Fine structures of intrinsically disordered proteins.

We report simulation studies of 33 single intrinsically disordered proteins (IDPs) using coarse-grained bead-spring models where interactions among different amino acids are introduced through a hydropathy matrix and additional screened Coulomb interaction for the charged amino acid beads. Our simulation studies of two different hydropathy scales (HPS1, HPS2) [Dignon et al., PLoS Comput. Biol. 14, e1005941 (2018); Tesei et al. Proc. Natl. Acad. Sci. U. S. A. 118, e2111696118 (2021)] and the comparison with the existing experimental data indicate an optimal interaction parameter ϵ = 0.1 and 0.2 kcal/mol for the HPS1 and HPS2 hydropathy scales. We use these best-fit parameters to investigate both the universal aspects as well as the fine structures of the individual IDPs by introducing additional characteristics. (i) First, we investigate the polymer-specific scaling relations of the IDPs in comparison to the universal scaling relations [Bair et al., J. Chem. Phys. 158, 204902 (2023)] for the homopolymers. By studying the scaled end-to-end distances ⟨RN2⟩/(2Lℓp) and the scaled transverse fluctuations l̃⊥2=⟨l⊥2⟩/L, we demonstrate that IDPs are broadly characterized with a Flory exponent of ν ≃ 0.56 with the conclusion that conformations of the IDPs interpolate between Gaussian and self-avoiding random walk chains. Then, we introduce (ii) Wilson charge index (W) that captures the essential features of charge interactions and distribution in the sequence space and (iii) a skewness index (S) that captures the finer shape variation of the gyration radii distributions as a function of the net charge per residue and charge asymmetry parameter. Finally, our study of the (iv) variation of ⟨Rg⟩ as a function of salt concentration provides another important metric to bring out finer characteristics of the IDPs, which may carry relevant information for the origin of life.

Universality in conformations and transverse fluctuations of a semi-flexible polymer in a crowded environment.

We study the universal aspects of polymer conformations and transverse fluctuations for a single swollen chain characterized by a contour length L and a persistence length ℓp in two dimensions (2D) and three dimensions (3D) in the bulk, as well as in the presence of excluded volume (EV) particles of different sizes occupying different area/volume fractions. In the absence of the EV particles, we extend the previously established universal scaling relations in 2D [Huang et al., J. Chem. 140, 214902 (2014)] to include 3D and demonstrate that the scaled end-to-end distance ⟨RN2⟩/(2Lℓp) and the scaled transverse fluctuation ⟨l⊥2⟩/L as a function of L/ℓp collapse onto the same master curve, where ⟨RN2⟩ and ⟨l⊥2⟩ are the mean-square end-to-end distance and transverse fluctuations. However, unlike in 2D, where the Gaussian regime is absent due to the extreme dominance of the EV interaction, we find that the Gaussian regime is present, albeit very narrow in 3D. The scaled transverse fluctuation in the limit L/ℓp ≪ 1 is independent of the physical dimension and scales as ⟨l⊥2⟩/L∼(L/ℓp)ζ-1, where ζ = 1.5 is the roughening exponent. For L/ℓp ≫ 1, the scaled fluctuation scales as ⟨l⊥2⟩/L∼(L/ℓp)ν-1, where ν is the Flory exponent for the corresponding spatial dimension (ν2D = 0.75 and ν3D = 0.58). When EV particles of different sizes for different area or volume fractions are added into 2D and 3D systems, our results indicate that the crowding density either does not or does only weakly affect the universal scaling relations. We discuss the implications of these results in living matter by showing the experimental result for a dsDNA on the master plot.

How capture affects polymer translocation in a solitary nanopore.

