Attraction controls the entropy of fluctuations in isosceles triangular networks

We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of the stable phase by changing the entropy of fluctuations around the ground-state configurations. By using a real-space shell-expansion method, we compute the exact expression of the entropy for harmonic interactions, while for repulsive harmonic interactions we obtain the entropy arising from a limited subset of the system by numerical integration. We compare these results with a three-dimensional triangular-network model, which shows the same attraction-mediated selection mechanism of the stable phase, and conclude that this effect is general with respect to the dimensionality of the system

The storage of semantic memories in the cortex: a computational study

The main object of this thesis is the design of structured distributed memories for the purpose of studying their storage and retrieval properties in large scale cortical auto-associative networks. For this, an autoassociative network of Potts units, coupled via tensor connections, has been proposed and analyzed as an effective model of an extensive cortical network with distinct short and long-range synaptic connections. Recently, we have clarified in what sense it can be regarded as an effective model. While the fully-connected (FC) and the very sparsely connected, that is, highly diluted (HD) limits of the model have thoroughly analyzed, the realistic case of the intermediate partial connectivity has been simply assumed to interpolate the FC and HD cases. In this thesis, we first study the storage capacity of Potts network with such intermediate connectivity. We corroborate the outcome of the analysis by showing that the resulting mean field equations are consistent with the FC and HD equations under the appropriate limits. The mean-field equations are only derived for randomly diluted connectivity (RD). Through simulations, we also study symmetric dilution (SD) and state dependent random dilution (SDRD). We find that the Potts network has a higher capacity for symmetric than for random dilution. We then turn to the core question: how to use a model originally conceived for the storage of p unrelated patterns of activity, in order to study semantic memory, which is organized in terms of the relations between the facts and the attributes of real-world knowledge. To proceed, we first formulate a mathematical model of generating patterns with correlations, as an extension of a hierarchical procedure for generating ultrametrically organized patterns. The model ascribes the correlations between patterns to the influence of underlying "factors"; if many factors act with comparable strength, their influences balance out and correlations are low; whereas if a few factors dominate, which in the model occurs for increasing values of a control parameter \u3b6, correlations between memory patterns can become much stronger. We show that the extension allows for correlations between patterns that are neither trivial (as in the random case) nor a plain tree (as in the ultrametric case), but that are highly sensitive to the values of the correlation parameters that we define. Next, we study the storage capacity of the Potts network when the patterns are correlated by way of our algorithm. We show that fewer correlated patterns can be stored and retrieved than random ones, and that the higher the degree of correlation, the lower the capacity. We find that the mean-field equations yielding the storage capacity are different from those obtained with uncorrelated patterns through only an additional term in the noise, proportional to the number of learned patterns p and to the difference between the average correlation between correlated patterns and independently generated patterns of the same sparsity. Of particular interest is the role played by the parameter we have introduced, \u3b6, which controls the strength of the influences of different factors (the "parents") in generating the memory patterns (the "children"). In particular, we find that for high values of \u3b6, so that only a handful of parents are effective, the network exhibits correlated retrieval, in which the network, though not being able to retrieve the pattern cued, settles into a configuration of high overlap with another pattern. This behavior of the network can be interpreted as reflecting the semantic structure of the correlations, in which even after capacity collapse, what the network can still do is to recognize the strongest features associated with the pattern. This observation is better quantified using the mutual information between the pattern cued and the configuration the network settles into, after retrieval dynamics. This information is found to increase from zero to a non-zero value abruptly when increasing the parameter \u3b6, akin to a phase transition. Two alternative phases are then identified, \u3b6 \u3b6 c , memories form clusters, such that while the specifics of the cued pattern cannot be retrieved, some of the structure informing the cluster of memories can still be retrieved. In a final short chapter, we attempt to understand the implications of having stored correlated memories on latching dynamics, the spontaneous behavior which has been proposed to be an emergent property, beyond the simple cued retrieval paradigm, of large cortical networks. Progress made in this direction, studying the Potts network, has so far focused on uncorrelated memories. Introducing correlations, we find a rich phase space of behaviors, from sequential retrieval of memories, to parallel retrieval of clusters of highly correlated memories and oscillations, depending on the various correlation parameters. The parameters of our algorithm may be found to emerge as critical control parameters, corresponding to the statistical features in human semantic memory most important in determining the dynamics of our trains of thoughts

