Purohit, Prashant K

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  • Publication
    Geometry of mediating protein affects the probability of loop formation in DNA.
    (2008-04-15) Agrawal, Neeraj J; Radhakrishnan, Ravi; Purohit, Prashant K
    Recent single molecule experiments have determined the probability of loop formation in DNA as a function of the DNA contour length for different types of looping proteins. The optimal contour length for loop formation as well as the probability density functions have been found to be strongly dependent on the type of looping protein used. We show, using Monte Carlo simulations and analytical calculations, that these observations can be replicated using the wormlike-chain model for double-stranded DNA if we account for the nonzero size of the looping protein. The simulations have been performed in two dimensions so that bending is the only mode of deformation available to the DNA while the geometry of the looping protein enters through a single variable which is representative of its size. We observe two important effects that seem to directly depend on the size of the enzyme: 1), the overall propensity of loop formation at any given value of the DNA contour length increases with the size of the enzyme; and 2), the contour length corresponding to the first peak as well as the first well in the probability density functions increases with the size of the enzyme. Additionally, the eigenmodes of the fluctuating shape of the looped DNA calculated from simulations and theory are in excellent agreement, and reveal that most of the fluctuations in the DNA occur in regions of low curvature.
  • Publication
    Confinement and Manipulation of Actin Filaments by Electric Fields
    (2007-08-01) Purohit, Prashant K; Arsenault, Mark E; Goodman, Yale E; Zhao, Hui; Bau, Haim H
    When an AC electric field was applied across a small gap between two metal electrodes elevated above a surface, rhodamine-phalloidin-labeled actin filaments were attracted to the gap and became suspended between the two electrodes. The variance 〈s2(x)〉 of each filament's horizontal, lateral displacement was measured as a function of electric field intensity and position along the filament. 〈s2(x)〉 markedly decreased as the electric field intensity increased. Hypothesizing that the electric field induces tension in the filament, we estimated the tension using a linear, Brownian dynamic model. Our experimental method provides a novel means for trapping and manipulating biological filaments and for probing the surface conductance and mechanical properties of single polymers.
  • Publication
    Plectoneme formation in twisted fluctuating rods
    (2008-05-01) Purohit, Prashant K
    The mechanics of DNA supercoiling is a subject of crucial importance to uncover the mechanism and kinetics of several enzymes. It is therefore being investigated using several biochemical and biophysical methods including single molecule experimental techniques. An interesting problem within this realm is that of torsional buckling and plectoneme formation in DNA as it is simultaneously put under tensile and torsional stress. Analytical solutions to this problem are difficult to find since it involves nonlinear kinematics and thermal fluctuations. In this paper we use ideas from the Kirchhoff theory of filaments to find semi-analytical solutions for the average shape of the fluctuating DNA under the assumption that there is no self-contact. The basic step in our method consists of combining a helical solution of the rod with a non-planar localizing solution in such a way that the force, moment, position and slope remain continuous everywhere along the rod. Our solutions allow us to predict the extension vs. linking number behavior of long pieces of DNA for various values of the tension and temperature. An interesting outcome of our calculations is the prediction of a sudden change in extension at buckling which does not seem to have been emphasized in earlier theoretical models or experiments. Our predictions are amenable to falsification by recently developed single molecule techniques which can simultaneously track the force–extension as well as the torque–rotation behavior of DNA.
  • Publication
    Effect of supercoiling on formation of protein-mediated DNA loops
    (2006-12-21) Purohit, Prashant K; Nelson, Philip C
    DNA loop formation is one of several mechanisms used by organisms to regulate genes. The free energy of forming a loop is an important factor in determining whether the associated gene is switched on or off. In this paper we use an elastic rod model of DNA to determine the free energy of forming short 50–100 basepair, protein mediated DNA loops. Superhelical stress in the DNA of living cells is a critical factor determining the energetics of loop formation, and we explicitly account for it in our calculations. The repressor protein itself is regarded as a rigid coupler; its geometry enters the problem through the boundary conditions it applies on the DNA. We show that a theory with these ingredients is sufficient to explain certain features observed in modulation of in vivo gene activity as a function of the distance between operator sites for the lac repressor. We also use our theory to make quantitative predictions for the dependence of looping on superhelical stress, which may be testable both in vivo and in single-molecule experiments such as the tethered particle assay and the magnetic bead assay.
