Shafigh Mehraeen

Tension-dependent structural deformation alters single-molecule transition kinetics

We analyze the response of a single nucleosome to tension, which serves as a prototypical biophysical measurement where tension-dependent deformation alters transition kinetics. We develop a statistical-mechanics model of a nucleosome as a wormlike chain bound to a spool, incorporating fluctuations in the number of bases bound, the spool orientation, and the conformations of the unbound polymer segments. With the resulting free-energy surface, we perform dynamic simulations that permit a direct comparison with experiments. This simple approach demonstrates that the experimentally observed structural states at nonzero tension are a consequence of the tension and that these tension-induced states cease to exist at zero tension. The transitions between states exhibit substantial deformation of the unbound polymer segments. The associated deformation energy increases with tension; thus, the application of tension alters the kinetics due to tension-induced deformation of the transition states. This mechanism would arise in any system where the tether molecule is deformed in the transition state under the influence of tension.

Correlating Non-Geminate Recombination with Film Structure: A Comparison of Polythiophene: Fullerene Bilayer and Blend Films

The morphology of the active layer in polymer:fullerene solar cells is a key parameter in determining their performance. In this study we monitor the charge carrier dynamics in bilayers of poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) (fabricated by sequential spin coating and vacuum deposition) before and after thermal annealing, and compare these against conventional solution processed bulk heterojunction (BHJ) blend films. Transmission electron microscopy images, supported by field effect mobility data show that while not-annealed P3HT/PC61BM bilayers possess a sharp interface, intermixing proceeds upon annealing. Transient absorption studies indicate that the not-annealed bilayer yields fewer, but longer lived, charge carriers compared to the BHJ. Monte Carlo (MC) simulations further suggest that the difference in non-geminate recombination dynamics observed for the BHJ and bilayer films could be related to the confinement of charge carriers to the interface, with the lower dimensionality for the flat interface bilayer films relative to the intercalated donor-acceptor network BHJ films leading to lower recombination.

Membrane fluctuations destabilize clathrin protein lattice order.

We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.

Impact of Defect Creation and Motion on the Thermodynamics and Large-Scale Reorganization of Self-Assembled Clathrin Lattices

We develop a theoretical model for the thermodynamics and kinetics of clathrin self-assembly. Our model addresses the behavior in two dimensions and can be easily extended to three dimensions, facilitating the study of membrane, surface, and bulk assembly. The clathrin triskelia are modeled as flexible pinwheels that form leg-leg associations and resist bending and stretching deformations. Thus, the pinwheels are capable of forming a range of ring structures, including 5-, 6-, and 7-member rings that are observed experimentally. Our theoretical model employs Brownian dynamics to track the motion of clathrin pinwheels at sufficiently long time scales to achieve complete assembly. Invoking theories of dislocation-mediated melting in two dimensions, we discuss the phase behavior for clathrin self-assembly as predicted by our theoretical model. We demonstrate that the generation of 5–7 defects in an otherwise perfect honeycomb lattice resembles creation of two dislocations with equal and opposite Burgers vectors. We use orientational- and translational-order correlation functions to predict the crystalline-hexatic and hexatic-liquid phase transitions in clathrin lattices. These results illustrate the pivotal role that molecular elasticity plays in the physical behavior of self-assembling and self-healing materials.

Theoretical Modeling of the Weaving of Clathrin into Nanoscale Baskets

Many biological systems are capable of spontaneously assembling a diverse set of molecular architectures from a single subunit, without the need to pre-pattern the assembly. Cellular uptake of external substances is accomplished by a highly adaptive endocytosis process that accommodates a wide range of cargo shapes and sizes. Clathrin-mediated endocytosis involves the formation of a pit that is surrounded by a honeycomb coating whose pinwheel-shaped subunit is a clathrin-protein complex. We develop a theoretical model for the thermodynamics and kinetics of clathrin assembly, addressing the behavior in 2 and 3 dimensions, relevant to membrane and bulk assembly, respectively. The clathrin triskelions are modeled as effective flexible pinwheels that form leg-leg associations and resist elastic deformation. Thus, the pinwheels are capable of forming a range of ring structures, including 5-, 6-, and 7-member rings that are observed experimentally. Our theoretical model employs Monte Carlo simulations to address thermodynamic behavior and Brownian dynamics simulations to track the motion of clathrin pinwheels at sufficiently long time scales to achieve complete assembly. With this theoretical model, we predict the phase diagram for clathrin assembly incorporating binding interactions, elastic deformation, and defect-pair coupling, utilizing Kosterlitz-Thouless theory of defect-induced melting in 2 dimensions. Using analytical theory and computational simulations, we explore the role of binding strength and clathrin elasticity in the ability for clathrin lattices to dynamically reorganize due to local changes in membrane elasticity and tension. We then proceed to discuss the dynamics of lattice reorganization during the process of a clathrin-coated membrane wrapping around a nanoscale cargo.

A Predictive Theoretical Model For Clathrin Self-Assembly

Clathrin is a protein that plays a major role in the creation of membrane-bound transport vesicles in cells. Clathrin forms soccer-ball-shaped lattices that coat a new vesicle as it forms. The clathrin molecule is known to take the shape of a triskelion, a figure with three bent legs. In vitro assembly of clathrin within a solution results in closed, nanoscale assemblies with various shapes and sizes. To understand how clathrin functions, particularly how it forms the lattice, we develop a theoretical model for the thermodynamics and kinetics of clathrin assembly in order to guide experiments toward the design of targeted nanoscale structures. Our model addresses the behavior in 2 and 3 dimensions, relevant to membrane/surface and bulk assembly, respectively. The clathrin triskelions are modeled as effective flexible pinwheels that form leg-leg associations and resist elastic bending and stretching deformations. Thus, the pinwheels are capable of forming a range of ring structures including 5-, 6-, and 7-member rings that are observed experimentally. Our theoretical model employs Brownian dynamics to track the motion of clathrin pinwheels at sufficiently long time scales to achieve complete assembly. With this theoretical model, we predict the phase diagram for clathrin assembly incorporating binding interactions, elastic deformation, and phonon modes. To verify the phase diagram, we perform dynamic simulations for a range of quenches into the phase diagram and compare phase separation across the binodal curve. We show that resulting Brownian dynamics simulations exhibit the hallmark behavior of spinodal decomposition with subsequent coarsening of ordered domains. These simulations demonstrate the effect of quench rate and leg elasticity on the final configurations of the lattice network and cluster-size distribution. We then proceed to discuss the assembly of specific nanoscale structures.