Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session T40: Focus Session: Knots and Loops in Biomolecules |
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Sponsoring Units: DBP Chair: Joanna Sulkowska, University of California, San Diego Room: 412 |
Wednesday, March 18, 2009 2:30PM - 3:06PM |
T40.00001: Dodging the crisis of folding proteins with knots Invited Speaker: Proteins with nontrivial topology, containing knots and slipknots, have the ability to fold to their native states without any additional external forces invoked. A mechanism is suggested for folding of these proteins, such as YibK and YbeA, which involves an intermediate configuration with a slipknot. It elucidates the role of topological barriers and backtracking during the folding event. It also illustrates that native contacts are sufficient to guarantee folding in around 1-2\% of the simulations, and how slipknot intermediates are needed to reduce the topological bottlenecks. As expected, simulations of proteins with similar structure but with knot removed fold much more efficiently, clearly demonstrating the origin of these topological barriers. Although these studies are based on a simple coarse-grained model, they are already able to extract some of the underlying principles governing folding in such complex topologies. [Preview Abstract] |
Wednesday, March 18, 2009 3:06PM - 3:18PM |
T40.00002: Size and Shape of Knotted Polymers Eric Rawdon We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their size and shape. In particular, we analyze different types of geometric containers that envelope polymer configurations and describe the similarities and differences between them. This work has been done in collaborations with Akos Dobay, John Kern, Kenneth Millett, Michael Piatek, Patrick Plunkett, and Andrzej Stasiak. [Preview Abstract] |
Wednesday, March 18, 2009 3:18PM - 3:30PM |
T40.00003: On the geometry of stiff knots Olivier Pierre-Louis We report on the geometry and mechanics of knotted strings. We focus on the situation where the string is stiff (it has a large bending rigidity), and thin (its width is much smaller than its length). We find that: (i) the equilibrium energy depends on the type of knot as the square of the bridge number; (ii) braid localization is a general feature of stiff strings entanglements; (iii) there is an upper bound for the multiplicity of the braids and contact points in the ground state. (iv) Finally, a general confinement inequality is used to derive an upper bound on the knot gyration radius. We shall also discuss the asymptotic behavior of the knot when the filament width is small, both in the presence and in the absence of torsion (twist) energy. We conjecture a universal ground state geometry for thin strings with torsion rigidity in the presence of a large twists. Ref: R. Gallotti, O. Pierre-Louis, Phys. Rev. E 75, 031801 (2007). [Preview Abstract] |
Wednesday, March 18, 2009 3:30PM - 3:42PM |
T40.00004: Conformation and Dynamics of Linear Chains, Circular and Partial Loops Jen-Fang Chang, Yeng-Long Chen Recent single molecule experiments have reported the diffusivity ratio between circular and linear DNA of the same molecular weight to be 1.3, between the ratio predict by renormalization group theory (1.45) and classical Kirkwood theory (1.18). In earlier light and neutron scattering measurements of synthetic polymers, the ratio has been reported to be around 1.1-1.2. Our work employs the Lattice-Boltzmann method with Brownian dynamics to examine the diffusivity ratio for a long chain (N=320). We also examined partially closed loops that are half-closed, quarter-closed, and eighth-closed with the same contour length. Surprisingly, we find that the loop with the smallest radiuses of gyration and the highest diffusivity is not the fully closed (circular) loop, but a partially-closed one. [Preview Abstract] |
Wednesday, March 18, 2009 3:42PM - 3:54PM |
T40.00005: Modeling the behavior of DNA-loop-extruding enzymes Elnaz A. Baum-Snow, John F. Marko Condensin proteins are large complexes belonging to a family of ATP hydrolyzing proteins known as SMC (Structural Maintenance of Chromosomes). Condensins are believed to play a vital role in chromosomal assembly and segregation in eukaryotic cells but the details of their function along chromatin are poorly understood. Here, we propose a model to describe the behavior of DNA-loop-inducing proteins, such as type I restriction enzymes, which we believe can be used to understand condensin's function. We assume an effective motor behavior for these enzymes in which the bias of the two dimer heads is to travel away from each other, which results in loop formation along the DNA lattice. Processivity causes the enzymes to stack on top of each other. We further discuss the results of theory and computer simulations for different values of motor bias and processivity. [Preview Abstract] |
Wednesday, March 18, 2009 3:54PM - 4:30PM |
