergoes a subdiffusion dynamics subjected to fractional Gaussian noise with power-law memory kernel. Such a FB model facilitates us to obtain the analytical result of the averaged survival probability as a function of time, which can be directly compared to experimental results. Particularly, we have applied our theory to address the escape kinetics of DNA through α-hemolysin nanopores. We find that our theoretical framework can reproduce the experimental results very well in the whole time range with quite reasonable estimation for the intrinsic parameters of the kinetics processes. We believe that FB model has caught some key features regarding the long time kinetics of DNA escape through a nanopore and it might provide a sound starting point to study much wider problems involving anomalous dynamics in confined fluctuating channels.

Influence of the Composition and Surface Roughness of TiCaPCON–Ag Coatings on the Escape Kinetics of Silver into a Physiological Solution

Coatings TiCaPCON–Ag with the silver content of 1,0 and 2,5 at.% were obtained by magnetron sputtering. Two types of substrates with different roughness were used for their deposition, notably, polished titanium (average roughness Ra = 20 nm) and the surface modified by pulsed electric-spark treatment (Ra = 8 μm). Structural studies showed that the introduction of silver into the composition of coatings leads to the formation of nanoparticles 5–10 nm in size on their surface. The yield kinetics of silver from coatings into the physiological solution is investigated by mass spectrometry with inductively coupled plasma. It is shown that the yield of silver ions into the biological medium can be controlled due to varying the substrate surface roughness.

Escape from hypercube driven by multi-variate α-stable noises: role of independence

We explore properties of the escape kinetics from the d-dimensional hypercube driven by multi-variate α-stable noises. Using methods of stochastic dynamics we show complex dependence of the mean first passage time for the escape from the hypercube as a function of the hypercube dimension d. Finally, we show how the escape process can be used to quantify independence of components of multi-variate α-stable noises.

Antibody escape kinetics of equine infectious anemia virus infection of horses.

Lentivirus escape from neutralizing antibodies (NAbs) is not well understood. In this work, we quantified antibody escape of a lentivirus, using antibody escape data from horses infected with equine infectious anemia virus. We calculated antibody blocking rates of wild-type virus, fitness costs of mutant virus, and growth rates of both viruses. These quantitative kinetic estimates of antibody escape are important for understanding lentiviral control by antibody neutralization and in developing NAb-eliciting vaccine strategies.

Kinetics of promoter escape by bacterial RNA polymerase: effects of promoter contacts and transcription bubble collapse.

Promoter escape by RNA polymerase, the transition between the initiation and elongation, is a critical step that defines transcription output at many promoters. In the present study we used a real-time fluorescence assay for promoter melting and escape to study the determinants of the escape. Perturbation of core promoter-polymerase contacts had opposing effects on the rates of melting and escape, demonstrating a direct role of core promoter elements sequence in setting not only the kinetics of promoter melting, but also the kinetics of promoter escape. The start of RNA synthesis is accompanied by an enlargement of the transcription bubble and pulling in of the downstream DNA into the enzyme, resulting in DNA scrunching. Promoter escape results in collapse of the enlarged bubble. To test whether the energy that could be potentially released by the collapse of the bubble plays a role in determining escape kinetics, we measured the rates of promoter escape in promoter constructs, in which the amount of this energy was perturbed by introducing sequence mismatches. We found no significant changes in the rate of promoter escape with these promoter constructs suggesting that the energy released upon bubble collapse does not play a critical role in determining the kinetics of promoter escape.

Resonant activation in 2D and 3D systems driven by multi-variate Lévy noise

Resonant activation is one of the classical effects demonstrating the constructive role of noise. In resonant activation, the cooperative action of a barrier modulation process and noise lead to the optimal escape kinetics as measured by the mean first passage time. Resonant activation has been observed in versatile systems for various types of barrier modulation process and noise type. Here, we show that resonant activation is also observed in 2D and 3D systems driven by bi-variate and tri-variate α-stable noise. The strength of resonant activation is sensitive to the exact value of the noise parameters. In particular, the decrease in the stability index α results in the disappearance of the resonant activation.

Communication: Escape kinetics of self-propelled Janus particles from a cavity: numerical simulations.

We numerically investigate the escape kinetics of elliptic Janus particles from narrow two-dimensional cavities with reflecting walls. The self-propulsion velocity of the Janus particle is directed along either their major (prolate) or minor (oblate) axis. We show that the mean exit time is very sensitive to the cavity geometry, particle shape, and self-propulsion strength. The mean exit time is found to be a minimum when the self-propulsion length is equal to the cavity size. We also find the optimum mean escape time as a function of the self-propulsion velocity, translational diffusion, and particle shape. Thus, effective transport control mechanisms for Janus particles in a channel can be implemented.

Quantifying a resonant-activation-like phenomenon in non-Markovian systems.

