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The thesis presents detailed results of theoretical analyses based on extensive computer simulation studies with an aim to explore, quantify whenever possible, and understand structure and dynamics of polymers and proteins in several complex solvents. In order to make the Thesis coherent, we also study certain aspects of binary mixtures. Based on the phenomena studied, the thesis has been divided into four major parts: I. Dynamics of biological water: Distance dependent variation of dielectric constants in aqueous protein solutions II. Temperature dependent study of structural transformations in aqueous binary mixtures III. Conformation and dynamics of polymers in solution: Role of aqueous binary mixtures IV. Conformational change and unfolding dynamics of proteins: Role of sol-vent environment The above mentioned four parts have further been divided into thirteen chapters. In the following we provide a brief chapter-wise outline of the thesis. Part I consists of two chapters, where we focus on the study of dynamics of biological water and distance dependent variation of static and dynamic proper-ties (including dielectric constant) of water near different proteins. To start with, chapter 1 provides an introduction to the structure and dynamics of biological water. Here we discuss different experimental studies; including dielectric relaxation, NMR and salvation dynamics those explore the bimolecular hydration dynamics in great detail. We also discuss the wide range of computer simulation and theoretical studies that have been carried out to understand the dynamical behaviour of biological water. In chapter 2, we present our molecular dynamics simulation study to ex-plore the distance dependent static and dynamic behaviour of biological water near four different protein surfaces. Proteins are known to have large permanent dipole moments that can influence structure and dynamics of even distant water molecules. Therefore, distance dependence of polarization punctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different char-acteristics and varying sizes. We find that the calculated dielectric constants of the systems show a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water is found to be sensitive to the nature of the protein. We also define and calculate the effective dielectric constant of successive layers and find that the layer adjacent to protein always has significantly lower value (∼ 50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4–5 layers away. Theoretical analysis providing simple method for calculation of shellwise local dielectric constant and implication of these findings are elaborately discussed in this chapter. Part II deals with the temperature dependent study of aqueous DMSO and ethanol solutions and consists of three chapters. Chapter 3 provides a general introduction to the non-ideality (deviation from Raoult’s law) encountered in different binary mixtures. We discuss different theoretical models for treatment of binary mixtures. Finally we provide a systematic study about the non-ideality observed in aqueous binary mixtures. Here we discuss the anomalies observed in such systems and carry out a brief survey on the existing ideas of structural transformations associated with the solvation of a foreign molecule in water. In chapter 4, we discuss the results of temperature dependent study of struc-tural and dynamic properties of aqueous dimethyl sulfoxide (DMSO) mixture. It is now well-known that aqueous DMSO mixture exhibits signature of perco-lation driven structural aggregation at a mole fraction range xDMSO ≈ 0.15. We study the structural and dynamical change in this binary mixture below and above the percolation threshold along with decreasing temperature. Significant change in the molecular structure of DMSO as well as that of water is observed above the percolation threshold at a lower temperature, particularly at 200K. The structural arrangement of the DMSO molecules is found to be progressively more ordered with increasing DMSO concentration and decreasing temperature. On the other hand, water structure is found to be significantly deviated from tetrahedral arrangement in presence of DMSO clusters even at low temperature. The dynamics of water is also found to be considerably affected with increase of concentration and lowering of temperature. Similar phenomenon is observed for another amphiphilic molecule, ethanol, and has been discussed in chapter 5. Aqueous ethanol mixture is a widely studied solvent, both experimentally and using computer simulations. All the studies indicate several distinct salvation regimes. In recent molecular dynamics simulation studies, the reason for formation of micro-aggregates of ethanol is again attributed to percolation driven structural transformation. We carry out a temperature dependent study of water-ethanol binary mixture, particularly at low ethanol concentration to understand the molecular origin of such structural transformation. We find that the structural arrangement of ethanol as well as water molecules is similarly affected as that of DMSO with lowering of temperature. However, dynamics of water molecules in aqueous ethanol solution is found to be marginally affected, unlike the case of aqueous DMSO solution. We discuss the microscopic reason for such behaviour in a detailed manner. In Part III, we discuss the dynamics of linear polymer chains in different aqueous binary mixtures. Here we have three chapters. In chapter 6, we carry out a brief survey of the existing theories of polymers in solution. We discuss the quality of solvents depending on the preferred interactions between the polymer and the solvent or the polymer with its own. We also discuss the celebrated Flory-Huggins theory. We derive the expression of free energy of the Flory-Huggins theory in terms of the volume fraction of monomer and solvent molecules. In chapter 7, we discuss the results of our study of polymer dynamics in aqueous DMSO solution. We find that at a mole fraction 0.05 of DMSO (xDMSO ≈ 0.05) in aqueous solution, a linear polymer chain of intermediate length (n=30) adopts collapsed conformation as the most stable conformational state. The same chain exhibits an intermittent oscillation between the collapsed and the extended coiled conformations in neat water. Even when the mole fraction of DMSO in the