3-D Shape Estimation of DNA Molecules from Stereo Cryo-Electron Micro-Graphs Using a Projection-Steerable Snake

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we introduce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well

Parametric shape processing in biomedical imaging

In this thesis, we present a coherent and consistent approach for the estimation of shape and shape attributes from noisy images. As compared to the traditional sequential approach, our scheme is centered on a shape model which drives the feature extraction, shape optimization, and the attribute evaluation modules. In the first section, we deal with the detection of image features that guide the shape-extraction process. We propose a general approach for the design of 2-D feature detectors from a class of steerable functions, based on the optimization of a Canny-like criterion. As compared to previous computational designs, our approach is truly 2-D and yields more orientation selective detectors. We then address the estimation of the global shape from an image. Specifically, we propose to use cubic-spline-based parametric active contour models to solve two shape-extraction problems: (i) the segmentation of closed objects and (ii) the 3-D reconstruction of DNA filaments from their stereo cryo-electron micrographs. We present several enhancements of existing snake algorithms for segmentation. For the detection of 3-D DNA filaments from their orthogonal projections, we introduce the concept of projection-steerable matched filtering. We then use a 3-D snake algorithm to reconstruct the shape. Next, we analyze the efficiency of curve representations using refinable basis functions for the description of shape boundaries. We derive an exact expression for the error when we approximate a periodic signal in a scaling-function basis. Finally, we present a method for the exact computation of the area moments of such shapes

3D reconstruction and comparison of shapes of DNA minicircles observed by cryo-electron microscopy

We use cryo-electron microscopy to compare 3D shapes of 158 bp long DNA minicircles that differ only in the sequence within an 18 bp block containing either a TATA box or a catabolite activator protein binding site. We present a sorting algorithm that correlates the reconstructed shapes and groups them into distinct categories. We conclude that the presence of the TATA box sequence, which is believed to be easily bent, does not significantly affect the observed shapes

Bending modes of DNA directly addressed by cryo-electron microscopy of DNA minicircles

We use cryo-electron microscopy (cryo-EM) to study the 3D shapes of 94-bp-long DNA minicircles and address the question of whether cyclization of such short DNA molecules necessitates the formation of sharp, localized kinks in DNA or whether the necessary bending can be redistributed and accomplished within the limits of the elastic, standard model of DNA flexibility. By comparing the shapes of covalently closed, nicked and gapped DNA minicircles, we conclude that 94-bp-long covalently closed and nicked DNA minicircles do not show sharp kinks while gapped DNA molecules, containing very flexible single-stranded regions, do show sharp kinks. We corroborate the results of cryo-EM studies by using Bal31 nuclease to probe for the existence of kinks in 94-bp-long minicircles

Bending modes of DNA directly addressed by cryo-electron microscopy of DNA minicircles

We use cryo-electron microscopy (cryo-EM) to study the 3D shapes of 94-bp-long DNA minicircles and address the question of whether cyclization of such short DNA molecules necessitates the formation of sharp, localized kinks in DNA or whether the necessary bending can be redistributed and accomplished within the limits of the elastic, standard model of DNA flexibility. By comparing the shapes of covalently closed, nicked and gapped DNA minicircles, we conclude that 94-bp-long covalently closed and nicked DNA minicircles do not show sharp kinks while gapped DNA molecules, containing very flexible single-stranded regions, do show sharp kinks. We corroborate the results of cryo-EM studies by using Bal31 nuclease to probe for the existence of kinks in 94-bp-long minicircle

Effects of base-pair sequence, nicks and gaps on DNA minicircle shapes:analysis and experiment

