Computational methods for the analysis of protein structure and function

The vast majority of known proteins have not yet been experimentally characterized and little is known about their function. The design and implementation of computational tools can provide insight into the function of proteins based on their sequence, their structure, their evolutionary history and their association with other proteins. Knowledge of the three-dimensional (3D) structure of a protein can lead to a deep understanding of its mode of action and interaction, but currently the structures of <1% of sequences have been experimentally solved. For this reason, it became urgent to develop new methods that are able to computationally extract relevant information from protein sequence and structure. The starting point of my work has been the study of the properties of contacts between protein residues, since they constrain protein folding and characterize different protein structures. Prediction of residue contacts in proteins is an interesting problem whose solution may be useful in protein folding recognition and de novo design. The prediction of these contacts requires the study of the protein inter-residue distances related to the specific type of amino acid pair that are encoded in the so-called contact map. An interesting new way of analyzing those structures came out when network studies were introduced, with pivotal papers demonstrating that protein contact networks also exhibit small-world behavior. In order to highlight constraints for the prediction of protein contact maps and for applications in the field of protein structure prediction and/or reconstruction from experimentally determined contact maps, I studied to which extent the characteristic path length and clustering coefficient of the protein contacts network are values that reveal characteristic features of protein contact maps. Provided that residue contacts are known for a protein sequence, the major features of its 3D structure could be deduced by combining this knowledge with correctly predicted motifs of secondary structure. In the second part of my work I focused on a particular protein structural motif, the coiled-coil, known to mediate a variety of fundamental biological interactions. Coiled-coils are found in a variety of structural forms and in a wide range of proteins including, for example, small units such as leucine zippers that drive the dimerization of many transcription factors or more complex structures such as the family of viral proteins responsible for virus-host membrane fusion. The coiled-coil structural motif is estimated to account for 5-10% of the protein sequences in the various genomes. Given their biological importance, in my work I introduced a Hidden Markov Model (HMM) that exploits the evolutionary information derived from multiple sequence alignments, to predict coiled-coil regions and to discriminate coiled-coil sequences. The results indicate that the new HMM outperforms all the existing programs and can be adopted for the coiled-coil prediction and for large-scale genome annotation. Genome annotation is a key issue in modern computational biology, being the starting point towards the understanding of the complex processes involved in biological networks. The rapid growth in the number of protein sequences and structures available poses new fundamental problems that still deserve an interpretation. Nevertheless, these data are at the basis of the design of new strategies for tackling problems such as the prediction of protein structure and function. Experimental determination of the functions of all these proteins would be a hugely time-consuming and costly task and, in most instances, has not been carried out. As an example, currently, approximately only 20% of annotated proteins in the Homo sapiens genome have been experimentally characterized. A commonly adopted procedure for annotating protein sequences relies on the "inheritance through homology" based on the notion that similar sequences share similar functions and structures. This procedure consists in the assignment of sequences to a specific group of functionally related sequences which had been grouped through clustering techniques. The clustering procedure is based on suitable similarity rules, since predicting protein structure and function from sequence largely depends on the value of sequence identity. However, additional levels of complexity are due to multi-domain proteins, to proteins that share common domains but that do not necessarily share the same function, to the finding that different combinations of shared domains can lead to different biological roles. In the last part of this study I developed and validate a system that contributes to sequence annotation by taking advantage of a validated transfer through inheritance procedure of the molecular functions and of the structural templates. After a cross-genome comparison with the BLAST program, clusters were built on the basis of two stringent constraints on sequence identity and coverage of the alignment. The adopted measure explicity answers to the problem of multi-domain proteins annotation and allows a fine grain division of the whole set of proteomes used, that ensures cluster homogeneity in terms of sequence length. A high level of coverage of structure templates on the length of protein sequences within clusters ensures that multi-domain proteins when present can be templates for sequences of similar length. This annotation procedure includes the possibility of reliably transferring statistically validated functions and structures to sequences considering information available in the present data bases of molecular functions and structures.