DNA capture with high fidelity is an essential part of nanopore translocation. We report several important aspects of the capture process and subsequent translocation of a model DNA polymer through a solid-state nanopore in the presence of an extended electric field using the Brownian dynamics simulation that enables us to record statistics of the conformations at every stage of the translocation process. By releasing the equilibrated DNAs from different equipotentials, we observe that the capture time distribution depends on the initial starting point and follows a Poisson process. The field gradient elongates the DNA on its way toward the nanopore and favors a successful translocation even after multiple failed threading attempts. Even in the limit of an extremely narrow pore, a fully flexible chain has a finite probability of hairpin-loop capture, while this probability decreases for a stiffer chain and promotes single file translocation. Our in silico studies identify and differentiate characteristic distributions of the mean first passage time due to single file translocation from those due to translocation of different types of folds and provide direct evidence of the interpretation of the experimentally observed folds [M. Gershow and J. A. Golovchenko, Nat. Nanotechnol. 2, 775 (2007) and Mihovilovic et al., Phys. Rev. Lett. 110, 028102 (2013)] in a solitary nanopore. Finally, we show a new finding-that a charged tag attached at the 5' end of the DNA enhances both the multi-scan rate and the uni-directional translocation (5' → 3') probability that would benefit the genomic barcoding and sequencing experiments.

Polymer escape through a three dimensional double-nanopore system.

We study the escape dynamics of a double-stranded DNA (dsDNA) through an idealized double nanopore geometry subject to two equal and opposite forces (tug-of-war) using Brownian dynamics (BD) simulation. In addition to the geometrical restrictions imposed on the cocaptured dsDNA segment in between the pores, the presence of tug-of-war forces at each pore results in a variation of the local chain stiffness for the segment of the chain in between the pores, which increases the overall stiffness of the chain. We use the BD simulation results to understand how the intrinsic chain stiffness and the tug-of-war forces affect the escape dynamics by monitoring the local chain persistence length ℓp, the residence time of the individual monomers W(m) in the nanopores, and the chain length dependence of the escape time ⟨τ⟩ and its distribution. Finally, we generalize the scaling theory for the unbiased single nanopore translocation for a fully flexible chain for the escape of a semi-flexible chain through a double nanopore in the presence of tug-of-war forces. We establish that the stiffness dependent part of the escape time is approximately independent of the translocation mechanism so that ⟨τ⟩∼ℓp 2/D+2, and therefore, the generalized escape time for a semi-flexible chain can be written as ⟨τ⟩=ANαℓp 2/D+2. We use the BD simulation results to compare the predictions of the scaling theory. Our numerical studies supplemented by scaling analysis provide fundamental insights to design new experiments where a dsDNA moves slowly through a series of graphene nanopores.

DNA Barcodes Using a Dual Nanopore Device.

We report a novel method based on the current blockade (CB) characteristics obtained from a dual nanopore device that can determine DNA barcodes with near-perfect accuracy using a Brownian dynamics simulation strategy. The method supersedes our previously reported velocity correction algorithm (S. Seth and A. Bhattacharya, RSC Advances, 11:20781-20787, 2021), taking advantage of the better measurement of the time-of-flight (TOF) protocol offered by the dual nanopore setup. We demonstrate the efficacy of the method by comparing our simulation data from a coarse-grained model of a polymer chain consisting of 2048 excluded volume beads of diameter 𝜎 = 24 bp using with those obtained from experimental CB data from a 48,500 bp λ-phage DNA, providing a 48500 2400 ≅ 24 base pair resolution in simulation. The simulation time scale is compared to the experimental time scale by matching the simulated time-of-flight (TOF) velocity distributions with those obtained experimentally (Rand et al., ACS Nano, 16:5258-5273, 2022). We then use the evolving coordinates of the dsDNA and the molecular features to reconstruct the current blockade characteristics on the fly using a volumetric model based on the effective van der Waal radii of the species inside and in the immediate vicinity of the pore. Our BD simulation mimics the control-zoom-in-logic to understand the origin of the TOF distributions due to the relaxation of the out-of-equilibrium conformations followed by a reversal of the electric fields. The simulation algorithm is quite general and can be applied to differentiate DNA barcodes from different species.

Discriminating protein tags on a dsDNA construct using a Dual Nanopore Device.

We report Brownian dynamics simulation results with the specific goal to identify key parameters controlling the experimentally measurable characteristics of protein tags on a dsDNA construct translocating through a double nanopore setup. First, we validate the simulation scheme in silico by reproducing and explaining the physical origin of the asymmetric experimental dwell time distributions of the oligonucleotide flap markers on a 48 kbp long dsDNA at the left and the right pore. We study the effect of the electric field inside and beyond the pores, critical to discriminate the protein tags based on their effective charges and masses revealed through a generic power-law dependence of the average dwell time at each pore. The simulation protocols monitor piecewise dynamics at a sub-nanometer length scale and explain the disparate velocity using the concepts of nonequilibrium tension propagation theory. We further justify the model and the chosen simulation parameters by calculating the Péclet number which is in close agreement with the experiment. We demonstrate that our carefully chosen simulation strategies can serve as a powerful tool to discriminate different types of neutral and charged tags of different origins on a dsDNA construct in terms of their physical characteristics and can provide insights to increase both the efficiency and accuracy of an experimental dual-nanopore setup.

