Intermittency as metastability: a predictive approach to evolution in disordered environments

Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative stasis and short bursts of activity. This behaviour, known as intermittency in physics and punctuated equilibrium in evolutionary theory, is difficult to forecast; in particular there is no general principle to locate the regions where the system will settle, how long it will stay there, or where it will jump next. Here I introduce a predictive theory of linear intermittency that closes these gaps. I show that any positive linear system can be mapped onto a generalization of the "maximal entropy random walk", a Markov process on graphs with non-local transition rates. This construction reveals the localization islands as local minima of an effective potential, and intermittent jumps as barrier crossings in that potential. My results unify the concepts of intermittency in linear systems and Markovian metastability, and provide a generally applicable method to reduce, and predict, the dynamics of disordered linear systems. Applications span physics, evolutionary dynamics and epidemiology.Comment: Extension of arXiv:1912.0589

Towards Visualization of Discrete Optimization Problems and Search Algorithms

Diskrete Optimierung beschäftigt sich mit dem Identifizieren einer Kombination oder Permutation von Elementen, die im Hinblick auf ein gegebenes quantitatives Kriterium optimal ist. Anwendungen dafür entstehen aus Problemen in der Wirtschaft, der industriellen Fertigung, den Ingenieursdisziplinen, der Mathematik und Informatik. Dazu gehören unter anderem maschinelles Lernen, die Planung der Reihenfolge und Terminierung von Fertigungsprozessen oder das Layout von integrierten Schaltkreisen. Häufig sind diskrete Optimierungsprobleme NP-hart. Dadurch kommt der Erforschung effizienter, heuristischer Suchalgorithmen eine große Bedeutung zu, um für mittlere und große Probleminstanzen überhaupt gute Lösungen finden zu können. Dabei wird die Entwicklung von Algorithmen dadurch erschwert, dass Eigenschaften der Probleminstanzen aufgrund von deren Größe und Komplexität häufig schwer zu identifizieren sind. Ebenso herausfordernd ist die Analyse und Evaluierung von gegebenen Algorithmen, da das Suchverhalten häufig schwer zu charakterisieren ist. Das trifft besonders im Fall von emergentem Verhalten zu, wie es in der Forschung der Schwarmintelligenz vorkommt. Visualisierung zielt auf das Nutzen des menschlichen Sehens zur Datenverarbeitung ab. Das Gehirn hat enorme Fähigkeiten optische Reize von den Sehnerven zu analysieren, Formen und Muster darin zu erkennen, ihnen Bedeutung zu verleihen und dadurch ein intuitives Verstehen des Gesehenen zu ermöglichen. Diese Fähigkeit kann im Speziellen genutzt werden, um Hypothesen über komplexe Daten zu generieren, indem man sie in einem Bild repräsentiert und so dem visuellen System des Betrachters zugänglich macht. Bisher wurde Visualisierung kaum genutzt um speziell die Forschung in diskreter Optimierung zu unterstützen. Mit dieser Dissertation soll ein Ausgangspunkt geschaffen werden, um den vermehrten Einsatz von Visualisierung bei der Entwicklung von Suchheuristiken zu ermöglichen. Dazu werden zunächst die zentralen Fragen in der Algorithmenentwicklung diskutiert und daraus folgende Anforderungen an Visualisierungssysteme abgeleitet. Mögliche Forschungsrichtungen in der Visualisierung, die konkreten Nutzen für die Forschung in der Optimierung ergeben, werden vorgestellt. Darauf aufbauend werden drei Visualisierungssysteme und eine Analysemethode für die Erforschung diskreter Suche vorgestellt. Drei wichtige Aufgaben von Algorithmendesignern werden dabei adressiert. Zunächst wird ein System für den detaillierten Vergleich von Algorithmen vorgestellt. Auf der Basis von Zwischenergebnissen der Algorithmen auf einer Probleminstanz wird der Suchverlauf der Algorithmen dargestellt. Der Fokus liegt dabei dem Verlauf der Qualität der Lösungen über die Zeit, wobei die Darstellung durch den Experten mit zusätzlichem Wissen oder Klassifizierungen angereichert werden kann. Als zweites wird ein System für die Analyse von Suchlandschaften vorgestellt. Auf Basis von Pfaden und Abständen in der Landschaft wird eine Karte der Probleminstanz gezeichnet, die strukturelle Merkmale intuitiv erfassbar macht. Der zweite Teil der Dissertation beschäftigt sich mit der topologischen Analyse von Suchlandschaften, aufbauend auf einer Schwellwertanalyse. Ein Visualisierungssystem wird vorgestellt, dass ein topologisch equivalentes Höhenprofil der Suchlandschaft darstellt, um die topologische Struktur begreifbar zu machen. Dieses System ermöglicht zudem, den Suchverlauf eines Algorithmus direkt in der Suchlandschaft zu beobachten, was insbesondere bei der Untersuchung von Schwarmintelligenzalgorithmen interessant ist. Die Berechnung der topologischen Struktur setzt eine vollständige Aufzählung aller Lösungen voraus, was aufgrund der Größe der Suchlandschaften im allgemeinen nicht möglich ist. Um eine Anwendbarkeit der Analyse auf größere Probleminstanzen zu ermöglichen, wird eine Methode zur Abschätzung der Topologie vorgestellt. Die Methode erlaubt eine schrittweise Verfeinerung der topologischen Struktur und lässt sich