Quantum mechanical calculation of the effects of stiff and rigid constraints in the conformational equilibrium of the Alanine dipeptide

If constraints are imposed on a macromolecule, two inequivalent classical models may be used: the stiff and the rigid one. This work studies the effects of such constraints on the Conformational Equilibrium Distribution (CED) of the model dipeptide HCO-L-Ala-NH2 without any simplifying assumption. We use ab initio Quantum Mechanics calculations including electron correlation at the MP2 level to describe the system, and we measure the conformational dependence of all the correcting terms to the naive CED based in the Potential Energy Surface (PES) that appear when the constraints are considered. These terms are related to mass-metric tensors determinants and also occur in the Fixman's compensating potential. We show that some of the corrections are non-negligible if one is interested in the whole Ramachandran space. On the other hand, if only the energetically lower region, containing the principal secondary structure elements, is assumed to be relevant, then, all correcting terms may be neglected up to peptides of considerable length. This is the first time, as far as we know, that the analysis of the conformational dependence of these correcting terms is performed in a relevant biomolecule with a realistic potential energy function.Comment: 37 pages, 4 figures, LaTeX, BibTeX, AMSTe

Dynamics of filaments and membranes in a viscous fluid

Motivated by the motion of biopolymers and membranes in solution, this article presents a formulation of the equations of motion for curves and surfaces in a viscous fluid. We focus on geometrical aspects and simple variational methods for calculating internal stresses and forces, and we derive the full nonlinear equations of motion. In the case of membranes, we pay particular attention to the formulation of the equations of hydrodynamics on a curved, deforming surface. The formalism is illustrated by two simple case studies: (1) the twirling instability of straight elastic rod rotating in a viscous fluid, and (2) the pearling and buckling instabilities of a tubular liposome or polymersome.Comment: 26 pages, 12 figures, to be published in Reviews of Modern Physic

Development of design criteria for novel 3D-printed quadric-surfaced sludge digesters for wastewater infrastructure

The quadric-surfaced sludge digester (QSD), also known as the egg-shaped sludge digester, has proven its advantages over traditional cylindrical digesters recently. A reduction in operational cost is the dominant factor. Its shell can be described as a revolution of a parabola with the apex and base being either tapered or spherical. This shape provides a surface free of discontinuities, which is advantageous regarding the efficiency during mixing. Since the shape does not produce areas of inactive fluid motion within the tank, sludge settlement and an eventual grit build-up are avoided. The stresses developed in the shell of the sludge digester, vary along the meridian and equatorial diameters. A non-dimensional parameter, ξ, defines the height-to-diameter aspect ratio which is used to delineate the parametric boundary conditions of the shell’s surface. Three groups of analyses were conducted to determine the orthogonal stresses in the shell of the QSD. The first-principles numerical models ran reasonably quickly, and many iterations were made during the study. The results showed that they were in within the range 5.34% to 7.2% to 2D FEA simulations. The 3D FEA simulations were within the range of 8.3% to 9.2% to the MATLAB time-history models. This is a good indicator that the first principles numerical models are an excellent time-saving method to predict the behaviour of the QSD under seismic excitation. Upon examining the criteria for the design, analysing the results for the 2D FEA simulations showed that the fill height is not a significant variable with sloshing however the 3D FEA showed that the hydrostatic pressure is a significant variable. With the maximum tensile stress of the 3D-printed ABS being 24.4 MPa, the overall maximum stress of 5.45 MPa, the material can be a viable option for the use of QSD construction in small island developing states (SIDS)

