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Register a new userModeling the relative dynamics of DNA-coated colloids
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Added by
Miranda Holmes-Cerfon
Publication date
2018
fields
Physics
and research's language is
English
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We construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1$mu$m colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger than the corresponding coefficient of hydrodynamic friction. We use a mean-field extension of the model to higher dimensions to estimate the friction tensor for a disc rotating and translating horizontally along a line. When the DNA strands are very stiff and short, the friction coefficient for the disc rolling approaches zero while the friction for the disc sliding remains large. Together, these results could have significant implications for the dynamics of DNA-coated colloids or other ligand-receptor systems, implying that DNA-induced friction between colloids can be stronger than hydrodynamic friction and should be incorporated into simulations, and that it depends nontrivially on the type of relative motion, possibly causing the particles to assemble into out-of-equilibrium metastable states governed by the pathways with the least friction.
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Colloids coated with single-stranded DNA (ssDNA) can bind selectively to other colloids coated with complementary ssDNA. The fact that DNA-coated colloids (DNACCs) can bind to specific partners opens the prospect of making colloidal `molecules. However, in order to design DNACC-based molecules, we must be able to control the valency of the colloids, i.e. the number of partners to which a given DNACC can bind. One obvious, but not very simple approach is to decorate the colloidal surface with patches of single-stranded DNA that selectively bind those on other colloids. Here we propose a design principle that exploits many-body effects to control the valency of otherwise isotropic colloids. Using a combination of theory and simulation, we show that we can tune the valency of colloids coated with mobile ssDNA, simply by tuning the non-specific repulsion between the particles. Our simulations show that the resulting effective interactions lead to low-valency colloids self-assembling in peculiar open structures, very different from those observed in DNACCs with immobile DNA linkers.
Responsive particles, such as biomacromolecules or hydrogels, display a broad and polymodal distribution of conformations and have thus the ability to change their properties (e.g, size, shape, charge density, etc.) substantially in response to external fields or to their local environment (e.g., mediated by cosolutes or pH). Here, we discuss the basic statistical mechanics for a model of responsive colloids (RCs) by introducing an additional property degree of freedom as a collective variable in a formal coarse-graining procedure. The latter leads to an additional one-body term in the coarse-grained (CG) free energy, defining a single-particle property distribution for an individual polydisperse RC. We argue that in the equilibrium thermodynamic limit such a CG system of RCs behaves like a conventional polydisperse system of non-responsive particles. We then illustrate the action of external fields, which impose local (position-dependent) property distributions leading to non-trivial effects on the spatial one-body property and density profiles, even for an ideal (non-interacting) gas of RCs. We finally apply density functional theory in the local density approximation (LDA-DFT) to discuss the effects of particle interactions for specific examples of i) a suspension of RCs in an external field linear in both position and property, ii) a suspension of RCs with highly localized properties (sizes) confined between two walls, and iii) a two-component suspension where an inhomogeneously distributed (non-responsive) cosolute component, as found, e.g., in the studies of osmolyte- or salt-induced collapse/swelling transitions of thermosensitive polymers, modifies the local properties and density of the RC liquid.
We investigate the dynamics of DNA translocation through a nanopore driven by an external force using Langevin dynamics simulations in two dimensions (2D) to study how the translocation dynamics depend on the details of the DNA sequences. We consider a coarse-grained model of DNA built from two bases $A$ and $C$, having different base-pore interactions, {textit e.g.}, a strong (weak) attractive force between the pore and the base $A$ ($C$) inside the pore. From a series of studies on hetero-DNAs with repeat units $A_mC_n$, we find that the translocation time decreases exponentially as a function of the volume fraction $f_C$ of the base $C$. %($epsilon_{pC} < epsilon_{pA}$). For longer $A$ sequences with $f_C le 0.5$, the translocation time strongly depends on the orientation of DNA, namely which base enters the pore first. Our studies clearly demonstrate that for a DNA of certain length $N$ with repeat units $A_mC_n$, the pattern exhibited by the waiting times of the individual bases and their periodicity can unambiguously determine the values of $m$, $n$ and $N$ respectively. Therefore, a prospective experimental realization of this phenomenon may lead to fast and efficient sequence detection technic.
We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well-known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number Wi$_{text c}$, analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.
The flexibility and stiffness of small DNA play a fundamental role ranging from several biophysical processes to nano-technological applications. Here, we estimate the mechanical properties of short double-stranded DNA (dsDNA) having length ranging from 12 base-pairs (bps) to 56 bps, paranemic crossover (PX) DNA, and hexagonal DNA nanotubes (DNTs) using two widely used coarse-grain models $-$ Martini and oxDNA. To calculate the persistence length ($L_p$) and the stretch modulus ($gamma$) of the dsDNA, we incorporate the worm-like chain and elastic rod model, while for DNT, we implement our previously developed theoretical framework. We compare and contrast all the results with previously reported all-atom molecular dynamics (MD) simulation and experimental results. The mechanical properties of dsDNA ($L_p$ $sim$ 50nm, $gamma sim$ 800-1500 pN), PX DNA ($gamma sim$ 1600-2000 pN) and DNTs ($L_p sim 1-10 mu$m, $gamma sim$ 6000-8000 pN) estimated using Martini soft elastic network and oxDNA are in very good agreement with the all-atom MD and experimental values, while the stiff elastic network Martini reproduces order of magnitude higher values of $L_p$ and $gamma$. The high flexibility of small dsDNA is also depicted in our calculations. However, Martini models proved inadequate to capture the salt concentration effects on the mechanical properties with increasing salt molarity. OxDNA captures the salt concentration effect on small dsDNA mechanics. But it is found to be ineffective to reproduce the salt-dependent mechanical properties of DNTs. Also, unlike Martini, the time evolved PX DNA and DNT structures from the oxDNA models are comparable to the all-atom MD simulated structures. Our findings provide a route to study the mechanical properties of DNA nanostructures with increased time and length scales and has a remarkable implication in the context of DNA nanotechnology.
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