DNA is a long polymer with the form of a double helix of about two nanometers diameter (2.10-9 meters). It is composed of nucleotides whose sequence carries the information of heredity. The four possible nucleotides have slightly different geometries, and their sequence along the DNA molecule are thought to influence the shape and the stiffness of the double helix on a scale of few tens to a few hundred base pairs, and thereby its biological activity. DNA minicircles (or miniplasmids) are closed loops with lengths of the order of a few tens or hundreds of base pairs in which the double helix bends around to close on its own tail with some number of twists. Its minimal energy shape and its energy of formation depend on the sequence of base pairs, and can be efficiently computed by polymer and rod models, if shape and stiffness parameters of DNA are provided as inputs. This structure is therefore an interesting experimental motif to test sequence-dependent mechanical properties of the DNA molecule. The purpose of this thesis is to explore the experimental methods to determine the shape and free energy of formation of DNA minicircles. The shapes have been be determined from cryo-electron micrographs. Efficiency of formation has been investigated by a novel method called annealing-cyclization. Cryo-electron microscopy allows observation of very small molecules (here 17 or 11 nm diameter) in vitrified water, in order to keep the 3D shape of the molecules as close as possible to the shape they had in solution. In Chapter 1, I used stereo cryo-electron micrographs to determine and compare the three-dimensional shape of 95 individual DNA minicircles of 158 base pairs, which were identical in sequence except within a 18 bp block which contained either a TATA box sequence or a CAP site. I defined the notion of shape-distance which I used to estimate the error of reconstruction, and I detected clusters of shapes using an appropriate sorting algorithm. However the cluster did not seem to be associated with the variable sequence (TATA or CAP). I then analyzed (in Chapter 2) two-dimensional shapes of shorter DNA minicircles (94 bp) determined by negative staining electron microscopy, designed with either two nicks (breaks in one of the strands) or two gaps (missing nucleotides) at diametrically opposite sites of the minicircles. I observed that the gapped minicircles have an elongated shape with respect to the nicked minicircles, and I used this result together with the results of atomic level molecular dynamics simulations to conclude that the gap flexibility, perhaps together with base unpairing at the gap site, is responsible for this elongated minicircle shape. Finally, I proposed a ligase-free assay to measure the minicircle formation efficiency, which can give a high yield of nicked minicircles. The method avoids the use of ligase and the associated concerns about the effect of ligase concentration on the measurements. I determined an equation from a chemical model of the reaction that fits the experimental data, and I defined the Ja factor which gives a measure of the cyclization yield independent of DNA initial concentration. This method seems to confirm that minicircles with two gaps cyclize more efficiently that minicircles with two nicks, probably because of the gap flexibility. As a perspective, the conclusions of this thesis could be used for the design of minicircle constructs whose shape would be sensitive enough to sequence mutation in order to be detected by electron microscopy. Such shapes could be then compared, thanks to the shape-distance tool defined herein, to shapes computed with known or putative DNA models

Regulating Gene Expression Through DNA Mechanics: Tightly Looped DNA Represses Transcription.

It is now widely accepted that the mechanical state of DNA can play a major role in regulating the activity of RNA polymerase (RNAP). Not only have the global levels of supercoiling been shown to regulate transcription, but supercoiling has also been implicated in the transcriptional coupling of divergently oriented genes with closely spaced promoters. Additionally, many transcriptional repressors form tight loops of DNA by binding to multiple sites on a DNA template, challenging polymerases to transcribe a DNA template sustaining significant bending curvature. Many studies have provided evidence that the regulatory features of divergent promoter and loop-forming repressor systems share a dependence on the mechanical state of DNA, but these observations have been phenomenological in nature and fail to provide us with a mechanistic understanding of the relationship between RNAP activity as a function of the bending and twisting of DNA in these systems. Consequently, the direct role played by DNA mechanics in these systems remains unclear. I have hypothesized that the mechanical stress within highly bent DNA is itself sufficient to repress transcription. To test this hypothesis, I have developed an assay capable of quantifying the ability of bacteriophage T7 RNAP to transcribe small, circular DNA templates sustaining high levels of bending and torsional stresses. I have characterized both the pre-elongation and elongation kinetics using a highly untwisted 100 bp minicircle, an overtwisted 106 bp minicircle, and a mildly untwisted 108 bp minicircle template. In addition, I have used cryo-electron microscopy to directly observe the topological consequences of the torsional stress sustained within each DNA minicircle species at the single molecule level. Herein, I show that DNA minicircles on the order of 100bp can sustain significant torsional stress without relief by supercoiling, highly bent DNA is directly repressive to transcription, and torsional stress sustained within the DNA template modulates the elongation velocity and processivity of T7 RNAP. The data support a model in which DNA bending can directly control RNAP activity and call for more detailed studies to relate the mechanistic details emerging from this work to regulatory systems known to impart significant bends within the DNA template.Ph.D.Cellular & Molecular BiologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75859/1/talion_1.pd