bulk is 0.05, the concentration of the same in the first hydration layer around the polymer is found to be as large as 17 %. Formation of such hydrophobic environment around the hydrocarbon chain may be viewed as the reason for the collapsed conformation gaining additional stability. We find a second anomalous behaviour to emerge near xDMSO ≈ 0.15 that is attributed to the percolation driven structural aggregation of DMSO that lowers the relative concentration of the DMSO molecules in the hydration layer. In chapter 8, we carry out similar study of linear polymer chain in water– ethanol binary mixture. In this case also, we find a sudden collapse of the poly-merat xEtOH ≈ 0.05. Since ethanol molecules are known to form micro-aggregates in this concentration range, stability of collapsed state of polymer at this con-centration is anticipated to be correlated to this phenomenon. In fact, a purely hydrophobic polymer chain, in its collapsed form is anticipated to assist in the formation of spanning cluster comprised of hydrophobic ethyl groups at this concentration range thereby facilitating the percolation transition. We discuss these prospects in this chapter. Part IV deals with the solvent sensitivity to the conformational change and unfolding dynamics of protein. Part IV consists of five chapters. In chapter 9, we develop an understanding of protein folding and unfolding dynamics by discussing the fundamental theories developed in the last few decades. We also discuss the major role of solvents in stabilizing or destabilizing the native, ordered state. In chapter 10, we present a detailed study of unfolding of a small protein, chicken villin headpiece (HP36) in water-ethanol binary mixture, using molecular dynamics simulations. The prime objective of this work is to explore the sensitivity of protein dynamics towards increasing concentration of the cosolvent and unravel essential features of intermediates formed in the unfolding path-way. In water–ethanol binary mixtures, HP36 is found to unfold partially, under ambient conditions, that otherwise requires temperature as high as ∼ 600K to denature in pure aqueous solvent. The study unravels certain interesting aspects about the pathway of unfolding, guided by the formation of unique intermediates. Unfolding is initiated by the separation of hydrophoic core comprising three phenylalanine residues (Phe7, Phe11, Phe18). This separation initiates the melting of the helix2 of the protein. However, with an increase of cosolvent concentration different partially unfolded intermediates are found to be formed. We attribute the emergence of such partially unfolded states to the preferential solvation of hydrophobic residues by the ethyl groups of ethanol. We explore and subsequently quantify the detailed dynamics of unfolding in water-ethanol that appear to be more complex and sensitive to solvent composition. With an aim to develop a general understanding of the role of water–ethanol binary mixture in facilitating anomalous conformational dynamics of proteins, we carry out combined theoretical and experimental studies to explore detailed structural change of a larger protein, Myoglobin with increasing ethanol concentration. These studies are described in chapter 11. In agreement with our pre-vious observations, we identify in this case two well-defined structural regimes, one at xEtOH ≈ 0.05 and the other at xEtOH ≈ 0.25, characterized by formation of distinct partially folded conformations and separated by a unique partially unfolded intermediate state at xEtOH ≈ 0.15. We also find non-monotonic com-position dependence of (i) radius of gyration (ii) long range contact order (iii) residue specific solvent accessible surface area of tryptophan (iv) circular dichro-ism spectra and UV-absorption peaks. Multiple structural transformations, well-known in water-ethanol binary mixture, appear to have considerably stronger effects on the conformation and dynamics of protein Myoglobin. In chapter 12, we explore the free energy surface of unfolding pathway through umbrella sampling, for the small globular alpha-helical protein chicken-villin headpiece (HP36) in three different solvent conditions (water, xDMSO ≈ 0.15 and xDMSO ≈ 0.3). Recently established as a facilitator of helix melting, DMSO is found to be a good denaturant for HP36 and at a mole fraction of xDMSO ≈ 0.3, complete melting of the protein is ensured. The unfolding proceeds through initial separation or melting of the same aggregated hydrophobic core that com-prises three phenylalanine residues (Phe7, Phe11 and Phe18) accompanied by simultaneous melting of the helix2. Unfolding is found to be a multistage process involving crossing of three consecutive minima and two barriers at the initial stage. At a molecular level, Phe18 is observed to reorient itself towards other hy-drophobic grooves to stabilize the intermediate states. We identify the configuration of intermediates in all the solvent conditions which are found to be unique for the corresponding minima with similar structural arrangement. Consider-able softening of the barriers is observed with increasing DMSO concentration. Higher concentration of DMSO tunes the unfolding pathway by destabilizing the third minimum and stabilizing the second one, indicating the development of solvent modified, less rugged pathway. Chapter 13 provides a detailed microscopic mechanism of DMSO induced unfolding of HP36. We analyze the free energy contours of the protein HP36, obtained from molecular dynamics simulation in xDMSO ≈ 0.15 and xDMSO ≈ 0.3. The most probable intermediates obtained from the free energy contours are found to be similar to those obtained from umbrella sampling which again sup-ports the fact that the melting proceeds through formation of a series of unique intermediates. We characterize the preferential hydrophobic salvation of the hydrophobic core that drives the melting of secondary structure, by calculating time dependent radial distribution function and identifying the formation of strong orientation order between methyl groups of DMSO and phenyl alanine residues. Finally we employ Kramer’s rate equation to calculate the rate of bar-rier crossing that reveals significantly faster rate of unfolding with increasing DMSO concentration that is in agreement with simulation results. Whenever possible, we have discussed the scope of future work at the end of each chapter.

