Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.

Machine learning methods for prediction of disulphide bonding states of cysteine residues in proteins

The goal of this thesis work is to develop a computational method based on machine learning techniques for predicting disulfide-bonding states of cysteine residues in proteins, which is a sub-problem of a bigger and yet unsolved problem of protein structure prediction. Improvement in the prediction of disulfide bonding states of cysteine residues will help in putting a constraint in the three dimensional (3D) space of the respective protein structure, and thus will eventually help in the prediction of 3D structure of proteins. Results of this work will have direct implications in site-directed mutational studies of proteins, proteins engineering and the problem of protein folding. We have used a combination of Artificial Neural Network (ANN) and Hidden Markov Model (HMM), the so-called Hidden Neural Network (HNN) as a machine learning technique to develop our prediction method. By using different global and local features of proteins (specifically profiles, parity of cysteine residues, average cysteine conservation, correlated mutation, sub-cellular localization, and signal peptide) as inputs and considering Eukaryotes and Prokaryotes separately we have reached to a remarkable accuracy of 94% on cysteine basis for both Eukaryotic and Prokaryotic datasets, and an accuracy of 90% and 93% on protein basis for Eukaryotic dataset and Prokaryotic dataset respectively. These accuracies are best so far ever reached by any existing prediction methods, and thus our prediction method has outperformed all the previously developed approaches and therefore is more reliable. Most interesting part of this thesis work is the differences in the prediction performances of Eukaryotes and Prokaryotes at the basic level of input coding when ‘profile’ information was given as input to our prediction method. And one of the reasons for this we discover is the difference in the amino acid composition of the local environment of bonded and free cysteine residues in Eukaryotes and Prokaryotes. Eukaryotic bonded cysteine examples have a ‘symmetric-cysteine-rich’ environment, where as Prokaryotic bonded examples lack it.

Computational studies on the structure and stabilities of magnetic inter-metallic compounds

The purpose of this thesis is to further the understanding of the structural, electronic and magnetic properties of ternary inter-metallic compounds using density functional theory (DFT). Four main problems are addressed. First, a detailed analysis on the ternary Heusler compounds is made. It has long been known that many Heusler compounds ($X_2YZ$; $X$ and $Y$ transition elements, $Z$ main group element) exhibit interesting half-metallic and ferromagnetic properties. In order to understand these, the dependence of magnetic and electronic properties on the structural parameters, the type of exchange-correlation functional and electron-electron correlation was examined. It was found that almost all Co$_2YZ$ Heusler compounds exhibit half-metallic ferromagnetism. It is also observed that $X$ and $Y$ atoms mainly contribute to the total magnetic moment. The magnitude of the total magnetic moment is determined only indirectly by the nature of $Z$ atoms, and shows a trend consistent with Slater-Pauling behaviour in several classes of these compounds. In contrast to experiments, calculations give a non-integer value of the magnetic moment in certain Co$_2$-based Heusler compounds. To explain deviations of the calculated magnetic moment, the LDA+$U$ scheme was applied and it was found that the inclusion of electron-electron correlation beyond the LSDA and GGA is necessary to obtain theoretical description of some Heusler compounds that are half-metallic ferromagnets. The electronic structure and magnetic properties of substitutional series of the quaternary Heusler compound Co$_2$Mn$_{1-x}$Fe$_x$Si were investigated under LDA+$U$. The calculated band structure suggest that the most stable compound in a half-metallic state will occur at an intermediate Fe concentration. These calculated findings are qualitatively confirmed by experimental studies. Second, the effect of antisite disordering in the Co$_2$TiSn system was investigated theoretically as well as experimentally. Preservation of half-metallicity for Co$_2$TiSn was observed with moderate antisite disordering and experimental findings suggest that the Co and Ti antisites disorder amounts to approximately 10~% in the compound. Third, a systematic examination was carried out for band gaps and the nature (covalent or ionic) of bonding in semiconducting 8- and 18-electron or half-metallic ferromagnet half-Heusler compounds. It was found that the most appropriate description of these compounds from the viewpoint of electronic structures is one of a $YZ$ zinc blende lattice stuffed by the $X$ ion. Simple valence rules are obeyed for bonding in the 8- and 18-electron compounds. Fourth, hexagonal analogues of half-Heusler compounds have been searched. Three series of compounds were investigated: GdPdSb, GdAutextit{X} (textit{X} = Mn, Cd and In) and EuNiP. GdPdSb is suggested as a possible half-metallic weak ferromagnet at low temperature. GdAutextit{X} (textit{X} = Mn, Cd and In) and EuNiP were investigated because they exhibit interesting bonding, structural and magnetic properties. The results qualitatively confirm experimental studies on magnetic and structural behaviour in GdPdSb, GdAutextit{X} (textit{X} = Mn, Cd and In) and EuNiP compounds. ~