heuristisch steuern. Dadurch können Wissen und Hypothesen des Experten einfließen um eine möglichst hohe Qualität der Annäherung zu erreichen bei gleichzeitig überschaubarem Berechnungsaufwand.Discrete optimization deals with the identification of combinations or permutations of elements that are optimal with regard to a specific, quantitative criterion. Applications arise from problems in economy, manufacturing, engineering, mathematics and computer sciences. Among them are machine learning, scheduling of production processes, and the layout of integrated electrical circuits. Typically, discrete optimization problems are NP hard. Thus, the investigation of efficient, heuristic search algorithms is of high relevance in order to find good solutions for medium- and large-sized problem instances, at all. The development of such algorithms is complicated, because the properties of problem instances are often hard to identify due to the size and complexity of the instances. Likewise, the analysis and evaluation of given algorithms is challenging, because the search behavior of an algorithm is hard to characterize, especially in case of emergent behavior as investigated in swarm intelligence research. Visualization targets taking advantage of human vision in order to do data processing. The visual brain possesses tremendous capabilities to analyse optical stimulation through the visual nerves, perceive shapes and patterns, assign meaning to them and thus facilitate an intuitive understanding of the seen. In particular, this can be used to generate hypotheses about complex data by representing them in a well-designed depiction and making it accessible to the visual system of the viewer. So far, there is only little use of visualization to support the discrete optimization research. This thesis is meant as a starting point to allow for an increased application of visualization throughout the process of developing discrete search heuristics. For this, we discuss the central questions that arise from the development of heuristics as well as the resulting requirements on visualization systems. Possible directions of research for visualization are described that yield a specific benefit for optimization research. Based on this, three visualization systems and one analysis method are presented. These address three important tasks of algorithm designers. First, a system for the fine-grained comparison of algorithms is introduced. Based on the intermediate results of algorithm runs on a given problem instance the search process is visualized. The focus is on the progress of the solution quality over time while allowing the algorithm expert to augment the depiction with additional domain knowledge and classification of individual solutions. Second, a system for the analysis of search landscapes is presented. Based on paths and distances in the landscape, a map of the problem instance is drawn that facilitates an intuitive cognition of structural properties. The second part of this thesis focuses on the topological analysis of search landscapes, based on barriers. A visualization system is presented that shows a topological equivalent height profile of the search landscape. Further, the system facilitates to observe the search process of an algorithm directly within the search landscape. This is of particular interest when researching swarm intelligence algorithms. The computation of topological structure requires a complete enumeration of all solutions which is not possible in the general case due to the size of the search landscapes. In order to enable an application to larger problem instances, we introduce a method to approximate the topological structure. The method allows for an incremental refinement of the topological approximation that can be controlled using a heuristic. Thus, the domain expert can introduce her knowledge and also hypotheses about the problem instance into the analysis so that an approximation of good quality is achieved with reasonable computational effort

Energy landscapes of a pair of adsorbed peptides

The wide relevance of peptide adsorption in natural and synthetic contexts means it has attracted much attention. Molecular dynamics (MD) simulation has been widely used in these endeavors. Much of this has focused on single peptides due to the computational effort required to capture the rare events that characterize their adsorption. This focus is, however, of limited practical relevance as in reality, most systems of interest operate in the nondilute regime where peptides will interact with other adsorbed peptides. As an alternative to MD simulation, we have used energy landscape mapping (ELM) to investigate two met-enkephalin molecules adsorbed at a gas/graphite interface. Major conformations of the adsorbed peptides and the connecting transition states are elucidated along with the associated energy barriers and rates of exchange. The last of these makes clear that MD simulations are currently of limited use in probing the co-adsorption of two peptides, let alone more. The constant volume heat capacity as a function of temperature is also presented. Overall, this study represents a significant step toward characterizing peptide adsorption beyond the dilute limit

