Recent experimental techniques in biology made possible the acquisition of overwhelming amounts of data concerning complex biological networks, such as neural networks, gene regulation networks and protein-protein interaction networks. These techniques are able to record states of individual components of such networks (neurons, genes, proteins) for a large number of configurations. However, the most biologically relevantinformation lies in their connectivity and in the way their components interact, information that these techniques aren't able to record directly. The aim of this thesis is to study statistical methods for inferring information about the connectivity of complex networks starting from experimental data. The subject is approached from a statistical physics point of view drawing from the arsenal of methods developed in the study of spin glasses. Spin-glasses are prototypes of networks of discrete variables interacting in a complex way and are widely used to model biological networks. After an introduction of the models used and a discussion on the biological motivation of the thesis, all known methods of network inference are introduced and analysed from the point of view of their performance. Then, in the third part of the thesis, a new method is proposed which relies in the remark that the interactions in biology are not necessarily symmetric (i.e. the interaction from node A to node B is not the same as the one from B to A). It is shown that this assumption leads to methods that are both exact and efficient. This means that the interactions can be computed exactly, given a sufficient amount of data, and in a reasonable amount of time. This is an important original contribution since no other method is known to be both exact and efficient.

Des techniques expérimentales récentes ont donné la possibilité d'acquérir un très grand nombre de données concernant des réseaux biologiques complexes, comme des réseaux de neurones, des réseaux de gènes et des réseaux d'interactions de protéines. Ces techniques sont capables d'enregistrer les états des composantes individuelles de ces réseaux (neurones, gènes, protéines) pour un grand nombre de configurations. Cependant, l'information la plus pertinente biologiquement se trouve dans la connectivité de ces systèmes et dans la façon précise avec laquelle ces composantes interagissent, information que les techniques expérimentales ne sont pas au point d'observer directement. Le bût de cette thèse est d'étudier les méthodes statistiques nécessaires pour inférer de l'information sur la connectivité des réseaux complexes en partant des données expérimentales. Ce sujet est traité par le point de vue de la physique statistique, en puisant de l'arsenal de méthodes théoriques qui ont été développées pour l'étude des verres de spins. Les verres de spins sont des exemples de réseaux à variables discrètes qui interagissent de façon complexe et sont souvent utilisés pour modéliser des réseaux biologiques. Après une introduction sur les modèles utilisés ainsi qu'une discussion sur la motivation biologique de cette thèse, toutes les méthodes d'inférence de réseaux connues sont présentées et analysées du point de vue de leur performance. Par la suite, dans la troisième partie de la thèse, un nouvelle méthode est proposée qui s'appuie sur la remarque que les interactions en biologie ne sont pas nécessairement symétriques (c'est-à-dire l'interaction entre les noeuds A et B n'est pas la même dans les deux directions). Il est démontré que cette assomption conduit à des méthodes qui sont capables de prédire les interactions de façon exacte, étant donné un nombre suffisant de données, tout en utilisant un temps de calcul polynomial. Ceci est un résultat original important car toutes les autres méthodes connues sont soit exactes et non-polynomiales soit inexactes et polynomiales. / Recent experimental techniques in biology made possible the acquisition of overwhelming amounts of data concerning complex biological networks, such as neural networks, gene regulation networks and protein-protein interaction networks. These techniques are able to record states of individual components of such networks (neurons, genes, proteins) for a large number of configurations. However, the most biologically relevantinformation lies in their connectivity and in the way their components interact, information that these techniques aren't able to record directly. The aim of this thesis is to study statistical methods for inferring information about the connectivity of complex networks starting from experimental data. The subject is approached from a statistical physics point of view drawing from the arsenal of methods developed in the study of spin glasses. Spin-glasses are prototypes of networks of discrete variables interacting in a complex way and are widely used to model biological networks. After an introduction of the models used and a discussion on the biological motivation of the thesis, all known methods of network inference are introduced and analysed from the point of view of their performance. Then, in the third part of the thesis, a new method is proposed which relies in the remark that the interactions in biology are not necessarily symmetric (i.e. the interaction from node A to node B is not the same as the one from B to A). It is shown that this assumption leads to methods that are both exact and efficient. This means that the interactions can be computed exactly, given a sufficient amount of data, and in a reasonable amount of time. This is an important original contribution since no other method is known to be both exact and efficient.

