Dissipation and control in microscopic nonequilibrium systems

Quantifying the flow of energy, entropy, and information within and through nonequilibrium systems remains a central challenge in understanding the microscopic physics of biological systems. Over the past two and a half decades, parallel developments in the fields of theoretical stochastic thermodynamics and single-molecule experiments have made tremendous steps towards this end, advancing our understanding of the fundamental physical limitations and constraints faced by biological systems in vivo. Central in this focus are molecular machines: nanoscale protein complexes which interconvert between different forms of energy to perform useful functions to the cell. While single-molecule experiments on molecular machines have predicted impressively high efficiencies, much is still unknown about their performance in vivo. In this thesis we build upon these primitives, largely by making use of near-equilibrium phenomenological models to simplify and make tractable the problem of quantifying dissipation in molecular machines and predicting the operational modes which are imperative to minimizing their dissipation. By exploring the relevance of near-equilibrium models in the experimental investigation of a DNA hairpin, we find that such an approach can provide utility in understanding the strategies to reduce dissipation in nonequilibrium processes. However, single-molecule manipulations are significantly separated from the in vivo dynamics of molecular machines, and thus for the remainder of the thesis we expand upon this approach in various ways, generalizing the existing theoretical framework to more closely parallel the dynamics of molecular machines. By incorporating the inter-system feedback present in molecular machines, we find that familiar intuitions about how excess work and entropy production are related break down. Finally, we derive a phenomenological expression for the energy flows communicated within the components of a mechanochemical molecular machine. Ultimately, our analysis shows that intersystem feedback can lead to nonvanishing energy flows which are the manifestation of a Maxwell demon in the molecular machine itself

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.Comment: 28 pages, 18 figure

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field

Pseudo generators of spatial transfer operators

Metastable behavior in dynamical systems may be a significant challenge for a simulation based analysis. In recent years, transfer operator based approaches to problems exhibiting metastability have matured. In order to make these approaches computationally feasible for larger systems, various reduction techniques have been proposed: For example, Sch\"utte introduced a spatial transfer operator which acts on densities on configuration space, while Weber proposed to avoid trajectory simulation (like Froyland et al.) by considering a discrete generator. In this manuscript, we show that even though the family of spatial transfer operators is not a semigroup, it possesses a well defined generating structure. What is more, the pseudo generators up to order 4 in the Taylor expansion of this family have particularly simple, explicit expressions involving no momentum averaging. This makes collocation methods particularly easy to implement and computationally efficient, which in turn may open the door for further efficiency improvements in, e.g., the computational treatment of conformation dynamics. We experimentally verify the predicted properties of these pseudo generators by means of two academic examples

All-Atom Modeling of Protein Folding and Aggregation

Theoretical investigations of biorelevant processes in the life-science research require highly optimized simulation methods. Therefore, massively parallel Monte Carlo algorithms, namely MTM, were successfully developed and applied to the field of reversible protein folding allowing the thermodynamic characterization of proteins on an atomistic level. Further, the formation process of trans-membrane pores in the TatA system could be elucidated and the structure of the complex could be predicted

DNA PROGRAMMABLE SOFT MATTER DEVICES

The ability to program soft materials to undergo observable shape transformations in response to environmental stimuli is critical to the development soft programmable matter. In recent years, chemomechanical shape-changing hydrogels have garnered interest because they do not require wires or batteries and can operate untethered at smaller size scales. Devices comprised of these materials can respond to only a limited set of spatially non-specific stimuli such as temperature or pH - and are therefore restricted to a small set of final states. On the other hand, due to the large sequence space and programmable interactions of DNA molecules, devices comprised of DNA-conjugated hydrogel domains can potentially access a much larger set of final configurations through sequence-specific, addressable actuation of individual domains. To investigate the shape-changing properties of single domain DNA-conjugated hydrogels, we first determine the swelling extent of DNA-crosslinked acrylamide networks in response to sequence-specific DNA stimuli. By coupling the DNA crosslinks to a DNA hybridization chain reaction that enables further incorporation of DNA to the crosslink sites, we demonstrate that specific DNA molecules can induce up to 100-fold volumetric hydrogel expansion. This large degree of swelling is then used to actuate approximately centimeter-sized gels containing multiple DNA-sensitive gel domains that each change shape in response to different DNA sequences. From swelling experiments and finite-element simulations we develop a simple design rule for the DNA-controlled shape change of a hydrogel bilayer. The next generation of soft programmable matter and robotics will require materials that not only respond to distinct chemical species, but mechanical forces as well. Prior work in developing mechanochemically responsive polymers makes use of mechanophores - molecules that change configuration and initiate chemical reactions in response to mechanical forces - to instill bulk materials with force sensing properties. In this work, we use established thermodynamic models to design two DNA mechanophore complexes capable of responding to two distinct ranges of applied force. We micromold PEGDA copolymer hydrogels containing DNA mechanophore complexes and examine the force-sensing properties of the bulk material through the use of a multifunctional force microscope and a DNA-based fluorescence reporting scheme. Because DNA molecules can be coupled to molecular sensors, amplifiers, and logic circuits, the incorporation of DNA complexes into hydrogel networks - whether as mechanophores or chemical crosslinkers -introduces the possibility of building soft matter devices that respond to numerous, distinct inputs and autonomously implement chemical control programs. These soft matter constructs have the potential to exhibit the multistage, goal-directed behaviors that are currently impossible to achieve in other soft robotic devices