Artificial Brownian motors: Controlling transport on the nanoscale

In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases, one speaks of "Brownian motors". In this review the constructive role of Brownian motion is exemplified for various one-dimensional setups, mostly inspired by the cell molecular machinery: working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are reviewed with particular attention to transport in artificial nanopores and optical traps, where single particle currents have been first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented hereby. Another area with promising potential for realization of artificial Brownian motors are microfluidic or granular set-ups.....Comment: 57 pages, 39 figures; submitted to Reviews Modern Physics, revised versio

14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS

From Preface: This is the fourteen time when the conference “Dynamical Systems – Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and the Ministry of Science and Higher Education. It is a great pleasure that our invitation has been accepted by so many people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcome nearly 250 persons from 38 countries all over the world. They decided to share the results of their research and many years experiences in the discipline of dynamical systems by submitting many very interesting papers. This booklet contains a collection of 375 abstracts, which have gained the acceptance of referees and have been qualified for publication in the conference proceedings [...]

Mechanics and dynamics of twisted DNA

Aufgrund einer komplexen Wechselwirkung mit Proteinen ist das Genom in einer Zelle ständig mechanischer Spannung und Torsion ausgesetzt. Daher ist es wichtig die Mechanik und die Dynamik von verdrillter DNA unter Spannung zu verstehen. Diese Situation wurde experimentell mittels einer sog. magnetischen Pinzette nachgestellt, indem sowohl Kraft als auch Drehmoment auf ein einzelnes DNA Molekül ausgeübt und gleichzeitig die mechanische Antwort des Polymers aufgezeichnet wurde. Als erstes Beispiel wurde der Übergang von linearer zu sog. plectonemischer DNA untersucht, d.h. die Absorption eines Teils der induzierten Verdrillung in einer superhelikalen Struktur. Eine abrupte Längenänderung am Anfang dieses Übergangs wurde bereits im Vorfeld publiziert. In der vorliegenden Arbeit wird gezeigt, dass diese abrupte DNA Verkürzung insbesondere von der Länge der DNA und der Ionenkonzentration der Lösung abhängt. Dieses Verhalten kann mittels eines Modells verstanden werden, in dem die Energie pro Verwringung der ersten Schlinge innerhalb der Superhelix größer ist als die aller nachfolgenden. Des Weiteren wurden DNA-DNA Wechselwirkungen in der Umgebung monovalenter Ionen durch die Analyse des Superspiralisierungsverhaltens einzelner DNA Moleküle bei konstanter Kraft charakterisiert. Solche Wechselwirkungen sind für die Kompaktierung des Genoms und die Regulation der Transkription wichtig. Oft wird DNA als gleichmäßig geladener Zylinder modelliert und ihre elektrostatischen Wechselwirkungen im Rahmen der Poisson-Boltzmann-Gleichung mit einem Ladungsanpassungsfaktor berechnet. Trotz erheblicher Anstrengung ist eine präzise Bestimmung dieses Parameters bisher nicht gelungen. Ein theoretisches Modell dieses Prozesses zeigte nun eine erstaunlich kleine effektive DNA Ladung von ~40% der nominalen Ladungsdichte. Abgesehen von Gleichgewichtsprozessen wurde auch die Dynamik eines Faltungsvorgangs von DNA untersucht. Spontane Branch Migration einer homologen Holliday-Struktur wurde genutzt, um die intramolekulare Reibung der DNA zu erforschen. Mittels einer magnetischen Pinzette wurde eine torsionslimitierte Holliday-Struktur gestreckt während die Längenfluktuationen der Zweige mit schneller Videomikroskopie bei ~3 kHz aufgezeichnet wurden. Einzelne diffusive Schritte der Basenpaare sollten auf einer sub-Millisekunden Zeitskala auftreten und viel kleiner als die Gesamtfluktuationen der DNA sein. Eine Analyse der spektralen Leistungsdichte der Längenfluktuationen ermöglicht eine eindeutige Beschreibung der Dynamik der Branch Migration. Die Holliday-Struktur