The thesis involves computer simulation and theoretical studies of dynamics of water under confinement and structural transformation in different complex systems. Based on the systems and phenomena of interest, the work has been classified in to three major parts: I. Dynamics of water under confinement II. Dynamics of water in presence of amphiphilic solutes III. Structural transformation in complex systems The three parts have further been divided into nine chapters. Brief chapter wise outline of the thesis is discussed below. Part I deals with the dynamics of water in confined systems. In Chapter I.1, we provide a brief introduction of water dynamics inc on fined systems. We also give a brief outline of relevant experimental and theoretical techniques used to study the water dynamics under confinement. Chapter I.2 describes a model based analytical study of dynamical correlation in confined systems. Here, we introduce a novel one dimensional Ising model to investigate the propagation and annihilation of dynamical correlations in confined systems and to understand the intriguing shortening of the orientational relaxation time that has been reported for small sized reverse micelles (RMs).In our model, the two spins located at the two end cells are oriented in the opposite directions to mimic the surface effects present in the real systems. These produce opposing polarizations which propagate from the surface to the center, thus producing bulk like condition at the center. This model can be solved analytically for short chains. For long chains, we solve the model numerically with Glauber spin flip dynamics (and also with Metropolis single-spin flip Monte Carlo algorithm).We show that the model satisfactorily reproduces many of the features observed in experiments. Due to the destructive interference among correlations that propagate from the surface to the core, one of the rotational relaxation time components decays faster than the bulk. In general, the relaxation of spins is non-exponential due to the interplay between various interactions. In the limit of strong coupling between the spins or in the limit of low temperature, the nature of the relaxation of spins undergoes a change with the emergence of homogeneous dynamics, where the decay is predominantly exponential. In Chapter I.3, layer-wise distance dependent orientation relaxation of water confined in reverse micelle s(RM)is studied using theoretical and computational tools. We use both a newly constructed spins on a ring (SOR) Ising-type model with modified Shore-Zwanzig rotational dynamics and atomistic simulations with explicit water. Our study explores the size effect of RMs and the role of intermolecular correlations, compromised by the presence of a highly polar surface, on the distance (from the surface) dependence of water relaxation. The SOR model can capture some aspects of distance dependent orientation relaxation, such as acceleration of orientation relaxation at intermediate layers. In atomistic simulations, layer-wise decomposition of hydrogen bond (H-bond) formation pattern clearly reveal that the H-bond arrangement of water at a certain distance away from the surface can remain frustrated due to interaction with the polar surface head groups. We show that this layer-wise analysis also reveals the presence of a non-monotonic, slow relaxation component which can be attributed to the frustration effect and is accentuated in small to intermediate size RMs. For larger RMs, the long-time component decreases monotonically from the interface to the interior of the RMs with slowest relaxation observed at the interface. In ChapterI.4, we present theoretical two dimensional infrared spectroscopic (2D-IR) studies of water confined within RMs of various sizes. Here we focus again mainly on the altered dynamics of confined water by performing a layer-wise decomposition of water. We aim to quantify the relative contributions to the calculated 2D-IR spectra by water molecules located in different layers. The spectra of 0-1 transition clearly show substantial elongation along the diagonal, due to in homogeneous broadening and incomplete spectral diffusion, in the surface water layer of different size of RMs studied in this work. Our study reveals that the motion of the surface water molecules is sub-diffusive, establishing the constrained nature of their dynamics. This is further supported by the two peak nature of the angular analogue of the van Hove correlation function. With increasing system size the motion of water molecules becomes more diffusive in nature and the structural diffusion is observed to be almost completed in the central layer of larger RMs. Comparisons between experiment and