  • Publication
    Entropically Driven Motion of Polymers in Nonuniform Nanochannels
    (2011-06-07) Su, Tianxiang; Purohit, Prashant K
    In nanofluidic devices, nonuniform confinement induces an entropic force that automatically drives biopolymers toward less-confined regions to gain entropy. To understand this phenomenon, we first analyze the diffusion of an entropy-driven particle system. The derived Fokker-Planck equation reveals an effective driving force as the negative gradient of the free energy. The derivation also shows that both the diffusion constant and drag coefficient are location dependent on an arbitrary free-energy landscape. As an application, DNA motion and deformation in nonuniform channels are investigated. Typical solutions reveal large gradients of stress on the polymer where the channel width changes rapidly. Migration of DNA in several nonuniform channels is discussed.
  • Publication
    Material Properties of Caenorhabditis Elegans Swimming at Low Reynolds Number
    (2010-02-01) Purohit, Prashant Kishore; Krajacic, Predrag; Lamitina, Samuel Todd; Sznitman, Josué; Arratia, Paulo E
    Undulatory locomotion, as seen in the nematode Caenorhabditis elegans, is a common swimming gait of organisms in the low Reynolds number regime, where viscous forces are dominant. Although the nematode’s motility is expected to be a strong function of its material properties, measurements remain scarce. Here, the swimming behavior of C. elegans is investigated in experiments and in a simple model. Experiments reveal that nematodes swim in a periodic fashion and generate traveling waves that decay from head to tail. The model is able to capture the experiments’ main features and is used to estimate the nematode’s Young’s modulus E and tissue viscosity η. For wild-type C. elegans, we find E ≈ 3.77 kPa and η ≈ –860 Pa•s; values of η for live C. elegans are negative because the tissue is generating rather than dissipating energy. Results show that material properties are sensitive to changes in muscle functional properties, and are useful quantitative tools with which to more accurately describe new and existing muscle mutants.
  • Publication
    The mechanics of short rod-like molecules in tension
    (2008-05-01) Purohit, Prashant K; Goldman, Yale; Bau, Haim H; Arsenault, Mark E
    The rapid development of single molecule experimental techniques in the last two decades has made it possible to accurately measure the force-extension response as well as the transverse fluctuations of individual rod-like macromolecules. This information is used in conjunction with a statistical mechanical model based on the treatment of the molecule as a fluctuating elastic rod to extract its bending and extension moduli. The models most commonly used to interpret the experimental data assume that the magnitude of the Brownian fluctuations are independent of the length of the macromolecule, an assumption that holds only in the asymptotic limit of infinitely long rods, and is violated in most experiments. As an alternative, we present a theoretical treatment of a finite length, fluctuating rod and determine its mechanical behavior by measuring the transverse Brownian fluctuations under the action of large stretching forces. to validate of our theory, we have applied our methods to an experiment on short actin filaments whose force-extension relation is difficult to measure, but whose transverse deflections can be captured by current microscopy techniques. An important consequence of the short contour lengths is that the boundary conditions applied in the experiment affect the fluctuations and can no longer be neglected as is commonly done when interpreting data from force-extension measurements. Our theoretical methods account for boundary conditions and can therefore be deployed in conjunction with force extension measurements to obtain detailed information about the mechanical response of rod-like macromolecules.
  • Publication
    Sedimentary Bed Evolution as a Mean-Reverting Random Walk: Implications for Tracer Statistics
    (2014-09-16) Purohit, Prashant K; Martin, Raleigh L; Jerolmack, Douglas J
    Sediment tracers are increasingly employed to estimate bed load transport and landscape evolution rates. Tracer trajectories are dominated by periods of immobility (“waiting times”) as they are buried and reexcavated in the stochastically evolving river bed. Here we model bed evolution as a random walk with mean-reverting tendency (Ornstein-Uhlenbeck process) originating from the restoring effect of erosion and deposition. The Ornstein-Uhlenbeck model contains two parameters, a and b, related to the particle feed rate and range of bed elevation fluctuations, respectively. Observations of bed evolution in flume experiments agree with model predictions; in particular, the model reproduces the asymptotic t−1 tail in the tracer waiting time exceedance probability distribution. This waiting time distribution is similar to that inferred for tracers in natural gravel streams and avalanching rice piles, indicating applicability of the Ornstein-Uhlenbeck mean-reverting model to many disordered transport systems with tracer burial and excavation.