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Starr CH, Bryant Z, Spakowitz AJ. Coarse-grained modeling reveals the impact of supercoiling and loop length in DNA looping kinetics. Biophys J 2022; 121:1949-1962. [PMID: 35421389 PMCID: PMC9199097 DOI: 10.1016/j.bpj.2022.04.009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2021] [Revised: 11/19/2021] [Accepted: 04/06/2022] [Indexed: 11/02/2022] Open
Abstract
Measurements of protein-mediated DNA looping reveal that in vivo conditions favor the formation of loops shorter than those that occur in vitro, yet the precise physical mechanisms underlying this shift remain unclear. To understand the extent to which in vivo supercoiling may explain these shifts, we develop a theoretical model based on coarse-grained molecular simulation and analytical transition state theory, enabling us to map out looping energetics and kinetics as a function of two key biophysical parameters: superhelical density and loop length. We show that loops on the scale of a persistence length respond to supercoiling over a much wider range of superhelical densities and to a larger extent than longer loops. This effect arises from a tendency for loops to be centered on the plectonemic end region, which bends progressively more tightly with superhelical density. This trend reveals a mechanism by which supercoiling favors shorter loop lengths. In addition, our model predicts a complex kinetic response to supercoiling for a given loop length, governed by a competition between an enhanced rate of looping due to torsional buckling and a reduction in looping rate due to chain straightening as the plectoneme tightens at higher superhelical densities. Together, these effects lead to a flattening of the kinetic response to supercoiling within the physiological range for all but the shortest loops. Using experimental estimates for in vivo superhelical densities, we discuss our model's ability to explain available looping data, highlighting both the importance of supercoiling as a regulatory force in genetics and the additional complexities of looping phenomena in vivo.
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Affiliation(s)
- Charles H Starr
- Biophysics Program, Stanford University, Stanford, California
| | - Zev Bryant
- Biophysics Program, Stanford University, Stanford, California; Department of Bioengineering, Stanford University, Stanford, California
| | - Andrew J Spakowitz
- Biophysics Program, Stanford University, Stanford, California; Department of Chemical Engineering, Stanford University, Stanford, California; Department of Materials Science and Engineering, Stanford University, Stanford, California; Department of Applied Physics, Stanford University, Stanford, California.
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2
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Borba AR, Serra TS, Górska A, Gouveia P, Cordeiro AM, Reyna-Llorens I, Kneřová J, Barros PM, Abreu IA, Oliveira MM, Hibberd JM, Saibo NJM. Synergistic Binding of bHLH Transcription Factors to the Promoter of the Maize NADP-ME Gene Used in C4 Photosynthesis Is Based on an Ancient Code Found in the Ancestral C3 State. Mol Biol Evol 2018; 35:1690-1705. [PMID: 29659975 PMCID: PMC5995220 DOI: 10.1093/molbev/msy060] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
C4 photosynthesis has evolved repeatedly from the ancestral C3 state to generate a carbon concentrating mechanism that increases photosynthetic efficiency. This specialized form of photosynthesis is particularly common in the PACMAD clade of grasses, and is used by many of the world's most productive crops. The C4 cycle is accomplished through cell-type-specific accumulation of enzymes but cis-elements and transcription factors controlling C4 photosynthesis remain largely unknown. Using the NADP-Malic Enzyme (NADP-ME) gene as a model we tested whether mechanisms impacting on transcription in C4 plants evolved from ancestral components found in C3 species. Two basic Helix-Loop-Helix (bHLH) transcription factors, ZmbHLH128 and ZmbHLH129, were shown to bind the C4NADP-ME promoter from maize. These proteins form heterodimers and ZmbHLH129 impairs trans-activation by ZmbHLH128. Electrophoretic mobility shift assays indicate that a pair of cis-elements separated by a seven base pair spacer synergistically bind either ZmbHLH128 or ZmbHLH129. This pair of cis-elements is found in both C3 and C4 Panicoid grass species of the PACMAD clade. Our analysis is consistent with this cis-element pair originating from a single motif present in the ancestral C3 state. We conclude that C4 photosynthesis has co-opted an ancient C3 regulatory code built on G-box recognition by bHLH to regulate the NADP-ME gene. More broadly, our findings also contribute to the understanding of gene regulatory networks controlling C4 photosynthesis.