Bioimaging of animal embryogenesis: mathematical methods and computational algorithms

Some fundamental biological processes such as embryonic development have been preserved during evolution and are common to species belonging to different phylogenetic positions, but are nowadays largely unknown. The understanding of cell morphodynamics leading to the formation of organized spatial distribution of cells such as tissues and organs can be achieved through the reconstruction of cells shape and position during the development of a live animal embryo. We design in this work a chain of image processing methods to automatically segment and track cells nuclei and membranes during the development of a zebrafish embryo, which has been largely validates as model organism to understand vertebrate development, gene function and healingrepair mechanisms in vertebrates. The embryo is previously labeled through the ubiquitous expression of fluorescent proteins addressed to cells nuclei and membranes, and temporal sequences of volumetric images are acquired with laser scanning microscopy. Cells position is detected by processing nuclei images either through the generalized form of the Hough transform or identifying nuclei position with local maxima after a smoothing preprocessing step. Membranes and nuclei shapes are reconstructed by using PDEs based variational techniques such as the Subjective Surfaces and the Chan Vese method. Cells tracking is performed by combining informations previously detected on cells shape and position with biological regularization constraints. Our results are manually validated and reconstruct the formation of zebrafish brain at 7-8 somite stage with all the cells tracked starting from late sphere stage with less than 2% error for at least 6 hours. Our reconstruction opens the way to a systematic investigation of cellular behaviors, of clonal origin and clonal complexity of brain organs, as well as the contribution of cell proliferation modes and cell movements to the formation of local patterns and morphogenetic fields.

Oxidation and pyrolysis of methane and methyl formate in a plug flow reactor: computational and experimenal studies

Biodiesel represents a possible substitute to the fossil fuels; for this reason a good comprehension of the kinetics involved is important. Due to the complexity of the biodiesel mixture a common practice is the use of surrogate molecules to study its reactivity. In this work are presented the experimental and computational results obtained for the oxidation and pyrolysis of methane and methyl formate conducted in a plug flow reactor. The work was divided into two parts: the first one was the setup assembly whilst, in the second one, was realized a comparison between the experimental and model results; these last was obtained using models available in literature. It was started studying the methane since, a validate model was available, in this way was possible to verify the reliability of the experimental results. After this first study the attention was focused on the methyl formate investigation. All the analysis were conducted at different temperatures, pressures and, for the oxidation, at different equivalence ratios. The results shown that, a good comprehension of the kinetics is reach but efforts are necessary to better evaluate kinetics parameters such as activation energy. The results even point out that the realized setup is adapt to study the oxidation and pyrolysis and, for this reason, it will be employed to study a longer chain esters with the aim to better understand the kinetic of the molecules that are part of the biodiesel mixture.

Engineering Complex Computational Ecosystems

Self-organising pervasive ecosystems of devices are set to become a major vehicle for delivering infrastructure and end-user services. The inherent complexity of such systems poses new challenges to those who want to dominate it by applying the principles of engineering. The recent growth in number and distribution of devices with decent computational and communicational abilities, that suddenly accelerated with the massive diffusion of smartphones and tablets, is delivering a world with a much higher density of devices in space. Also, communication technologies seem to be focussing on short-range device-to-device (P2P) interactions, with technologies such as Bluetooth and Near-Field Communication gaining greater adoption. Locality and situatedness become key to providing the best possible experience to users, and the classic model of a centralised, enormously powerful server gathering and processing data becomes less and less efficient with device density. Accomplishing complex global tasks without a centralised controller responsible of aggregating data, however, is a challenging task. In particular, there is a local-to-global issue that makes the application of engineering principles challenging at least: designing device-local programs that, through interaction, guarantee a certain global service level. In this thesis, we first analyse the state of the art in coordination systems, then motivate the work by describing the main issues of pre-existing tools and practices and identifying the improvements that would benefit the design of such complex software ecosystems. The contribution can be divided in three main branches. First, we introduce a novel simulation toolchain for pervasive ecosystems, designed for allowing good expressiveness still retaining high performance. Second, we leverage existing coordination models and patterns in order to create new spatial structures. Third, we introduce a novel language, based on the existing ``Field Calculus'' and integrated with the aforementioned toolchain, designed to be usable for practical aggregate programming.