Machine-learning methods for structure prediction of β-barrel membrane proteins

Different types of proteins exist with diverse functions that are essential for living organisms. An important class of proteins is represented by transmembrane proteins which are specifically designed to be inserted into biological membranes and devised to perform very important functions in the cell such as cell communication and active transport across the membrane. Transmembrane β-barrels (TMBBs) are a sub-class of membrane proteins largely under-represented in structure databases because of the extreme difficulty in experimental structure determination. For this reason, computational tools that are able to predict the structure of TMBBs are needed. In this thesis, two computational problems related to TMBBs were addressed: the detection of TMBBs in large datasets of proteins and the prediction of the topology of TMBB proteins. Firstly, a method for TMBB detection was presented based on a novel neural network framework for variable-length sequence classification. The proposed approach was validated on a non-redundant dataset of proteins. Furthermore, we carried-out genome-wide detection using the entire Escherichia coli proteome. In both experiments, the method significantly outperformed other existing state-of-the-art approaches, reaching very high PPV (92%) and MCC (0.82). Secondly, a method was also introduced for TMBB topology prediction. The proposed approach is based on grammatical modelling and probabilistic discriminative models for sequence data labeling. The method was evaluated using a newly generated dataset of 38 TMBB proteins obtained from high-resolution data in the PDB. Results have shown that the model is able to correctly predict topologies of 25 out of 38 protein chains in the dataset. When tested on previously released datasets, the performances of the proposed approach were measured as comparable or superior to the current state-of-the-art of TMBB topology prediction.

Interpreting Judgements using Knowledge Representation Methods and Computational Models of Argument

The goal of the present research is to define a Semantic Web framework for precedent modelling, by using knowledge extracted from text, metadata, and rules, while maintaining a strong text-to-knowledge morphism between legal text and legal concepts, in order to fill the gap between legal document and its semantics. The framework is composed of four different models that make use of standard languages from the Semantic Web stack of technologies: a document metadata structure, modelling the main parts of a judgement, and creating a bridge between a text and its semantic annotations of legal concepts; a legal core ontology, modelling abstract legal concepts and institutions contained in a rule of law; a legal domain ontology, modelling the main legal concepts in a specific domain concerned by case-law; an argumentation system, modelling the structure of argumentation. The input to the framework includes metadata associated with judicial concepts, and an ontology library representing the structure of case-law. The research relies on the previous efforts of the community in the field of legal knowledge representation and rule interchange for applications in the legal domain, in order to apply the theory to a set of real legal documents, stressing the OWL axioms definitions as much as possible in order to enable them to provide a semantically powerful representation of the legal document and a solid ground for an argumentation system using a defeasible subset of predicate logics. It appears that some new features of OWL2 unlock useful reasoning features for legal knowledge, especially if combined with defeasible rules and argumentation schemes. The main task is thus to formalize legal concepts and argumentation patterns contained in a judgement, with the following requirement: to check, validate and reuse the discourse of a judge - and the argumentation he produces - as expressed by the judicial text.