DNA barcodes using a double nanopore system.

The potential of a double nanopore system to determine DNA barcodes has been demonstrated experimentally. By carrying out Brownian dynamics simulation on a coarse-grained model DNA with protein tag (barcodes) at known locations along the chain backbone, we demonstrate that due to large variation of velocities of the chain segments between the tags, it is inevitable to under/overestimate the genetic lengths from the experimental current blockade and time of flight data. We demonstrate that it is the tension propagation along the chain's backbone that governs the motion of the entire chain and is the key element to explain the non uniformity and disparate velocities of the tags and DNA monomers under translocation that introduce errors in measurement of the length segments between protein tags. Using simulation data we further demonstrate that it is important to consider the dynamics of the entire chain and suggest methods to accurately decipher barcodes. We introduce and validate an interpolation scheme using simulation data for a broad distribution of tag separations and suggest how to implement the scheme experimentally.

DNA barcode by flossing through a cylindrical nanopore.

We report an accurate method to determine DNA barcodes from the dwell time measurement of protein tags (barcodes) along the DNA backbone using Brownian dynamics simulation of a model DNA and use a recursive theoretical scheme which improves the measurements to almost 100% accuracy. The heavier protein tags along the DNA backbone introduce a large speed variation in the chain that can be understood using the idea of non-equilibrium tension propagation theory. However, from an initial rough characterization of velocities into "fast" (nucleotides) and "slow" (protein tags) domains, we introduce a physically motivated interpolation scheme that enables us to determine the barcode velocities rather accurately. Our theoretical analysis of the motion of the DNA through a cylindrical nanopore opens up the possibility of its experimental realization and carries over to multi-nanopore devices used for barcoding.

Tug of war in a double-nanopore system.

We simulate a tug-of-war (TOW) scenario for a model double-stranded DNA threading through a double nanopore (DNP) system. The DNA, simultaneously captured at both pores, is subject to two equal and opposite forces -f[over ⃗]_{L}=f[over ⃗]_{R} (TOW), where f[over ⃗]_{L} and f[over ⃗]_{R} are the forces applied to the left and the right pore, respectively. Even though the net force on the DNA polymer Δf[over ⃗]_{LR}=f[over ⃗]_{L}+f[over ⃗]_{R}=0, the mean first passage time (MFPT) 〈τ〉 depends on the magnitude of the TOW forces |f_{L}|=|f_{R}|=f_{LR}. We qualitatively explain this dependence of 〈τ〉 on f_{LR} from the known results for the single-pore translocation of a triblock copolymer A-B-A with ℓ_{pB}>ℓ_{pA}, where ℓ_{pA} and ℓ_{pB} are the persistence length of the A and B segments, respectively. We demonstrate that the time of flight of a monomer with index m [〈τ_{LR}(m)〉] from one pore to the other exhibits quasiperiodic structure commensurate with the distance between the pores d_{LR}. Finally, we study the situation where we offset the TOW biases so that Δf[over ⃗]_{LR}=f[over ⃗]_{L}+f[over ⃗]_{R}≠0, and qualitatively reproduce the experimental result of the dependence of the MFPT on Δf[over ⃗]_{LR}. We demonstrate that, for a moderate bias, the MFPT for the DNP system for a chain length N follows the same scaling ansatz as that for the single nanopore, 〈τ〉=(AN^{1+ν}+η_{pore}N)(Δf_{LR})^{-1}, where η_{pore} is the pore friction, which enables us to estimate 〈τ〉 for a long chain. Our Brownian dynamics simulation studies provide fundamental insights and valuable information about the details of the translocation speed obtained from 〈τ_{LR}(m)〉, and accuracy of the translation of the data obtained in the time domain to units of genomic distances.