wurde außerdem als nanomechanischer Linearversteller eingesetzt, um einen einzelnen fluoreszierenden Quantenpunkt durch ein exponentiell abfallendes evaneszentes Feld zu bewegen. Durch die Aufzeichnung der Emission des Quantenpunkts sowohl in dem evaneszenten Feld als auch unter gleichmäßiger Beleuchtung kann die Intensitätsverteilung des Anregungsfelds ohne weitere Dekonvolution bestimmt werden. Diese neue Technik ist von besonderem wissenschaftlichen Interesse, weil die Beschreibung dreidimensionaler inhomogener Beleuchtungsfelder eine große Herausforderung in der modernen Mikroskopie darstellt. Die Ergebnisse dieser Arbeit werden dem besseren Verständnis einer Vielzahl biologischer Prozesse, die in Verbindung mit DNA Superspiralisierung stehen, dienen und weitere technische Anwendungen des DNA-basierten Linearverstellers hervorbringen.The genome inside the cell is continuously subjected to tension and torsion primarily due to a complex interplay with a large variety of proteins. To gain insight into these processes it is crucial to understand the mechanics and dynamics of twisted DNA under tension. Here, this situation is mimicked experimentally by applying force and torque to a single DNA molecule with so called magnetic tweezers and measuring its mechanical response. As a first example a transition from a linear to a plectonemic DNA configuration is studied, i.e. the absorption of part of the applied twist in a superhelical structure. Recent experiments revealed the occurrence of an abrupt extension change at the onset of this transition. Here, it is found that this abrupt DNA shortening strongly depends on the length of the DNA molecule and the ionic strength of the solution. This behavior can be well understood in the framework of a model in which the energy per writhe for the initial plectonemic loop is larger than for subsequent turns of the superhelix. Furthermore DNA-DNA interactions in the presence of monovalent ions were comprehensively characterized by analyzing the supercoiling behavior of single DNA molecules held under constant tension. These interactions are important for genome compaction and transcription regulation. So far DNA is often modeled as a homogeneously charged cylinder and its electrostatic interactions are calculated within the framework of the Poisson-Boltzmann equation including a charge adaptation factor. Despite considerable efforts, until now a rigorous quantitative assessment of this parameter has been lacking. A theoretical model of this process revealed a surprisingly small effective DNA charge of ~40% of the nominal charge density. Besides describing equilibrium processes, also the dynamics during refolding of nucleic acids is investigated. Spontaneous branch migration of a homologous Holliday junction serves as an ideal system where the friction within the biomolecule can be studied. This is realized by stretching a torsionally constrained Holliday junction using magnetic tweezers and recording the length fluctuations of the arms with high-speed videomicroscopy at ~3 kHz. Single base pair diffusive steps are expected to occur on a sub-millisecond time scale and to be much smaller than the overall DNA length fluctuations. Power-spectral-density analysis of the length fluctuations is able to clearly resolve the overall dynamics of the branch migration process. Apart from studying intramolecular friction, the four-arm DNA junction was also used as a nanomechanical translation stage to move a single fluorescent quantum dot through an exponentially decaying evanescent field. Recording the emission of the quantum dot within the evanescent field as well as under homogeneous illumination allows to directly obtain the intensity distribution of the excitation field without additional deconvolution. This new technique is of particular scientific interest because the characterization of three-dimensional inhomogeneous illumination fields is a challenge in modern microscopy. The results presented in this work will help to better understand a large variety of biological processes related to DNA supercoiling and inspire further technical applications of the nanomechanical DNA gear