Resonant activation is an effect of a noise-induced escape over a modulated potential barrier. The modulation of an energy landscape facilitates the escape kinetics and makes it optimal as measured by the mean first-passage time. A canonical example of resonant activation is a Brownian particle moving in a time-dependent potential under action of Gaussian white noise. Resonant activation is observed not only in typical Markovian-Gaussian systems but also in far-from-equilibrium and far-from-Markovianity regimes. We demonstrate that using an alternative to the mean first-passage time, robust measures of resonant activation, the signature of this effect can be observed in general continuous-time random walks in modulated potentials, even in situations when the mean first-passage time diverges.

Dynamics of submicron aerosol droplets in a robust optical trap formed by multiple Bessel beams

In this paper, we model the three-dimensional escape dynamics of single submicron-sized aerosol droplets in optical multiple Bessel beam traps. Trapping in counter-propagating Bessel beams (CPBBs) is compared with a newly proposed quadruple Bessel beam (QBB) trap, which consists of two perpendicularly arranged CPBB traps. Calculations are performed for perfectly and imperfectly aligned traps. Mie-theory and finite-difference time-domain methods are used to calculate the optical forces. The droplet escape kinetics are obtained from the solution of the Langevin equation using a Verlet algorithm. Provided the traps are perfectly aligned, the calculations indicate very long lifetimes for droplets trapped either in the CPBB or in the QBB trap. However, minor misalignments that are hard to control experimentally already severely diminish the stability of the CPBB trap. By contrast, such minor misalignments hardly affect the extended droplet lifetimes in a QBB trap. The QBB trap is found to be a stable, robust optical trap, which should enable the experimental investigation of submicron droplets with radii down to 100 nm. Optical binding between two droplets and its potential role in preventing coagulation when loading a CPBB trap is briefly addressed.

Endosomal escape kinetics of mesoporous silica-based system for efficient siRNA delivery

The strategy of encapsulating small interference RNA (siRNA) into the mesopores enables mesoporous silica nanoparticles (MSNs) to be an attractive material for siRNA delivery. Nevertheless, the gene silencing efficiency mediated by this sort of vehicles has not been systematically investigated yet. In this work, through quantifying gene silencing efficiency by flow cytometry (FCM) and performing intracellular tracking by confocal laser scanning microscopy (CLSM), we found that the RNA interference (RNAi) efficiency mediated by MSNs-based delivery vehicles was strongly dependent on their endosomal escape capability. Thereafter, we investigated the correlation between the gene knockdown efficiency and the endosomal escape kinetics of such carriers. The results indicated that highly efficient MSNs-based siRNA delivery vectors must possess the capability of initiating effectively endosomal escape before the degradation of their packaged siRNA in endolysosomes.

Single-Molecule Tracking of Collagenase on Native Type I Collagen Fibrils Reveals Degradation Mechanism

Collagen, the most abundant human protein, is the principal component of the extracellular matrix and plays important roles in maintaining tissue and organ integrity. Highly resistant to proteolysis, fibrillar collagen is degraded by specific matrix metalloproteases (MMPs). Degradation of fibrillar collagen underlies processes including tissue remodeling, wound healing, and cancer metastasis. However, the mechanism of native collagen fibril degradation remains poorly understood. Here we present the results of high-resolution tracking of individual MMPs degrading type I collagen fibrils. MMP1 exhibits cleavage-dependent biased and hindered diffusion but spends 90% ± 3% of the time in one of at least two distinct pause states. One class of exponentially distributed pauses (class I pauses) occurs randomly along the fibril, whereas a second class of pauses (class II pauses) exhibits multistep escape kinetics and occurs periodically at intervals of 1.3 ± 0.2 μm and 1.5 ± 0.2 μm along the fibril. After these class II pauses, MMP1 moved faster and farther in one direction along the fibril, indicative of biased motion associated with cleavage. Simulations indicate that 5% ± 2% of the class II pauses result in the initiation of processive collagen degradation, which continues for bursts of 15 ± 4 consecutive cleavage events. These findings provide a mechanistic paradigm for type I collagen degradation by MMP1 and establish a general approach to investigate MMP-fibrillar collagen interactions. More generally, this work demonstrates the fundamental role of enzyme-substrate interactions including binding and motion in determining the activity of an enzyme on an extended substrate.

Transcription factor expression profiling to characterize differentiation of antigen-specific CD8 T cells induced by a live attenuated viral vaccine. (113.18)

Abstract Live attenuated SIV (SIVΔnef) is the most effective approach to induce protection to pathogenic SIV challenge in macaques. Protective immunity, in part mediated by CD8 T cell responses, correlates with phenotypic maturation of SIV-specific T cells, but remains incompletely understood. Expression profiling of T cell transcription factors (TF) offers a novel approach to characterize antigen-specific T cell differentiation. Highly parallel qRT-PCR was used to characterize the expression of 21 TF in naïve, central, transitional, and effector memory T cell subsets, and in SIV-specific CD8 T cells obtained at times associated with lesser protection (wk 5) and greater protection (wk 20) following SIVΔnef vaccination. Unsupervised clustering organized samples from CD4 and CD8 T cells into groups concordant with cell surface phenotype. TF expression in SIV-specific CD8+ T cells segregated by time, with wk 20 cells exhibiting increased expression of TF associated with both maintenance of quiescence (TCF7, BAZF) and promotion of effector function (Eomes, T-Bet). Different expression profiles were observed in T cells specific for different SIV epitopes, consistent with different epitope escape kinetics. TF expression profiling suggests T cell responses correlated with protection may include characteristics of both memory and effector cells. TF expression profiling can provide data complementary to the analysis of memory cell differentiation based on classical phenotypic markers.