Engineering Molecular Self-assembly and Reconfiguration in DNA Nanostructures

Smart electronics have developed ubiquitously to assist people in everything from navigation to health monitoring. The rise of complex electronics relied on rational design of platforms to build ever larger and more complex circuit networks and for frameworks to test those electronics. Biochemical circuits have also seen dramatic advancement in the last two decades within the field of DNA nanotechnology. As with electronics, DNA nanotechnology applied rational design to DNA molecules to build ever more complex biochemical networks that, beyond current electronics, also retain a significant measure of biological compatibility and plasticity akin to many networks of biological origin. Well situated for promising applications in diagnostics and therapeutics, advancing DNA nanotechnology devices will also rely upon larger platforms and testing frameworks. In roughly the last decade, researchers have been building upon the invention of DNA origami, a technique allowing the robust construction of biomolecular nano-structures capable of precise nanometer positioning of proteins, nanoparticles, and other molecules. DNA circuits have computed on the nanostructures; DNA robots have moved nanoparticles, made choices, and have even sorted cargo on the surface of a nanostructure. The complexity of circuits and devices continues to rise. In this thesis, we will discuss our contributions to the field of DNA nanotechnology by developing design rules and systematic approaches to controlling nanostructure complex assembly. These rules and approaches allow for the construction of molecular structures with a tunable diversity, large systems approaching the size of bacteria yet retaining nanometer precision, and biological plasticity inspired dynamic systems for arbitrary reconfiguration. Using a DNA origami tile tailored for array formation with a high continuous surface area, we create a framework inspired from molecular stochasticity for programming DNA array formation and gaining control over diversity of global properties through simple local rules. Three general forms of planar networks, random loops, mazes, and trees, were manipulated on the micron scale upon the self-assembled DNA arrays. We demonstrate control of several properties of the networks, such as branching rules, growth directions, the proximity between adjacent networks, and size distributions. The large diversity, in principle, allows for a wide, but tunable, testing environment for molecular circuits. By further applying these principles to subunits of finite assemblies, variable components may be mixed with fixed components potentially opening additional applications in high throughput device or drug screening. Next we turned to expanding the platform size biochemical circuits may be built upon. While DNA origami allows nanometer precise placement, the size remains roughly below 0.05 um2. Toward making large arbitrarily complex structures with only a set of simple tiles, multi-stage self-assembly has been explored in theory and for small DNA tiles. None were successful experimentally with DNA origami. We developed a strategy for DNA origami: a simple rule set applied recursively in each stage of a hierarchical self-assembly process, and to significantly reduce costs, a constant set of unique DNA strands regardless of size. We also developed a software tool to automatically compile a designed surface pattern into experimental protocols. We experimentally demonstrated DNA origami arrays approaching the size of small bacteria, 0.5 um2, with several arbitrary patterns, each consisting of 8,704 specifically chosen pixel locations with nanometer precision, including a bacteria sized portrait of a bacteria. The large platform opens the door to more advanced molecular circuits for applications such as diagnostics. Finally we demonstrated control over the dynamics of DNA origami reconfiguration in tile arrays. In an approach we call DNA tile displacement, we showed that a DNA origami array may have tiles arbitrarily replaced by another tile, including tiles of another shape or surface pattern. We also demonstrated control over the kinetics of tile displacement and performed several general purpose reconfigurations of DNA nanostructures. Examples include sequential reconfiguration, competitive reconfiguration, cooperative reconfiguration, and finally the scalability of multi-step reconfiguration as demonstrated through a fully playable nano-scale biomolecular tic-tac-toe game. The major ramifications are a plasticity more common to biology than to electronics—molecular platforms with arbitrary patterning that can reconfigure an arbitrary part of the nanostructure in an arbitrary order based on environmental signals. In principle, such reconfiguration can allow advanced circuits with the capacity to adapt to environmental needs or heal damaged components.</p