EXPERIMENTAL AND COMPUTATIONAL STUDIES OF ELECTROMAGNETIC CLOAKING AT MICROWAVES

An invisibility cloak is a device that can hide the target by enclosing it from the incident radiation. This intriguing device has attracted a lot of attention since it was first implemented at a microwave frequency in 2006. However, the problems of existing cloak designs prevent them from being widely applied in practice. In this dissertation, we try to remove or alleviate the three constraints for practical applications imposed by loosy cloaking media, high implementation complexity, and small size of hidden objects compared to the incident wavelength. To facilitate cloaking design and experimental characterization, several devices and relevant techniques for measuring the complex permittivity of dielectric materials at microwave frequencies are developed. In particular, a unique parallel plate waveguide chamber has been set up to automatically map the electromagnetic (EM) field distribution for wave propagation through the resonator arrays and cloaking structures. The total scattering cross section of the cloaking structures was derived based on the measured scattering field by using this apparatus. To overcome the adverse effects of lossy cloaking media, microwave cloaks composed of identical dielectric resonators made of low loss ceramic materials are designed and implemented. The effective permeability dispersion was provided by tailoring dielectric resonator filling fractions. The cloak performances had been verified by full-wave simulation of true multi-resonator structures and experimental measurements of the fabricated prototypes. With the aim to reduce the implementation complexity caused by metamaterials employment for cloaking, we proposed to design 2-D cylindrical cloaks and 3-D spherical cloaks by using multi-layer ordinary dielectric material (εr>1) coating. Genetic algorithm was employed to optimize the dielectric profiles of the cloaking shells to provide the minimum scattering cross sections of the cloaked targets. The designed cloaks can be easily scaled to various operating frequencies. The simulation results show that the multi-layer cylindrical cloak essentially outperforms the similarly sized metamaterials-based cloak designed by using the transformation optics-based reduced parameters. For the designed spherical cloak, the simulated scattering pattern shows that the total scattering cross section is greatly reduced. In addition, the scattering in specific directions could be significantly reduced. It is shown that the cloaking efficiency for larger targets could be improved by employing lossy materials in the shell. At last, we propose to hide a target inside a waveguide structure filled with only epsilon near zero materials, which are easy to implement in practice. The cloaking efficiency of this method, which was found to increase for large targets, has been confirmed both theoretically and by simulations.

Application of a computational model for complex fluvial ecosystems: The population dynamics of zebra mussel Dreissena polymorpha as a case study

The potential and adaptive flexibility of population dynamic P-systems (PDP) to study population dynamics suggests that they may be suitable for modelling complex fluvial ecosystems, characterized by a composition of dynamic habitats with many variables that interact simultaneously. Using as a model a reservoir occupied by the zebra mussel Dreissena polymorpha, we designed a computational model based on P systems to study the population dynamics of larvae, in order to evaluate management actions to control or eradicate this invasive species. The population dynamics of this species was simulated under different scenarios ranging from the absence of water flow change to a weekly variation with different flow rates, to the actual hydrodynamic situation of an intermediate flow rate. Our results show that PDP models can be very useful tools to model complex, partially desynchronized, processes that work in parallel. This allows the study of complex hydroecological processes such as the one presented, where reproductive cycles, temperature and water dynamics are involved in the desynchronization of the population dynamics both, within areas and among them. The results obtained may be useful in the management of other reservoirs with similar hydrodynamic situations in which the presence of this invasive species has been documented.