simulation help establishing the correspondence between the spectral decomposition available in experimental 2D-IR with the spatial decomposition of simulated 2D-IR. Simulations also allow a quantitative exploration of the relative role of water, sodium ions and sulfonate head groups in irrational dephasing. Interestingly, the negative cross correlation between forces on oxygen and hydrogen of O-H bond in bulk water significantly decreases in the surface layer of different RMs. This negative cross correlation gradually increases in the central layer with increasing size of the RMs and this is found to be partly responsible for the faster relaxation rate of water in the central layer. Part II consists of two chapters and focuses on the dynamics of water in presence of amphiphilic solutes. In Chapter II.1, we present a brief introduction of water – DMSO binary mixture and various anomalous properties of the same. In Chapter II.2, we present theoretical IR study of water dynamics in water–DMSO binary mixtures of different compositions. We show that with increasing DMSO concentration, the IR absorption peak maxima show the presence of structural transformation in similar concentration range, observed in earlier studies. Analysis of H-bonded network near hydrophilic and hydrophobic part of DMSO also suggests that average number of hydrogen bonds near the hydrophobic parts possess maxima at the same concentration range. We also show that with increasing DMSO concentration water dynamics becomes very slow. This has been supported by the diagonal elongation of the 2D-IR spectra and also the slow decay of frequency fluctuation correlation n function (FFCF) and the orientation time correlation function (OTCF). The decoupling of the OTCF establishes that water-DMSOH-bond is much stronger than that of water-water. The last part (Part III) consists of three chapters that deal with structural transformation in various complex systems. In Chapter III.1, we introduce polydisperse systems and present existing theoretical, computer simulation and experimental studies. It also contains the importance and diversity of polydisperse system in nature. In Chapter III.2, we present computer simulation study of melting of polydisperse Lennard-Jones (LJ) system with Gaussian polydispersity in size. The phase diagram reproduces the existence of an early temperature in variant terminal polydispersity (δt0.11), with no signature of re-entrant melting. The absence of re-entrant melting can be attributed to the influence of attractive part of the potential on melting. We find that at terminal polydispersity the fractional density change approaches zero that seems to arise from vanishingly small compressibility of the disordered phase. At constant temperature and volume fraction system undergoes a sharp transition from crystalline solid to disordered state with increasing polydispersity. This has been quantified by second and third order rotational invariant bond orientational orders as well as by the average inherent structure energy. The translational order parameter also indicates similar structural change The free energy calculation further supports the nature of the transition. The third order bond orientational order shows that with increasing polydispersity, local cluster favors more icosahedral-like arrangements and thus the system loses its crystalline symmetry. In Chapter III.3, we present study of phase transition and effect of confinement on it in SOR model. This system is similar to our SOR model discussed in Chapter I.3. The spins execute continuous rotation under a modified XY Hamiltonian. In order to understand the nature of phase transition in such confined spin systems we have performed extensive Monte Carlo simulations. The system size dependence of Binders cumulant, specific heat, order parameter and finite size scaling of order parameter universally suggest the existence of a phase transition. The absence of hysteresis and Scaling of Binders energy cumulant minimum confirm the continuous nature of the transition. The finite size scaling analyses give rise to the mean field nature of the transition. Plausible applications of the proposed model in modeling dipolar liquids in confined systems are also discussed. In Appendix A, we discuss a preliminary study of front propagation in a non-equilibrium system. The model system analogous to the super cooled liquid shows non-Avrami domain growth during rejuvenation. The origin of the non-Avrami nature of the domain growth and the presence of cross over are also discussed. In Appendix B, we discuss umbrella a sampling technique and WHAM analysis which is used in ChapterIII.2 to get the free energy of polydisperse LJ system.