New developments in state-specific multireference coupled-cluster theory

Coupled-cluster theory in its single-reference formulation represents one of the most successful approaches in quantum chemistry for the description of atoms and molecules. To extend the applicability of single-reference coupled-cluster theory to systems with degenerate or near-degenerate electronic configurations, multireference coupled-cluster methods have been suggested. One of the most promising formulations of multireference coupled cluster theory is the state-specific variant suggested by Mukherjee and co-workers (Mk-MRCC). Unlike other multireference coupled-cluster approaches, Mk-MRCC is a size-extensive theory and results obtained so far indicate that it has the potential to develop to a standard tool for high-accuracy quantum-chemical treatments. This work deals with developments to overcome the limitations in the applicability of the Mk-MRCC method. Therefore, an efficient Mk-MRCC algorithm has been implemented in the CFOUR program package to perform energy calculations within the singles and doubles (Mk-MRCCSD) and singles, doubles, and triples (Mk-MRCCSDT) approximations. This implementation exploits the special structure of the Mk-MRCC working equations that allows to adapt existing efficient single-reference coupled-cluster codes. The algorithm has the correct computational scaling of d*N^6 for Mk-MRCCSD and d*N^8 for Mk-MRCCSDT, where N denotes the system size and d the number of reference determinants. For the determination of molecular properties as the equilibrium geometry, the theory of analytic first derivatives of the energy for the Mk-MRCC method has been developed using a Lagrange formalism. The Mk-MRCC gradients within the CCSD and CCSDT approximation have been implemented and their applicability has been demonstrated for various compounds such as 2,6-pyridyne, the 2,6-pyridyne cation, m-benzyne, ozone and cyclobutadiene. The development of analytic gradients for Mk-MRCC offers the possibility of routinely locating minima and transition states on the potential energy surface. It can be considered as a key step towards routine investigation of multireference systems and calculation of their properties. As the full inclusion of triple excitations in Mk-MRCC energy calculations is computational demanding, a parallel implementation is presented in order to circumvent limitations due to the required execution time. The proposed scheme is based on the adaption of a highly efficient serial Mk-MRCCSDT code by parallelizing the time-determining steps. A first application to 2,6-pyridyne is presented to demonstrate the efficiency of the current implementation.

Computational Methods in Biophysics and Medicinal Chemistry: Applications and Challenges

In this thesis I described the theory and application of several computational methods in solving medicinal chemistry and biophysical tasks. I pointed out to the valuable information which could be achieved by means of computer simulations and to the possibility to predict the outcome of traditional experiments. Nowadays, computer represents an invaluable tool for chemists. In particular, the main topics of my research consisted in the development of an automated docking protocol for the voltage-gated hERG potassium channel blockers, and the investigation of the catalytic mechanism of the human peptidyl-prolyl cis-trans isomerase Pin1.

Learning with Kernels on Graphs: DAG-based kernels, data streams and RNA function prediction.

In many application domains data can be naturally represented as graphs. When the application of analytical solutions for a given problem is unfeasible, machine learning techniques could be a viable way to solve the problem. Classical machine learning techniques are defined for data represented in a vectorial form. Recently some of them have been extended to deal directly with structured data. Among those techniques, kernel methods have shown promising results both from the computational complexity and the predictive performance point of view. Kernel methods allow to avoid an explicit mapping in a vectorial form relying on kernel functions, which informally are functions calculating a similarity measure between two entities. However, the definition of good kernels for graphs is a challenging problem because of the difficulty to find a good tradeoff between computational complexity and expressiveness. Another problem we face is learning on data streams, where a potentially unbounded sequence of data is generated by some sources. There are three main contributions in this thesis. The first contribution is the definition of a new family of kernels for graphs based on Directed Acyclic Graphs (DAGs). We analyzed two kernels from this family, achieving state-of-the-art results from both the computational and the classification point of view on real-world datasets. The second contribution consists in making the application of learning algorithms for streams of graphs feasible. Moreover,we defined a principled way for the memory management. The third contribution is the application of machine learning techniques for structured data to non-coding RNA function prediction. In this setting, the secondary structure is thought to carry relevant information. However, existing methods considering the secondary structure have prohibitively high computational complexity. We propose to apply kernel methods on this domain, obtaining state-of-the-art results.