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Affiliation(s)
- Ana Rita Borba
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Tânia S Serra
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Alicja Górska
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Paulo Gouveia
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - André M Cordeiro
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Ivan Reyna-Llorens
- Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Jana Kneřová
- Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Pedro M Barros
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
| | - Isabel A Abreu
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Maria Margarida Oliveira
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
| | - Julian M Hibberd
- Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom
| | - Nelson J M Saibo
- Instituto de Tecnologia Química e Biológica António Xavier, Universidade Nova de Lisboa, Oeiras, Portugal
- Instituto de Biologia Experimental e Tecnológica, Oeiras, Portugal
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3
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Guérin T. Analytical expressions for the closure probability of a stiff wormlike chain for finite capture radius. Phys Rev E 2017; 96:022501. [PMID: 28950625 DOI: 10.1103/physreve.96.022501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2015] [Indexed: 11/07/2022]
Abstract
Estimating the probability that two monomers of the same polymer chain are close together is a key ingredient to characterize intramolecular reactions and polymer looping. In the case of stiff wormlike polymers (rigid fluctuating elastic rods), for which end-to-end encounters are rare events, we derive an explicit analytical formula for the probability η(r_{c}) that the distance between the chain extremities is smaller than some capture radius r_{c}. The formula is asymptotically exact in the limit of stiff chains, and it leads to the identification of two distinct scaling regimes for the closure factor, originating from a strong variation of the fluctuations of the chain orientation at closure. Our theory is compatible with existing analytical results from the literature that cover the cases of a vanishing capture radius and of nearly fully extended chains.
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Affiliation(s)
- T Guérin
- Laboratoire Ondes et Matiere d'Aquitaine, CNRS UMR 5798, Université de Bordeaux, Talence, France
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4
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Jeong J, Le TT, Kim HD. Single-molecule fluorescence studies on DNA looping. Methods 2016; 105:34-43. [PMID: 27064000 PMCID: PMC4967024 DOI: 10.1016/j.ymeth.2016.04.005] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2015] [Revised: 04/01/2016] [Accepted: 04/05/2016] [Indexed: 11/17/2022] Open
Abstract
Structure and dynamics of DNA impact how the genetic code is processed and maintained. In addition to its biological importance, DNA has been utilized as building blocks of various nanomachines and nanostructures. Thus, understanding the physical properties of DNA is of fundamental importance to basic sciences and engineering applications. DNA can undergo various physical changes. Among them, DNA looping is unique in that it can bring two distal sites together, and thus can be used to mediate interactions over long distances. In this paper, we introduce a FRET-based experimental tool to study DNA looping at the single molecule level. We explain the connection between experimental measurables and a theoretical concept known as the J factor with the intent of raising awareness of subtle theoretical details that should be considered when drawing conclusions. We also explore DNA looping-assisted protein diffusion mechanism called intersegmental transfer using protein induced fluorescence enhancement (PIFE). We present some preliminary results and future outlooks.
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Affiliation(s)
- Jiyoun Jeong
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta 30332, USA.
| | - Tung T Le
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta 30332, USA.
| | - Harold D Kim
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta 30332, USA.
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5
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Abstract
Loops undergoing thermal fluctuations are prevalent in nature. Ringlike or cross-linked polymers, cyclic macromolecules, and protein-mediated DNA loops all belong to this category. Stability of these molecules are generally described in terms of free energy, an average quantity, but it may also be impacted by local fluctuating forces acting within these systems. The full distribution of these forces can thus give us insights into mechanochemistry beyond the predictive capability of thermodynamics. In this paper, we study the force exerted by an inextensible semiflexible polymer constrained in a looped state. By using a simulation method termed "phase-space sampling," we generate the equilibrium distribution of chain conformations in both position and momentum space. We compute the constraint forces between the two ends of the loop in this chain ensemble using Lagrangian mechanics, and show that the mean of these forces is equal to the thermodynamic force. By analyzing kinetic and potential contributions to the forces, we find that the mean force acts in the direction of increasing extension not because of bending stress, but in spite of it. Furthermore, we obtain a distribution of constraint forces as a function of chain length, extension, and stiffness. Notably, increasing contour length decreases the average force, but the additional freedom allows fluctuations in the constraint force to increase. The force distribution is asymmetric and falls off less sharply than a Gaussian distribution. Our work exemplifies a system where large-amplitude fluctuations occur in a way unforeseen by a purely thermodynamic framework, and offers computational tools useful for efficient, unbiased simulation of a constrained system.