A study of the time complexity of an Elitist Genetic Algorithm used for associating optical observations of MEO and GEO Space Debris

Currently several thousands of objects are being tracked in the MEO and GEO regions through optical means. The problem faced in this framework is that of Multiple Target Tracking (MTT). In this context both the correct associations among the observations, and the orbits of the objects have to be determined. The complexity of the MTT problem is defined by its dimension S. Where S stands for the number of ’fences’ used in the problem, each fence consists of a set of observations that all originate from dierent targets. For a dimension of S ˃ the MTT problem becomes NP-hard. As of now no algorithm exists that can solve an NP-hard problem in an optimal manner within a reasonable (polynomial) computation time. However, there are algorithms that can approximate the solution with a realistic computational e ort. To this end an Elitist Genetic Algorithm is implemented to approximately solve the S ˃ MTT problem in an e cient manner. Its complexity is studied and it is found that an approximate solution can be obtained in a polynomial time. With the advent of improved sensors and a heightened interest in the problem of space debris, it is expected that the number of tracked objects will grow by an order of magnitude in the near future. This research aims to provide a method that can treat the correlation and orbit determination problems simultaneously, and is able to e ciently process large data sets with minimal manual intervention.

Riding out of the storm: How to deal with the complexity of grid and cloud management

Over the last decade, Grid computing paved the way for a new level of large scale distributed systems. This infrastructure made it possible to securely and reliably take advantage of widely separated computational resources that are part of several different organizations. Resources can be incorporated to the Grid, building a theoretical virtual supercomputer. In time, cloud computing emerged as a new type of large scale distributed system, inheriting and expanding the expertise and knowledge that have been obtained so far. Some of the main characteristics of Grids naturally evolved into clouds, others were modified and adapted and others were simply discarded or postponed. Regardless of these technical specifics, both Grids and clouds together can be considered as one of the most important advances in large scale distributed computing of the past ten years; however, this step in distributed computing has came along with a completely new level of complexity. Grid and cloud management mechanisms play a key role, and correct analysis and understanding of the system behavior are needed. Large scale distributed systems must be able to self-manage, incorporating autonomic features capable of controlling and optimizing all resources and services. Traditional distributed computing management mechanisms analyze each resource separately and adjust specific parameters of each one of them. When trying to adapt the same procedures to Grid and cloud computing, the vast complexity of these systems can make this task extremely complicated. But large scale distributed systems complexity could only be a matter of perspective. It could be possible to understand the Grid or cloud behavior as a single entity, instead of a set of resources. This abstraction could provide a different understanding of the system, describing large scale behavior and global events that probably would not be detected analyzing each resource separately. In this work we define a theoretical framework that combines both ideas, multiple resources and single entity, to develop large scale distributed systems management techniques aimed at system performance optimization, increased dependability and Quality of Service (QoS). The resulting synergy could be the key 350 J. Montes et al. to address the most important difficulties of Grid and cloud management.

Engineering Computational Emotion - A Reference Model for Emotion in Artificial Systems