Learning Methods and Algorithms for Semantic Text Classification across Multiple Domains

Information is nowadays a key resource: machine learning and data mining techniques have been developed to extract high-level information from great amounts of data. As most data comes in form of unstructured text in natural languages, research on text mining is currently very active and dealing with practical problems. Among these, text categorization deals with the automatic organization of large quantities of documents in priorly defined taxonomies of topic categories, possibly arranged in large hierarchies. In commonly proposed machine learning approaches, classifiers are automatically trained from pre-labeled documents: they can perform very accurate classification, but often require a consistent training set and notable computational effort. Methods for cross-domain text categorization have been proposed, allowing to leverage a set of labeled documents of one domain to classify those of another one. Most methods use advanced statistical techniques, usually involving tuning of parameters. A first contribution presented here is a method based on nearest centroid classification, where profiles of categories are generated from the known domain and then iteratively adapted to the unknown one. Despite being conceptually simple and having easily tuned parameters, this method achieves state-of-the-art accuracy in most benchmark datasets with fast running times. A second, deeper contribution involves the design of a domain-independent model to distinguish the degree and type of relatedness between arbitrary documents and topics, inferred from the different types of semantic relationships between respective representative words, identified by specific search algorithms. The application of this model is tested on both flat and hierarchical text categorization, where it potentially allows the efficient addition of new categories during classification. Results show that classification accuracy still requires improvements, but models generated from one domain are shown to be effectively able to be reused in a different one.

Deep learning for computer vision: a comparison between convolutional neural networks and hierarchical temporal memories on object recognition tasks

In recent years, Deep Learning techniques have shown to perform well on a large variety of problems both in Computer Vision and Natural Language Processing, reaching and often surpassing the state of the art on many tasks. The rise of deep learning is also revolutionizing the entire field of Machine Learning and Pattern Recognition pushing forward the concepts of automatic feature extraction and unsupervised learning in general. However, despite the strong success both in science and business, deep learning has its own limitations. It is often questioned if such techniques are only some kind of brute-force statistical approaches and if they can only work in the context of High Performance Computing with tons of data. Another important question is whether they are really biologically inspired, as claimed in certain cases, and if they can scale well in terms of "intelligence". The dissertation is focused on trying to answer these key questions in the context of Computer Vision and, in particular, Object Recognition, a task that has been heavily revolutionized by recent advances in the field. Practically speaking, these answers are based on an exhaustive comparison between two, very different, deep learning techniques on the aforementioned task: Convolutional Neural Network (CNN) and Hierarchical Temporal memory (HTM). They stand for two different approaches and points of view within the big hat of deep learning and are the best choices to understand and point out strengths and weaknesses of each of them. CNN is considered one of the most classic and powerful supervised methods used today in machine learning and pattern recognition, especially in object recognition. CNNs are well received and accepted by the scientific community and are already deployed in large corporation like Google and Facebook for solving face recognition and image auto-tagging problems. HTM, on the other hand, is known as a new emerging paradigm and a new meanly-unsupervised method, that is more biologically inspired. It tries to gain more insights from the computational neuroscience community in order to incorporate concepts like time, context and attention during the learning process which are typical of the human brain. In the end, the thesis is supposed to prove that in certain cases, with a lower quantity of data, HTM can outperform CNN.

Learning Spike-Based Population Codes by Reward and Population Feedback

We investigate a recently proposed model for decision learning in a population of spiking neurons where synaptic plasticity is modulated by a population signal in addition to reward feedback. For the basic model, binary population decision making based on spike/no-spike coding, a detailed computational analysis is given about how learning performance depends on population size and task complexity. Next, we extend the basic model to n-ary decision making and show that it can also be used in conjunction with other population codes such as rate or even latency coding.