Potential and Free Energy Surfaces of Adsorbed Peptides

Peptide adsorption on solid surfaces is a common process that occurs in nanotechnology and biology, with applications in the formation of nanomaterials, biosensing and drug delivery, amongst many others. Peptide adsorption involves complex processes that are difficult to characterise experimentally. Computational approaches such as molecular dynamics (MD) are often employed to better understand biomolecular systems. However, the computationally demanding nature of such systems combined with the long characteristic timescales of peptide adsorption means MD is not well suited to its study with current computing capacities. An alternative computational approach to characterising the behaviour of atoms and molecules is mapping the potential energy surface (PES) – the molecular energy as a function of the positions of all atoms – by determining its local energy minima and saddle points, which represent stable configurations and transition states that lie between them. These minima and saddle points may be located using optimisation algorithms. Harmonic approximations yield information about transition rates between minima via saddle points as well as the free energy surface (FES). This methodology – which is referred to as ‘energy landscape mapping’ (ELM) hereafter – is able to characterise fast and slow processes equally, only being limited by the size and complexity of the system studied, and the applicability of the potential energy models used. In the past, it has largely been applied to atomic and molecular clusters, and to biomolecules. It has never been applied to adsorption of peptides or any other biomolecule. In three journal papers included in this thesis, this approach is for the first time applied to adsorbed peptides. Firstly, ELM was applied to polyalanine adsorbed on surfaces of varying interactions strengths. Results obtained were comparable results to those obtained in a prior study of the same system using an evolutionary algorithm. In the second paper, ELM was applied to met-enkephalin at a gas/graphite interface, and compared with a molecular simulation technique designed for accelerating the simulation of slow processes, replica exchange molecular dynamics (REMD). In the final paper, ELM was applied to two met-enkephalin molecules at a gas/graphite interface, introducing an additional level of complexity and a step towards practical application, given real peptide adsorption processes often occur en masse. In all of these studies, information about transitions between conformations, energy barriers, rates, and the nature of the overall PES and FES, all of which were previously unknown for the systems studied, was obtained by ELM. The work conducted here has demonstrated the applicability of ELM to peptide/surface systems. Future work may consist of applying ELM to other similar processes of practical importance, developing and validating potential energy models suitable for modelling interfacial systems, including the effect of solvents, and continual development of the methodology to accelerate calculations.Thesis (Ph.D.) -- University of Adelaide, School of Chemical Engineering and Advanced Materials, 202

Energy Landscapes for Protein Folding

Proteins are involved in numerous functions in the human body, including chemical transport, molecular recognition, and catalysis. To perform their function most proteins must adopt a specific structure (often referred to as the folded structure). A microscopic description of folding is an important prerequisite for elucidating the underlying basis of protein misfolding and rational drug design. However, protein folding occurs on heterogeneous length and time scales, presenting a grand challenge to both experiments and simulations. In computer simulations, challenges are generally mitigated by adopting coarse-grained descriptions of the physical environment, employing enhanced sampling strategies, and improving computing code and hardware. While significant advances have been made in these areas, for numerous systems a large spatiotemporal gap between experiment and simulations still exists, due to the limited time and length scales achieved by simulation, and the inability of many experimental techniques to probe fast motions and short distances. In this thesis, kinetic transition networks (KTNs) are constructed for various protein folding systems, via approaches based on the potential energy landscape (PEL) framework. By applying geometry optimisation techniques, the PEL is discretised into stationary points (i.e.~low-energy minima and the transition states that connect them). Essentially, minima characterise the low-lying regions of the PEL (thermodynamics) and transition states encode the motion between these regions (dynamics). Principles from statistical mechanics and unimolecular rate theory may then be employed to derive free energy surfaces and folding rates, respectively, from the KTN. Furthermore, the PEL framework can take advantage of parallel and distributed computing, since stationary points from separate simulations can be easily integrated into one KTN. Moreover, the use of geometry optimisation facilitates greater conformational sampling than conventional techniques based on molecular dynamics. Accordingly, this framework presents an appealing means of probing complex processes, such as protein folding. In this dissertation, we demonstrate the application of state-of-the-art theory, combining PEL analysis and KTNs to three diverse protein systems. First, to improve the efficiency of protein folding simulations, the intrinsic rigidity of proteins is exploited by implementing a local rigid body (LRB) approach. The LRB approach effectively integrates out irrelevant degrees of freedom from the geometry optimisation procedure and further accelerates conformational sampling. The effects of this approach on the underlying PEL are analysed in a systematic fashion for a model protein (tryptophan zipper\,1). We demonstrate that conservative local rigidification can reproduce the thermodynamic and dynamic properties for the model protein. Next, the PEL framework is employed to model large-scale conformational changes in proteins, which have conventionally been difficult to probe \textit{in silico}. Methods based on geometry optimisation have proved useful in overcoming the broken ergodicity issue, which is associated with proteins that switch morphology. The latest PEL-based approaches are utilised to investigate the most extreme case of fold-switching found in the literature:~the $\alpha$-helical hairpin to $\beta$-barrel transition of the C-terminal domain of RfaH, a bacterial transcription factor. PEL techniques are employed to construct the free energy landscape (FEL) for the refolding process and to discover mechanistic details of the transition at an atomistic level. The final part of the thesis focuses on modelling intrinsically disordered proteins (IDPs). Due to their inherent structural plasticity, IDPs are generally difficult to characterise, both experimentally and via simulations. An approach for studying IDPs within the PEL framework is implemented and tested with various contemporary potential energy functions. The cytoplasmic tail of the human cluster of differentiation 4 (CD4), implicated in HIV-1 infection, is characterised. Metastable states identified on the FEL help to unify, and are consistent with, several earlier predictions.Gates Cambridge Trus