Emotion is generally argued to be an influence on the behavior of life systems, largely concerning flexibility and adaptivity. The way in which life systems acts in response to a particular situations of the environment, has revealed the decisive and crucial importance of this feature in the success of behaviors. And this source of inspiration has influenced the way of thinking artificial systems. During the last decades, artificial systems have undergone such an evolution that each day more are integrated in our daily life. They have become greater in complexity, and the subsequent effects are related to an increased demand of systems that ensure resilience, robustness, availability, security or safety among others. All of them questions that raise quite a fundamental challenges in control design. This thesis has been developed under the framework of the Autonomous System project, a.k.a the ASys-Project. Short-term objectives of immediate application are focused on to design improved systems, and the approaching of intelligence in control strategies. Besides this, long-term objectives underlying ASys-Project concentrate on high order capabilities such as cognition, awareness and autonomy. This thesis is placed within the general fields of Engineery and Emotion science, and provides a theoretical foundation for engineering and designing computational emotion for artificial systems. The starting question that has grounded this thesis aims the problem of emotion--based autonomy. And how to feedback systems with valuable meaning has conformed the general objective. Both the starting question and the general objective, have underlaid the study of emotion, the influence on systems behavior, the key foundations that justify this feature in life systems, how emotion is integrated within the normal operation, and how this entire problem of emotion can be explained in artificial systems. By assuming essential differences concerning structure, purpose and operation between life and artificial systems, the essential motivation has been the exploration of what emotion solves in nature to afterwards analyze analogies for man--made systems. This work provides a reference model in which a collection of entities, relationships, models, functions and informational artifacts, are all interacting to provide the system with non-explicit knowledge under the form of emotion-like relevances. This solution aims to provide a reference model under which to design solutions for emotional operation, but related to the real needs of artificial systems. The proposal consists of a multi-purpose architecture that implement two broad modules in order to attend: (a) the range of processes related to the environment affectation, and (b) the range or processes related to the emotion perception-like and the higher levels of reasoning. This has required an intense and critical analysis beyond the state of the art around the most relevant theories of emotion and technical systems, in order to obtain the required support for those foundations that sustain each model. The problem has been interpreted and is described on the basis of AGSys, an agent assumed with the minimum rationality as to provide the capability to perform emotional assessment. AGSys is a conceptualization of a Model-based Cognitive agent that embodies an inner agent ESys, the responsible of performing the emotional operation inside of AGSys. The solution consists of multiple computational modules working federated, and aimed at conforming a mutual feedback loop between AGSys and ESys. Throughout this solution, the environment and the effects that might influence over the system are described as different problems. While AGSys operates as a common system within the external environment, ESys is designed to operate within a conceptualized inner environment. And this inner environment is built on the basis of those relevances that might occur inside of AGSys in the interaction with the external environment. This allows for a high-quality separate reasoning concerning mission goals defined in AGSys, and emotional goals defined in ESys. This way, it is provided a possible path for high-level reasoning under the influence of goals congruence. High-level reasoning model uses knowledge about emotional goals stability, letting this way new directions in which mission goals might be assessed under the situational state of this stability. This high-level reasoning is grounded by the work of MEP, a model of emotion perception that is thought as an analogy of a well-known theory in emotion science. The work of this model is described under the operation of a recursive-like process labeled as R-Loop, together with a system of emotional goals that are assumed as individual agents. This way, AGSys integrates knowledge that concerns the relation between a perceived object, and the effect which this perception induces on the situational state of the emotional goals. This knowledge enables a high-order system of information that provides the sustain for a high-level reasoning. The extent to which this reasoning might be approached is just delineated and assumed as future work. This thesis has been studied beyond a long range of fields of knowledge. This knowledge can be structured into two main objectives: (a) the fields of psychology, cognitive science, neurology and biological sciences in order to obtain understanding concerning the problem of the emotional phenomena, and (b) a large amount of computer science branches such as Autonomic Computing (AC), Self-adaptive software, Self-X systems, Model Integrated Computing (MIC) or the paradigm of models@runtime among others, in order to obtain knowledge about tools for designing each part of the solution. The final approach has been mainly performed on the basis of the entire acquired knowledge, and described under the fields of Artificial Intelligence, Model-Based Systems (MBS), and additional mathematical formalizations to provide punctual understanding in those cases that it has been required. This approach describes a reference model to feedback systems with valuable meaning, allowing for reasoning with regard to (a) the relationship between the environment and the relevance of the effects on the system, and (b) dynamical evaluations concerning the inner situational state of the system as a result of those effects. And this reasoning provides a framework of distinguishable states of AGSys derived from its own circumstances, that can be assumed as artificial emotion.

Analysing the complexity of the model-based decision making processes within the industrial management context