Enhanced Carrier Escape in MSQW Solar Cell and Its Impact on Photovoltaics Performance

A multiple stepped quantum wells (MSQWs) solar cell, in which GaAs stepped-potential layers are sandwiched between strain-balanced InGaAs wells and GaAsP barriers, has been proposed, and improvements in short-circuit current and fill factor have been demonstrated. We have studied carrier recombination dynamics and carrier escape kinetics from the wells, comparing the MSQW with the normal multiple quantum well (MQW). Carrier recombination rate was examined by time-resolved photoluminescence (PL) and a longer carrier lifetime was observed for MSQWs than for MQWs. Carrier escape from the wells was also investigated in terms of temperature-dependent PL. Smaller thermal activation energy was observed for MSQWs than for MQWs. Carrier radiative recombination loss was investigated by bias-dependent PL, and it was found to be smaller for the MSQW than for the normal MQW. Such advantages of the MSQW allowed us to stack a sufficient number of quantum wells to increase short-circuit current without degrading fill factor. For normal MQW solar cells, degradation in fill factor is unavoidable.

Effect of binding on escape from cavity through narrow tunnel

When a diffusing particle escapes from a spherical cavity through a narrow, not too long tunnel, the escape kinetics is essentially single-exponential. The presence of reversible binding sites on the cavity wall leads to retention of the particle in the system and converts the single-exponential kinetics into bi-exponential. We develop a theory that describes these effects. The theory shows how the delay time and the average number of binding events depend on the geometric and kinetic parameters of the system. To study the effect of the cavity shape, we also analyze the kinetics when the particle escapes from a cylindrical cavity with reversible binding sites.

Anomalous reaction-diffusion as a model of nonexponential DNA escape kinetics

We show that data from recent experiments carried out on the kinetics of DNA escape from alpha-hemolysin nanopores [M. Wiggin, C. Tropini, C. T. Cossa, N. N. Jetha, and A. Marziali, Biophys. J. 95, 5317 (2008)] may be rationalized by a model of chain dynamics based on the anomalous diffusion of a particle moving in a harmonic well in the presence of a delta function sink. The experiments of Wiggin et al. found, among other things, that the occasional occurrence of unusually long escape times in the distribution of chain trapping events led to nonexponential decays in the survival probability, S(t), of the DNA molecules within the nanopore. Wiggin et al. ascribed this nonexponentiality to the existence of a distribution of trapping potentials, which they suggested was the result of stochastic interactions between the bases of the DNA and the amino acids located on the surface of the nanopore. Based on this idea, they showed that the experimentally determined S(t) could be well fit in both the short and long time regimes by a function of the form (1+t/tau)(-alpha) (the so called Becquerel function). In our model, S(t) is found to be given by a Mittag-Leffler function at short times and by a generalized Mittag-Leffler function at long times. By suitable choice of certain parameter values, these functions are found to fit the experimental S(t) even better than the Becquerel function. Anomalous diffusion of DNA within the trap prior to escape over a barrier of fixed height may therefore provide a second, plausible explanation of the data, and may offer fresh perspectives on similar trapping and escape problems.

One-dimensional description of diffusion in a tube of abruptly changing diameter: Boundary homogenization based approach.

Reduction of three-dimensional (3D) description of diffusion in a tube of variable cross section to an approximate one-dimensional (1D) description has been studied in detail previously only in tubes of slowly varying diameter. Here we discuss an effective 1D description in the opposite limiting case when the tube diameter changes abruptly, i.e., in a tube composed of any number of cylindrical sections of different diameters. The key step of our approach is an approximate description of the particle transitions between the wide and narrow parts of the tube as trapping by partially absorbing boundaries with appropriately chosen trapping rates. Boundary homogenization is used to determine the trapping rate for transitions from the wide part of the tube to the narrow one. This trapping rate is then used in combination with the condition of detailed balance to find the trapping rate for transitions in the opposite direction, from the narrow part of the tube to the wide one. Comparison with numerical solution of the 3D diffusion equation allows us to test the approximate 1D description and to establish the conditions of its applicability. We find that suggested 1D description works quite well when the wide part of the tube is not too short, whereas the length of the narrow part can be arbitrary. Taking advantage of this description in the problem of escape of diffusing particle from a cylindrical cavity through a cylindrical tunnel we can lift restricting assumptions accepted in earlier theories: We can consider the particle motion in the tunnel and in the cavity on an equal footing, i.e., we can relax the assumption of fast intracavity relaxation used in all earlier theories. As a consequence, the dependence of the escape kinetics on the particle initial position in the system can be analyzed. Moreover, using the 1D description we can analyze the escape kinetics at an arbitrary tunnel radius, whereas all earlier theories are based on the assumption that the tunnel is narrow.