Towards more robust and efficient methods for the calculation of Protein-Ligand binding affinities

Biological processes often depend on protein-ligand binding events, so that accurate prediction of protein-ligand binding affinities is of central importance in structural based drug design. Although many techniques exist for calculating protein-ligand binding affinities, ranging from techniques that should be accurate in principle, such as free energy perturbation (FEP) theory, to relatively simple approximations based on empirically derived scoring functions, the counterbalancing demands of speed and accuracy have left us with no completely satisfactory solution thus far. This thesis will be focused on the methodology development towards more robust and reliable Protein-Ligand binding affinity calculation. In Part I, we will present the WaterMap method, which will bridge the gap between the efficiency of empirical scoring functions and the accuracy of rigorous FEP methods. Unlike most other methods with the main focus on the direct interaction between the protein and the ligand, the WaterMap method we developed considers the explicit driving force from the solvent, in which several individual water molecules in the binding pocket play an active role in the binding process. We demonstrate that protein may adopt active site geometries that will destabilize the water molecules in the binding pocket through hydrophobic enclosure and/or correlated hydrogen bonds, and displacement of these water molecules by ligand groups complementary to protein surface will provide the driving force for ligand binding. In some extreme cases, the interactions are so unfavorable for water molecules that a void is formed in the binding pocket of protein. Our method also considers the contribution from occupation of ligand atoms in the dry regions of binding pocket, which in some cases provides the driving force for ligand binding. FEP provides an in-principle rigorous method to calculate protein-ligand binding affinities within the limitations of the potential energy model and it may have a potentially large impact on structure based drug design projects especially during late stage lead optimization when productive decisions about compound modification are made . However, converging explicit solvent simulations to the desired precision is far from trivial, especially when there are large structural reorganizations in the protein or in the ligand upon the formation of the binding complex or upon the alchemical transformation from one ligand to another. In these cases, there can be large energy barriers separating the different conformations and the ligand or the protein may remain kinetically trapped in the starting configuration for a very long time during brute-force FEP/MD simulations. The incomplete sampling of the configuration space results in the computed binding free energies being dependent on the starting protein or ligand configurations, thus giving rise to the well known quasi-nonergodicity problem in FEP. In Part II, we will present a new protocol called FEP/REST, which combines the recently developed enhanced sampling technique REST (Replica Exchange with Solute Tempering) into normal FEP to solve the sampling problem in brute force FEP calculation. The computational cost of this method is comparable with normal FEP, and it can be very easily generalized to more complicated systems of pharmaceutical interest. We apply this method to two modifications of protein-ligand complexes which lead to significant conformational changes, the first in the protein and the second in the ligand. The new approach is shown to facilitate sampling in these challenging cases where high free energy barriers separate the initial and final conformations, and leads to superior convergence of the free energy as demonstrated both by consistency of the results (independence from the starting conformation) and agreement with experimental binding affinity data. Part III focus on two topics towards the foundational understanding of hydrophobic interactions and electrostatic interactions. To be specific, the nonadditivity effect of hydrophobic interactions in model enclosures is studied in Chapter 9, and the competition between hydrophobic interaction and electrostatic interaction between a hydrophobe and model enclosure is studied in Chapter 10. The approximations in popular implicit solvent models, like the surface area model in hydrophobic interaction, and the quadratic dependence of electrostatic interaction on the magnitude of charge are investigated. Six of the Chapters (Chapter 2-4, Chapter 6, and Chapter 9-10) have been published and the other one (Chapter 7) has been accepted for publication and currently is in press. Each Part begins with its own introduction. Each chapter also contains its own abstract and introduction, and focus on one specific topic. They all share the common theme, that is to develop more robust and reliable methods to calculate protein-ligand binding affinities. The conclusions and discussions about future research directions are presented in Part IV

Enabling Capillary Self-Assembly for Microsystem Integration

Efficient and precise assembly of very-large quantities of sub-millimeter-sized devices onto pre-processed substrates is presently a key frontier for microelectronics, in its aspiration to large-scale mass production of devices with new functionalities and applications (e.g. thin dies embedded into flexible substrates, 3D microsystem integration). In this perspective, on the one hand established pick&place assembly techniques may be unsuitable, due to a trade-off between throughput and placement accuracy and to difficulties in predictably handling very-small devices. On the other hand, self-assembly processes are massively parallel, may run unsupervised and allow contactless manipulation of objects. The convergence between robotic assembly and self-assembly, epitomized by capillarity-enhanced flip-chip assembly, can therefore enable an ideal technology meeting short-to-medium-term electronic packaging and assembly needs. The objective of this thesis is bridging the gap between academic proofs-of- concept of capillary self-assembly and its industrial application. Our work solves several issues relevant to capillary self-assembly of thin dies onto preprocessed substrates. Very-different phenomena and aspects of both scientific and technological interest coexist in such a broad context. They were tackled both experimentally and theoretically. After a critical review of the state-of-the-art in microsystem integration, a complete quasi-static study of lateral capillary meniscus forces is presented. Our experimental setup enables also a novel method to measure the contact angle of liquids. Recessed binding sites are introduced to obtain perfectly-conformal fluid dip-coating of patterned surfaces, which enables the effective and robust coding of geometrical information into binding sites to direct the assembly of parts. A general procedure to establish solder-mediated electro-mechanical interconnections between parts and substrate is validated. Smart surface chemistries are invoked to solve the issue of mutual adhesion between parts during the capillary self-assembly process. Two chemical kinetic-inspired analytic models of fluidic self-assembly are presented and criticized to introduce a novel agent-based model of the process. The latter approach allows realistic simulations by taking into account spatial factors and collision dynamics. Concluding speculations propose envisioned solutions to residual open issues and further perspectives for this field of rapidly-growing importance