PURPOSE The decision-making process plays a key role in organizations. Every decision-making process produces a final choice that may or may not prompt action. Recurrently, decision makers find themselves in the dichotomous question of following a traditional sequence decision-making process where the output of a decision is used as the input of the next stage of the decision, or following a joint decision-making approach where several decisions are taken simultaneously. The implication of the decision-making process will impact different players of the organization. The choice of the decision- making approach becomes difficult to find, even with the current literature and practitioners’ knowledge. The pursuit of better ways for making decisions has been a common goal for academics and practitioners. Management scientists use different techniques and approaches to improve different types of decisions. The purpose of this decision is to use the available resources as well as possible (data and techniques) to achieve the objectives of the organization. The developing and applying of models and concepts may be helpful to solve managerial problems faced every day in different companies. As a result of this research different decision models are presented to contribute to the body of knowledge of management science. The first models are focused on the manufacturing industry and the second part of the models on the health care industry. Despite these models being case specific, they serve the purpose of exemplifying that different approaches to the problems and could provide interesting results. Unfortunately, there is no universal recipe that could be applied to all the problems. Furthermore, the same model could deliver good results with certain data and bad results for other data. A framework to analyse the data before selecting the model to be used is presented and tested in the models developed to exemplify the ideas. METHODOLOGY As the first step of the research a systematic literature review on the joint decision is presented, as are the different opinions and suggestions of different scholars. For the next stage of the thesis, the decision-making process of more than 50 companies was analysed in companies from different sectors in the production planning area at the Job Shop level. The data was obtained using surveys and face-to-face interviews. The following part of the research into the decision-making process was held in two application fields that are highly relevant for our society; manufacturing and health care. The first step was to study the interactions and develop a mathematical model for the replenishment of the car assembly where the problem of “Vehicle routing problem and Inventory” were combined. The next step was to add the scheduling or car production (car sequencing) decision and use some metaheuristics such as ant colony and genetic algorithms to measure if the behaviour is kept up with different case size problems. A similar approach is presented in a production of semiconductors and aviation parts, where a hoist has to change from one station to another to deal with the work, and a jobs schedule has to be done. However, for this problem simulation was used for experimentation. In parallel, the scheduling of operating rooms was studied. Surgeries were allocated to surgeons and the scheduling of operating rooms was analysed. The first part of the research was done in a Teaching hospital, and for the second part the interaction of uncertainty was added. Once the previous problem had been analysed a general framework to characterize the instance was built. In the final chapter a general conclusion is presented. FINDINGS AND PRACTICAL IMPLICATIONS The first part of the contributions is an update of the decision-making literature review. Also an analysis of the possible savings resulting from a change in the decision process is made. Then, the results of the survey, which present a lack of consistency between what the managers believe and the reality of the integration of their decisions. In the next stage of the thesis, a contribution to the body of knowledge of the operation research, with the joint solution of the replenishment, sequencing and inventory problem in the assembly line is made, together with a parallel work with the operating rooms scheduling where different solutions approaches are presented. In addition to the contribution of the solving methods, with the use of different techniques, the main contribution is the framework that is proposed to pre-evaluate the problem before thinking of the techniques to solve it. However, there is no straightforward answer as to whether it is better to have joint or sequential solutions. Following the proposed framework with the evaluation of factors such as the flexibility of the answer, the number of actors, and the tightness of the data, give us important hints as to the most suitable direction to take to tackle the problem. RESEARCH LIMITATIONS AND AVENUES FOR FUTURE RESEARCH In the first part of the work it was really complicated to calculate the possible savings of different projects, since in many papers these quantities are not reported or the impact is based on non-quantifiable benefits. The other issue is the confidentiality of many projects where the data cannot be presented. For the car assembly line problem more computational power would allow us to solve bigger instances. For the operation research problem there was a lack of historical data to perform a parallel analysis in the teaching hospital. In order to keep testing the decision framework it is necessary to keep applying more case studies in order to generalize the results and make them more evident and less ambiguous. The health care field offers great opportunities since despite the recent awareness of the need to improve the decision-making process there are many opportunities to improve. Another big difference with the automotive industry is that the last improvements are not spread among all the actors. Therefore, in the future this research will focus more on the collaboration between academia and the health care sector.