Local Geometric Transformations in Image Analysis

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric transformations such as rotation, translation, and scaling, with a special emphasis on wavelet representations. In the first part of the thesis, our main interest is in the analysis of directional patterns and the estimation of their location and orientation. We explore steerable representations that correspond to the notion of rotation. Contrarily to classical pattern matching techniques, they have no need for an a priori discretization of the angle and for matching the filter to the image at each discretized direction. Instead, it is sufficient to apply the filtering only once. Then, the rotated filter for any arbitrary angle can be determined by a systematic and linear transformation of the initial filter. We derive the Cramér-Rao bounds for steerable filters. They allow us to select the best harmonics for the design of steerable detectors and to identify their optimal radial profile. We propose several ways to construct optimal representations and to build powerful and effective detector schemes; in particular, junctions of coinciding branches with local orientations. The basic idea of local transformability and the general principles that we utilize to design steerable wavelets can be applied to other geometric transformations. Accordingly, in the second part, we extend our framework to other transformation groups, with a particular interest in scaling. To construct representations in tune with a notion of local scale, we identify the possible solutions for scalable functions and give specific criteria for their applicability to wavelet schemes. Finally, we propose discrete wavelet frames that approximate a continuous wavelet transform. Based on these results, we present a novel wavelet-based image-analysis software that provides a fast and automatic detection of circular patterns, combined with a precise estimation of their size

Mechanics and Function of DNA Looping and Supercoiling.

DNA is an essential molecule that enables the storage and retrieval of genetic information. Since the discovery of its structure (double helix), the relationship between the molecule's structure and function has been studied extensively. Here we extend beyond the static structure and consider how the mechanical properties and dynamics influence its function. To do so, we exercise an elasto-dynamic rod model for DNA. By exercising this model, we study two biologically relevant systems. First, we study DNA looping by Lac repressor. Although this is a classic gene regulatory system, the mechanics of the DNA loop remain largely unknown. Therefore, we compute the effects of inter-operator length, intrinsic curvature, and protein flexibility on the energetics and topology these loops. We calculate that anti-parallel loops are energetically preferred, the elastic energy of a family of intrinsically curved DNA loops spans 5-12 kT, and identify the sensitivity of elastic energy to protein flexibility. Our computations compare favorably with published experimental data and motivate experimental work in the Kahn lab at the University of Maryland. Furthermore, we contribute an efficient method to analyze a large family of intrinsically curved DNA molecules and a method to account for Lac repressor flexibility in our rod model. In addition, we analyze cryo-EM images (obtained by the Stasiak lab at the Université de Lausanne) of DNA minicircles with similar lengths to the Lac repressor DNA loops. Second, we study the relaxation of DNA supercoils by topoisomerase. In doing so, we make advancements to the rod model and perform the first multi-scale model of supercoil relaxation by topoisomerase. Specifically, we contribute an efficient method to account for self contact and electrostatics in our elastic rod model. In our multi-scale simulation we couple our rod model with recent data (from MD simulations by the Andricioaei lab at the University of California - Irvine) that characterizes the the mechanics of topoisomerase. In doing so we gain insight into the dynamics of supercoil relaxation and make a first prediction of the relaxation time (0.1-1.0 μs).Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75861/1/tlillian_1.pd