T40.00006: Intricate knots in proteins: statistics, function and evolution Invited Speaker: Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. These elusive knots are present in the backbone of only about 1 in 200 proteins. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In this talk I will present an overview of these peculiar structures from the current version of the Protein Data Bank and discuss some particularly intriguing examples of this set as well as evolutionary and functional implications. [Preview Abstract] |
Wednesday, March 18, 2009 4:30PM - 4:42PM |
T40.00007: The Role of Entropic Effects on DNA Loop Formation David Wilson, Alexei Tkachenko, Todd Lillian, Noel Perkins, Jens Christian Meiners The formation of protein mediated DNA loops often regulates gene expression. Typically, a protein is simultaneously bound to two DNA operator sites. An example is the lactose repressor which binds to the Lac operon of \textit{E. coli}. We characterize the mechanics of this system by calculating the free energy cost of loop formation. We construct a Hamiltonian that describes the change in DNA bending energy due to linear perturbations about the looped and open states,~starting from a non-linear mechanical rod model that determines the shape and bending energy of the inter-operator DNA loop while capturing the intrinsic curvature and sequence-dependent elasticity of the DNA. The crystal structure of the LacI protein provides the boundary conditions for the DNA. We then calculate normal modes of the open and closed loops to account for the thermal fluctuations. The ratio of determinants of the two Hamiltonians yields the partition function, and the enthalphic and entropic cost of looping. This calculation goes beyond standard elastic energy models because it fully accounts for the substantial entropic differences between the two states. It also includes effects of sequence dependent curvature and stiffness and allows anisotropic variations in persistence length. From the free energy we then calculate the J-factor and ratio of loop lifetimes. [Preview Abstract] |
Wednesday, March 18, 2009 4:42PM - 4:54PM |
T40.00008: Helical growth trajectories in plant roots interacting with stiff barriers Sharon Gerbode, Roslyn Noar, Maria Harrison Plant roots successfully navigate heterogeneous soil environments with varying nutrient and water concentrations, as well as a variety of stiff obstacles. While it is thought that the ability of roots to penetrate into a stiff lower soil layer is important for soil erosion, little is known about how a root actually responds to a rigid interface. We have developed a laser sheet imaging technique for recording the 3D growth dynamics of plant roots interacting with stiff barriers. We find that a root encountering an angled interface does not grow in a straight line along the surface, but instead follows a helical trajectory. These experiments build on the pioneering studies of roots grown on a tilted 2D surface, which reported ``root waving,'' a similar curved pattern thought to be caused by the root's sensitivity to both gravity and the rigid surface on which it is grown. Our measurements extend these results to the more physiologically relevant case of 3D growth, where the spiral trajectory can be altered by tuning the relative strengths of the gravity and touch stimuli, providing some intuition for the physical mechanism driving it. [Preview Abstract] |
Wednesday, March 18, 2009 4:54PM - 5:06PM |
T40.00009: The Penrose-Hameroff Orchestrated Objective-Reduction Proposal for Human Consciousness is Not Biologically Feasible Jeffrey Reimers, Laura McKemmish, Noel Hush, Ross McKenzie, Alan Mark Penrose and Hameroff have argued that conventional models of brain function based solely on neural linear-computational elements cannot account for human consciousness, claiming instead that quantum-computation elements are required. Specifically, in their Orchestrated Objective Reduction (Orch OR) model it is postulated that microtubules act as quantum processing units, with individual tubulin dimers forming the computational elements. This model requires that tubulin is able to switch between alternative conformational states in a coherent manner, and that this process be rapid on the physiological time scale. Here the biological feasibility of the Orch OR proposal is examined in light of recent experimental studies on microtubule assembly and dynamics. It is shown that tubulins do not possess essential properties required for the Orch OR proposal, as originally proposed, to hold. Further, we extensively consider the likelihood of Fr\"{o}hlich condensates producing coherent motions in biological systems, a feature critical to Orch OR, and show that no biologically feasible reformation of the proposal could lead to the production of a quantum processor. Hence the Orch OR model is not a feasible explanation of the origin of consciousness. [Preview Abstract] |
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