Study of flow behaviour in a three-product cyclone using computational fluid dynamics

Simplicity in design and minimal floor space requirements render the hydrocyclone the preferred classifier in mineral processing plants. Empirical models have been developed for design and process optimisation but due to the complexity of the flow behaviour in the hydrocyclone these do not provide information on the internal separation mechanisms. To study the interaction of design variables, the flow behaviour needs to be considered, especially when modelling the new three-product cyclone. Computational fluid dynamics (CFD) was used to model the three-product cyclone, in particular the influence of the dual vortex finder arrangement on flow behaviour. From experimental work performed on the UG2 platinum ore, significant differences in the classification performance of the three-product cyclone were noticed with variations in the inner vortex finder length. Because of this simulations were performed for a range of inner vortex finder lengths. Simulations were also conducted on a conventional hydrocyclone of the same size to enable a direct comparison of the flow behaviour between the two cyclone designs. Significantly, high velocities were observed for the three-product cyclone with an inner vortex finder extended deep into the conical section of the cyclone. CFD studies revealed that in the three-product cyclone, a cylindrical shaped air-core is observed similar to conventional hydrocyclones. A constant diameter air-core was observed throughout the inner vortex finder length, while no air-core was present in the annulus. (c) 2006 Elsevier Ltd. All rights reserved.

Computational mechanics reveals nanosecond time correlations in molecular dynamics of liquid systems

Statistical complexity, a measure introduced in computational mechanics has been applied to MD simulated liquid water and other molecular systems. It has been found that statistical complexity does not converge in these systems but grows logarithmically without a limit. The coefficient of the growth has been introduced as a new molecular parameter which is invariant for a given liquid system. Using this new parameter extremely long time correlations in the system undetectable by traditional methods are elucidated. The existence of hundreds of picosecond and even nanosecond long correlations in bulk water has been demonstrated. © 2008 Elsevier B.V. All rights reserved.

The dawn of the RNA World:toward functional complexity through ligation of random RNA oligomers

A main unsolved problem in the RNA World scenario for the origin of life is how a template-dependent RNA polymerase ribozyme emerged from short RNA oligomers obtained by random polymerization on mineral surfaces. A number of computational studies have shown that the structural repertoire yielded by that process is dominated by topologically simple structures, notably hairpin-like ones. A fraction of these could display RNA ligase activity and catalyze the assembly of larger, eventually functional RNA molecules retaining their previous modular structure: molecular complexity increases but template replication is absent. This allows us to build up a stepwise model of ligation- based, modular evolution that could pave the way to the emergence of a ribozyme with RNA replicase activity, step at which information-driven Darwinian evolution would be triggered. Copyright © 2009 RNA Society.

Complexity and chirality indices for molecular informatics::differential geometry approach

Novel molecular complexity measures are designed based on the quantum molecular kinematics. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determined the time derivatives for the dynamic quantities. This allows to define the average quantum kinematic characteristics closely related to the curvatures of the electron paths, particularly, the torsion reflecting the chirality of the dynamic system. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

Dynamic complexity of chaotic transitions in high-dimensional classical dynamics:Leu-Enkephalin folding

Leu-Enkephalin in explicit water is simulated using classical molecular dynamics. A ß-turn transition is investigated by calculating the topological complexity (in the "computational mechanics" framework [J. P. Crutchfield and K. Young, Phys. Rev. Lett., 63, 105 (1989)]) of the dynamics of both the peptide and the neighbouring water molecules. The complexity of the atomic trajectories of the (relatively short) simulations used in this study reflect the degree of phase space mixing in the system. It is demonstrated that the dynamic complexity of the hydrogen atoms of the peptide and almost all of the hydrogens of the neighbouring waters exhibit a minimum precisely at the moment of the ß-turn transition. This indicates the appearance of simplified periodic patterns in the atomic motion, which could correspond to high-dimensional tori in the phase space. It is hypothesized that this behaviour is the manifestation of the effect described in the approach to molecular transitions by Komatsuzaki and Berry [T. Komatsuzaki and R.S. Berry, Adv. Chem. Phys., 123, 79 (2002)], where a "quasi-regular" dynamics at the transition is suggested. Therefore, for the first time, the less chaotic character of the folding transition in a realistic molecular system is demonstrated. © Springer-Verlag Berlin Heidelberg 2006.