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Affiliation(s)
- James T Waters
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA
| | - Harold D Kim
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, Georgia 30332-0430, USA
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6
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Marple GR, Purohit PK, Veerapaneni S. Equilibrium shapes of planar elastic membranes. Phys Rev E 2015; 92:012405. [PMID: 26274184 DOI: 10.1103/physreve.92.012405] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2014] [Indexed: 11/07/2022]
Abstract
Using a rod theory formulation, we derive equations of state for a thin elastic membrane subjected to several different boundary conditions-clamped, simply supported, and periodic. The former is applicable to membranes supported on a softer substrate and subjected to uniaxial compression. We show that a wider family of quasistatic equilibrium shapes exist beyond the previously obtained analytical solutions. In the latter case of periodic membranes, we were able to derive exact solutions in terms of elliptic functions. These equilibria are verified by considering a fluid-structure interaction problem of a periodic, length-preserving bilipid membrane modeled by the Helfrich energy immersed in a viscous fluid. Starting from an arbitrary shape, the membrane dynamics to equilibrium are simulated using a boundary integral method.
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Affiliation(s)
- Gary R Marple
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Prashant K Purohit
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Shravan Veerapaneni
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, USA
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7
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Abstract
Sharp bending of double-stranded DNA (dsDNA) plays an essential role in genome structure and function. However, the elastic limit of dsDNA bending remains controversial. Here, we measured the opening rates of small dsDNA loops with contour lengths ranging between 40 and 200 bp using single-molecule Fluorescence Resonance Energy Transfer. The relationship of loop lifetime to loop size revealed a critical transition in bending stress. Above the critical loop size, the loop lifetime changed with loop size in a manner consistent with elastic bending stress, but below it, became less sensitive to loop size, indicative of softened dsDNA. The critical loop size increased from ∼60 bp to ∼100 bp with the addition of 5 mM magnesium. We show that our result is in quantitative agreement with the kinkable worm-like chain model, and furthermore, can reproduce previously reported looping probabilities of dsDNA over the range between 50 and 200 bp. Our findings shed new light on the energetics of sharply bent dsDNA.
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Affiliation(s)
- Tung T Le
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332, USA
| | - Harold D Kim
- School of Physics, Georgia Institute of Technology, 837 State Street, Atlanta, GA 30332, USA
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8
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Ayyaswamy PS, Muzykantov V, Eckmann DM, Radhakrishnan R. Nanocarrier Hydrodynamics and Binding in Targeted Drug Delivery: Challenges in Numerical Modeling and Experimental Validation. J Nanotechnol Eng Med 2013; 4:101011-1010115. [PMID: 23917383 PMCID: PMC3708709 DOI: 10.1115/1.4024004] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2012] [Revised: 03/06/2013] [Indexed: 11/08/2022]
Abstract
This review discusses current progress and future challenges in the numerical modeling of targeted drug delivery using functionalized nanocarriers (NC). Antibody coated nanocarriers of various size and shapes, also called functionalized nanocarriers, are designed to be injected in the vasculature, whereby they undergo translational and rotational motion governed by hydrodynamic interaction with blood particulates as well as adhesive interactions mediated by the surface antibody binding to target antigens/receptors on cell surfaces. We review current multiscale modeling approaches rooted in computational fluid dynamics and nonequilibrium statistical mechanics to accurately resolve fluid, thermal, as well as adhesive interactions governing nanocarrier motion and their binding to endothelial cells lining the vasculature. We also outline current challenges and unresolved issues surrounding the modeling methods. Experimental approaches in pharmacology and bioengineering are discussed briefly from the perspective of model validation.