Structure prediction of nano materials

This thesis is predominantly on the exploration of configurational space of different materials of different dimensions using ab initio techniques. We focus on understanding the predicted geometrical configurations and their electronic properties. For this purpose, we employed MHM to explore the PES as well as identify putative low lying energy structures

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr

The Folding Kinetics of RNA

RNAs are biomolecules ubiquitous in all living cells. Usually, they fold into complex molecular structures, which often mediate their biological function. In this work, models of RNA folding have been studied in detail. One can distinguish two fundamentally different approaches to RNA folding. The first one is the thermodynamic approach, which yields information about the distribution of structures in the ensemble in its equilibrium. The second approach, which is required to study the dynamics of folding during the course of time, is the kinetic folding analysis. It is much more computationally expensive, but allows to incorporate changing environmental parameters as well as time-dependent effects into the analysis. Building on these methods, the BarMap framework (Hofacker, Flamm, et al., 2010) allows to chain several pre-computed models and thus simulate folding reactions in a dynamically changing environment, e. g., to model co- transcriptional folding. However, there is no obvious way to identify spurious output, let alone assessing the quality of the simulation results. As a remedy, BarMap-QA, a semi-automatic software pipeline for the analysis of cotranscriptional folding, has been developed. For a given input sequence, it automatically generates the models for every step of the RNA elongation, applies BarMap to link them together, and runs the simulation. Post-processing scripts, visualizations, and an integrated viewer are provided to facilitate the evaluation of the unwieldy BarMap output. Three novel, complementary quality measures are computed on-the-fly, allowing the analyst to evaluate the coverage of the computed models, the exactness of the computed mapping between the individual states of each model, and the fraction of correctly mapped population during the simulation run. In case of deficiencies, the output is automatically re-rendered after parameter adjustment. Statistical evidence is presented that, even when coarse graining the ensemble, kinetic simulations quickly become infeasible for longer RNAs. However, within the individual gradient basins, most high-energy structures only have a marginal probability and could safely be excluded from the analysis. To tell relevant and irrelevant structures apart, a precise knowledge of the distribution of probability mass within a basin is necessary. Both a theoretical result concerning the shape of its density, and possible applications like the prediction of a basin’s partition function are given. To demonstrate the applicability of computational folding simulations to a real-world task of the life sciences, we conducted an in silico design process for a synthetic, transcriptional riboswitch responding to the ligand neomycin. The designed constructs were then transfected into the bacterium Escherichia coli by a collaborative partner and could successfully regulate a fluorescent reporter gene depending on the presence of its ligand. Additionally, it was shown that the sequence context of the riboswitch could have detrimental effects on its functionality, but also that RNA folding simulations are often capable to predict these interactions and provide solutions in the form of decoupling spacer elements. Taken together, this thesis offers the reader deep insights into the world of RNA folding and its models, and how these can be applied to design novel biomolecules

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

This report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.epsr