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol

Atomistic Monte Carlo simulation of lipid membranes

Biological membranes are complex assemblies of many different molecules of which analysis demands a variety of experimental and computational approaches. In this article, we explain challenges and advantages of atomistic Monte Carlo (MC) simulation of lipid membranes. We provide an introduction into the various move sets that are implemented in current MC methods for efficient conformational sampling of lipids and other molecules. In the second part, we demonstrate for a concrete example, how an atomistic local-move set can be implemented for MC simulations of phospholipid monomers and bilayer patches. We use our recently devised chain breakage/closure (CBC) local move set in the bond-/torsion angle space with the constant-bond-length approximation (CBLA) for the phospholipid dipalmitoylphosphatidylcholine (DPPC). We demonstrate rapid conformational equilibration for a single DPPC molecule, as assessed by calculation of molecular energies and entropies. We also show transition from a crystalline-like to a fluid DPPC bilayer by the CBC local-move MC method, as indicated by the electron density profile, head group orientation, area per lipid, and whole-lipid displacements. We discuss the potential of local-move MC methods in combination with molecular dynamics simulations, for example, for studying multi-component lipid membranes containing cholesterol

Mechanics, shape, and programmability in soft matter systems: From fluid membranes to spring and droplet networks

This thesis analyzes three different soft matter systems---membranes, polymers, and droplets---to answer questions about shape, mechanics, and programmability. For membranes, my collaborators and I have developed a theoretical model of endocytosis in yeast. Endocytosis is the process by which a cell membrane deforms to surround extracellular material to draw it into the cell. Endocytosis in yeast involves clathrin, actin, and Bar proteins. Our model breaks up the process into three stages: (i) initiation, where clathrin interacts with the cell membrane via adaptor proteins, (ii) elongation, where the membrane is then further deformed by polymerizing actin filaments, followed by (iii) pinch-off. Our results suggest that the pinch-off mechanism may be assisted by a pearling-like instability. In addition, we potentially rule out two of the three competing models for the organization of the actin filament network during the elongation stage. For polymers, the actin cytoskeleton network at the leading edge of the cell becomes anisotropic with filament alignment favoring the direction of motion of the cell. To begin to capture the mechanics of this anisotropic filament network, my collaborators and I have constructed an effective medium (mean field) theory of an anisotropic, disordered spring network. We find that increasing the anisotropy increases the filament density required for a nonzero shear modulus (rigidity). We also conduct numerical simulations and find good agreement with the effective medium theory. We then extend our analysis to include the mechanics of coupled disordered spring networks to study force transmission between the actin cytoskeletal network and DNA via the lamin filament network and potentially begin to establish a microscopic basis for the mechanical regulation of transcription via the actin cytoskeleton. For droplets, we study numerically a collection of aqueous droplets joined by single lipid bilayers to form a cohesive, tissue-like material. The droplets in these droplet networks can be programmed with different osmolarity gradients. These osmolarity gradients generate internal stresses via local flows and the network then folds into designed structures. In other words, global change is driven by local osmolarity gradients. Using molecular dynamics simulations, we study the formation of shapes ranging from rings to spirals to tetrahedra and determining the optimal range of parameters for such structures. By adding an osmotic interaction with a dynamic environment, a folding-unfolding process can also be realized. This latter result is a step towards osmotic robotics

An efficient algorithm to perform local concerted movements of a chain molecule

The devising of efficient concerted rotation moves that modify only selected local portions of chain molecules is a long studied problem. Possible applications range from speeding the uncorrelated sampling of polymeric dense systems to loop reconstruction and structure refinement in protein modeling. Here, we propose and validate, on a few pedagogical examples, a novel numerical strategy that generalizes the notion of concerted rotation. The usage of the Denavit-Hartenberg parameters for chain description allows all possible choices for the subset of degrees of freedom to be modified in the move. They can be arbitrarily distributed along the chain and can be distanced between consecutive monomers as well. The efficiency of the methodology capitalizes on the inherent geometrical structure of the manifold defined by all chain configurations compatible with the fixed degrees of freedom. The chain portion to be moved is first opened along a direction chosen in the tangent space to the manifold, and then closed in the orthogonal space. As a consequence, in Monte Carlo simulations detailed balance is easily enforced without the need of using Jacobian reweighting. Moreover, the relative fluctuations of the degrees of freedom involved in the move can be easily tuned. We show different applications: the manifold of possible configurations is explored in a very efficient way for a protein fragment and for a cyclic molecule; the "local backbone volume", related to the volume spanned by the manifold, reproduces the mobility profile of all-α helical proteins; the refinement of small protein fragments with different secondary structures is addressed. The presented results suggest our methodology as a valuable exploration and sampling tool in the context of bio-molecular simulations