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Affiliation(s)
- Portonovo S. Ayyaswamy
- Department of Mechanical Engineering and Applied Mechanics,University of Pennsylvania,Philadelphia, PA 19104
| | - Vladimir Muzykantov
- Department of Pharmacology,and Center for Targeted Therapeutics and Translational Nanomedicine,University of Pennsylvania,Philadelphia, PA 19104
| | - David M. Eckmann
- Institute of Translational Medicine and Therapeutics,Department of Anesthesiology and Critical Care,and Department of Bioengineering,University of Pennsylvania,Philadelphia, PA 19104
| | - Ravi Radhakrishnan
- Institute of Translational Medicine and Therapeutics,Department of Bioengineering,Department of Chemical and Biomolecular Engineering,University of Pennsylvania,Philadelphia, PA 19104e-mail:
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9
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Argudo D, Purohit PK. The dependence of DNA supercoiling on solution electrostatics. Acta Biomater 2012; 8:2133-43. [PMID: 22330280 DOI: 10.1016/j.actbio.2012.01.030] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2011] [Revised: 01/20/2012] [Accepted: 01/26/2012] [Indexed: 11/29/2022]
Abstract
We develop an elastic-isotropic rod model for twisted DNA in the plectonemic regime. We account for DNA elasticity, electrostatic interactions and entropic effects due to thermal fluctuations. We apply our model to single-molecule experiments on a DNA molecule attached to a substrate at one end, while subjected to a tensile force and twisted by a given number of turns at the other end. The free energy of the DNA molecule is minimized subject to the imposed end rotations. We compute values of the torsional stress, radius, helical angle and key features of the rotation-extension curves. We also include in our model the end loop energetic contributions and obtain estimates for the jumps in the external torque and extension of the DNA molecule seen in experiments. We find that, while the general trends seen in experiments are captured simply by rod mechanics, the details can be accounted for only with the proper choice of electrostatic and entropic interactions. We perform calculations with different ionic concentrations and show that our model yields excellent fits to mechanical data from a large number of experiments. Our methods also allow us to consider scenarios where we have multiple plectonemes or a series of loops forming in the DNA instead of plectonemes. For a given choice of electrostatic and entropic interactions, we find there is a range of forces in which the two regimes can coexist due to thermal motion.
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Affiliation(s)
- David Argudo
- Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA
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10
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Hirsh AD, Lillian TD, Lionberger TA, Perkins NC. DNA modeling reveals an extended lac repressor conformation in classic in vitro binding assays. Biophys J 2011; 101:718-26. [PMID: 21806940 DOI: 10.1016/j.bpj.2011.06.040] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2011] [Revised: 06/03/2011] [Accepted: 06/21/2011] [Indexed: 10/17/2022] Open
Abstract
Protein-mediated DNA looping, such as that induced by the lactose repressor (LacI) of Escherichia coli, is a well-known gene regulation mechanism. Although researchers have given considerable attention to DNA looping by LacI, many unanswered questions about this mechanism, including the role of protein flexibility, remain. Recent single-molecule observations suggest that the two DNA-binding domains of LacI are capable of splaying open about the tetramerization domain into an extended conformation. We hypothesized that if recent experiments were able to reveal the extended conformation, it is possible that such structures occurred in previous studies as well. In this study, we tested our hypothesis by reevaluating two classic in vitro binding assays using a computational rod model of DNA. The experiments and computations evaluate the looping of both linear DNA and supercoiled DNA minicircles over a broad range of DNA interoperator lengths. The computed energetic minima align well with the experimentally observed interoperator length for optimal loop stability. Of equal importance, the model reveals that the most stable loops for linear DNA occur when LacI adopts the extended conformation. In contrast, for DNA minicircles, optimal stability may arise from either the closed or the extended protein conformation depending on the degree of supercoiling and the interoperator length.