Spatio-temporal credit assignment in population learning

Learning by reinforcement is important in shaping animal behavior, and in particular in behavioral decision making. Such decision making is likely to involve the integration of many synaptic events in space and time. However, using a single reinforcement signal to modulate synaptic plasticity, as suggested in classical reinforcement learning algorithms, a twofold problem arises. Different synapses will have contributed differently to the behavioral decision, and even for one and the same synapse, releases at different times may have had different effects. Here we present a plasticity rule which solves this spatio-temporal credit assignment problem in a population of spiking neurons. The learning rule is spike-time dependent and maximizes the expected reward by following its stochastic gradient. Synaptic plasticity is modulated not only by the reward, but also by a population feedback signal. While this additional signal solves the spatial component of the problem, the temporal one is solved by means of synaptic eligibility traces. In contrast to temporal difference (TD) based approaches to reinforcement learning, our rule is explicit with regard to the assumed biophysical mechanisms. Neurotransmitter concentrations determine plasticity and learning occurs fully online. Further, it works even if the task to be learned is non-Markovian, i.e. when reinforcement is not determined by the current state of the system but may also depend on past events. The performance of the model is assessed by studying three non-Markovian tasks. In the first task, the reward is delayed beyond the last action with non-related stimuli and actions appearing in between. The second task involves an action sequence which is itself extended in time and reward is only delivered at the last action, as it is the case in any type of board-game. The third task is the inspection game that has been studied in neuroeconomics, where an inspector tries to prevent a worker from shirking. Applying our algorithm to this game yields a learning behavior which is consistent with behavioral data from humans and monkeys, revealing themselves properties of a mixed Nash equilibrium. The examples show that our neuronal implementation of reward based learning copes with delayed and stochastic reward delivery, and also with the learning of mixed strategies in two-opponent games.

Reinforcement learning in dendritic structures

The discovery of binary dendritic events such as local NMDA spikes in dendritic subbranches led to the suggestion that dendritic trees could be computationally equivalent to a 2-layer network of point neurons, with a single output unit represented by the soma, and input units represented by the dendritic branches. Although this interpretation endows a neuron with a high computational power, it is functionally not clear why nature would have preferred the dendritic solution with a single but complex neuron, as opposed to the network solution with many but simple units. We show that the dendritic solution has a distinguished advantage over the network solution when considering different learning tasks. Its key property is that the dendritic branches receive an immediate feedback from the somatic output spike, while in the corresponding network architecture the feedback would require additional backpropagating connections to the input units. Assuming a reinforcement learning scenario we formally derive a learning rule for the synaptic contacts on the individual dendritic trees which depends on the presynaptic activity, the local NMDA spikes, the somatic action potential, and a delayed reinforcement signal. We test the model for two scenarios: the learning of binary classifications and of precise spike timings. We show that the immediate feedback represented by the backpropagating action potential supplies the individual dendritic branches with enough information to efficiently adapt their synapses and to speed up the learning process.

Reinforcement learning in dendritic structures

The discovery of binary dendritic events such as local NMDA spikes in dendritic subbranches led to the suggestion that dendritic trees could be computationally equivalent to a 2-layer network of point neurons, with a single output unit represented by the soma, and input units represented by the dendritic branches. Although this interpretation endows a neuron with a high computational power, it is functionally not clear why nature would have preferred the dendritic solution with a single but complex neuron, as opposed to the network solution with many but simple units. We show that the dendritic solution has a distinguished advantage over the network solution when considering different learning tasks. Its key property is that the dendritic branches receive an immediate feedback from the somatic output spike, while in the corresponding network architecture the feedback would require additional backpropagating connections to the input units. Assuming a reinforcement learning scenario we formally derive a learning rule for the synaptic contacts on the individual dendritic trees which depends on the presynaptic activity, the local NMDA spikes, the somatic action potential, and a delayed reinforcement signal. We test the model for two scenarios: the learning of binary classifications and of precise spike timings. We show that the immediate feedback represented by the backpropagating action potential supplies the individual dendritic branches with enough information to efficiently adapt their synapses and to speed up the learning process.