Particles Confined by Fluid Interfaces: Imaging Particle Motion, Interface Deformation and Capillary Forces

Small solid particles, confined in two-dimensions by fluid interfaces, were studied by a variety of experimental methods to understand particle motion, menisci shapes near interface-supported particles, and capillary interactions among such particles. Unwanted evaporation was circumvented by adopting non-volatile ionic liquids to create the fluid interfaces. A related application, employment of ionic liquids to float cryo-microtomed polymer sections, was also developed. The Brownian motions of nanospheres and nanorods in free-standing ionic liquid films were visualized in situ by high resolution scanning electron microscopy, which images features almost 100× smaller than possible in an optical microscope. For suspensions that are dilute and films that are thick compared to the particle diameter, the translational and rotational diffusion coefficients determined by single-particle tracking agreed with existing theoretical predictions. In thinner films, a striking and unexpected dynamical pairing of nanospheres was observed, suggesting a balance of capillary and hydrodynamic interactions. Nanospheres at high concentration displayed subdiffusive caged motion and hexagonal-lattice crystallization. Concentrated nanorods in the thinner films transiently assembled into finite stacks but did not achieve high tetratic liquid crystalline order, perhaps because of spherical impurities. A small spherical microparticles on a cylindrically curved liquid interface, to maintain constant contact angle about its wetted periphery, locally induces a quadrupolar interface deformation. Measured by optical profilometry, this deformation was compared to a recent theoretical expression, and good agreement was noted. The interface quadrupoles lead to particle capillary interactions in analogy to a 2d electrostatic quadrupoles, and as one consequence, spheres on a cylindrical interface assemble tetragonally. The assembly was monitored in the optical microscope, with particles driven to assembly as predicted, into a tetragonal lattice aligned with the underlying cylindrical axis. Lastly, ionic liquids and their mixtures with low molecular weight solvents were applied as flotation liquids for cryo-ultramicrotomy. With control of glass transition temperature and liquid viscosity, flat and ultra-thin sections were reliably floated onto transmission electron microscopy grids at cryogenic temperature. Compared to established flotation media for soft polymer systems, the required time and skill are significantly reduced, and the operator was not exposed to noxious fumes

Probing the Structure and Photophysics of Porphyrinoid Systems for Functional Materials

Porphyrins (Pors) and their many cousins, including phthalocyanines (Pcs), corroles (Cors), subphthalocyanines (SubPcs), porphyrazines (Pzs), and naphthalocyanines (NPcs), play amazingly diverse roles in biological and non-biological systems because of their unique and tunable physical and chemical properties. These compounds, collectively known as porphyrinoids, can be employed in any number of functional devices that have the potential to address the challenges of modern society. Their incorporation into such devices, however, depends on many structural factors that must be well understood and carefully controlled in order to achieve the desired behavior. Self-assembly and self-organization are key processes for developing these new technologies, as they will allow for inexpensive, efficient, and scalable designs. The overall goal of this dissertation is to elucidate and ultimately control the interplay between the hierarchical structure and the photophysical properties of these kinds of systems. This includes several case studies concerning the design and spectroscopic analysis of supramolecular systems formed through simple, scalable synthetic methods. We also present detailed experimental and computational studies on some porphyrin and phthalocyanine compounds that provide evidence for fundamental changes in their molecular structure. In addition to their impact on the photophysics, these changes also have implications for the organization of these molecules into higher order materials and devices. It is our hope that these findings will help to drive chemists and engineers to look more closely at every level of hierarchical structure in the search for the next generation of advanced materials