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Affiliation(s)
- Andrew D Hirsh
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, USA
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11
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Cotta-Ramusino L, Maddocks JH. Looping probabilities of elastic chains: a path integral approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:051924. [PMID: 21230517 DOI: 10.1103/physreve.82.051924] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/05/2010] [Revised: 08/02/2010] [Indexed: 05/30/2023]
Abstract
We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.
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Affiliation(s)
- Ludovica Cotta-Ramusino
- Laboratory for Computation and Visualization in Mathematics and Mechanics, EPFL FSB IMB, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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12
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Becker NB, Rosa A, Everaers R. The radial distribution function of worm-like chains. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2010; 32:53-69. [PMID: 20517631 DOI: 10.1140/epje/i2010-10596-0] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2009] [Revised: 03/10/2010] [Accepted: 04/21/2010] [Indexed: 05/29/2023]
Abstract
Thermal conformations of semiflexible macromolecules are generically described by the worm-like chain model. The end-to-end distance distribution, a fundamental quantity of the model, is not yet known in closed form. We provide a solution to the practical problem of choosing an appropriate approximation. First, a comprehensive review of existing approximations and exact limiting results is given. We then propose an explicit expression which interpolates between all relevant limiting cases. We show that it accurately reproduces, at no computational cost, high-precision Monte Carlo data, covering a wide range from stiff to flexible chains and from looped to fully stretched configurations. Using this result we quantify the enhancement of short worm-like loop formation by (protein) bridges.
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Affiliation(s)
- N B Becker
- Laboratoire de Physique of the Ecole Normale Supérieure de Lyon, Université de Lyon, 46 allée d'Italie, 69364 Lyon cedex 07, France.
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13
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Towles KB, Beausang JF, Garcia HG, Phillips R, Nelson PC. First-principles calculation of DNA looping in tethered particle experiments. Phys Biol 2009; 6:025001. [PMID: 19571369 PMCID: PMC3298194 DOI: 10.1088/1478-3975/6/2/025001] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in tethered particle motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. We show how to compute both the 'looping J factor' (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on TPM, and then compare to our model's predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 k(B)T, for loops of length around 300 basepairs. More significantly, our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical 'open' conformation of the LacI tetramer.
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Affiliation(s)
- Kevin B Towles
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - John F Beausang
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
| | - Hernan G Garcia
- Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | - Rob Phillips
- Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
| | - Philip C Nelson
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA
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14
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Melzer R, Verelst W, Theissen G. The class E floral homeotic protein SEPALLATA3 is sufficient to loop DNA in 'floral quartet'-like complexes in vitro. Nucleic Acids Res 2008; 37:144-57. [PMID: 19033361 PMCID: PMC2615621 DOI: 10.1093/nar/gkn900] [Citation(s) in RCA: 108] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The organs of a eudicot flower are specified by four functional classes, termed class A, B, C and E, of MADS domain transcription factors. The combinatorial formation of tetrameric complexes, so called 'floral quartets', between these classes is widely believed to represent the molecular basis of floral organ identity specification. As constituents of all complexes, the class E floral homeotic proteins are thought to be of critical relevance for the formation of floral quartets. However, experimental support for tetrameric complex formation remains scarce. Here we provide physico-chemical evidence that in vitro homotetramers of the class E floral homeotic protein SEPALLATA3 from Arabidopsis thaliana bind cooperatively to two sequence elements termed 'CArG boxes' in a phase-dependent manner involving DNA looping. We further show that the N-terminal part of SEPALLATA3 lacking K3, a subdomain of the protein-protein interactions mediating K domain, and the C-terminal domain, is sufficient for protein dimerization, but not for tetramer formation and cooperative DNA binding. We hypothesize that the capacity of class E MADS domain proteins to form tetrameric complexes contributes significantly to the formation of floral quartets. Our findings further suggest that the spacing and phasing of CArG boxes are important parameters in the molecular mechanism by which floral homeotic proteins achieve target gene specificity.
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Affiliation(s)
- Rainer Melzer
- Department of Genetics, Friedrich Schiller University Jena, Jena, Germany
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