I started writing this thesis not only to obtain a doctoral degree, but also to compile in a particular way all the work that I have done during this time. The articles published during these years can only give a short overview of my research task. I decided to give my own perspective of the things I have learned and the results I have obtained. Some sections are directly the published articles, but some other are not and contain a significant amount of unpublished data. Even in some cases the published plots have been modified / altered to provide more insight or to maintain consistency. Historical perspectives often provide a deep understanding of the problems and have been briefly discussed in some chapters. This thesis contains theoretical and computer simulation studies to under-stand effects of spatial correlation on dynamics in several complex systems. Based on the different phenomena studied, the thesis has been divided into three major parts: I. Pair hydrophobicity, composition-dependent anomalies and structural trans-formations in aqueous binary mixtures II. Microscopic analysis of hydrophobic force law in a two dimensional (2D) water-like model system III. Diffusion of a tagged particle on a rugged energy landscape with spatial correlations The three parts have been further divided into ten chapters. In the following we provide part-wise and chapter-wise outline of the thesis. Part I consists of six chapters, where we focus on several important aqueous binary mixtures of amphiphilic molecules. To start with, Chapter 1 provides an introduction to non-ideality often encountered in aqueous binary mixtures. Here we briefly discuss the existing ideas of structural transformations associated with solvation of a foreign molecule in water, with particular emphasis on the classic “iceberg” model. Over the last decade, several investigations, especially neutron scattering and diffraction experiments, have questioned the validity of existing theories and have given rise to an alternate molecular picture involving micro aggregation of amphiphilic co-solvents in their aqueous binary mixtures. Such microheterogeneity was also supported by other experiments and simulations. In Chapter 2, we present our calculation of the separation dependence of potential of mean force (PMF) between two methane molecules in water-dimethyl sulfoxide (DMSO) mixture, using constrained molecular dynamics simulation. It helps us to understand the composition-dependence of pair hydrophobicity in this binary solvent. We find that pair hydrophobicity in the medium is surprisingly enhanced at DMSO mole fraction xDMSO ≈ 0.15, which explains several anomalous properties of this binary mixture – including the age-old mystery of DMSO being a protein stabilizer at lower concentration and protein destabilizer at higher concentration. Chapter 3 starts with discussion of non-monotonic composition dependence of several other properties in water-DMSO binary mixture, like diffusion coefficient, local composition fluctuation and fluctuations in total dipole moment of the system. All these properties exhibit weak to strong anomalies at low solute concentration. We attempt to provide a physical interpretation of such anomalies. Previous analyses often suggested occurrence of a “structural transformation” (or, microheterogeneity) in aqueous binary mixtures of amphiphilic molecules. We show that this structural transformation can be characterized and better understood under the purview of percolation theory. We define the self-aggregates of DMSO as clusters. Analysis of fractal dimension and cluster size distribution with reference to corresponding “universal” scaling exponents, combined with calculation of weight-averaged fraction of largest cluster and cluster size weight average, reveal a percolation transition of the clusters of DMSO in the anomalous concentration range. The percolation threshold appears at xDMSO ≈ 0.15. The molecular picture suggests that DMSO molecules form segregated islands or micro-aggregates at concentrations below the percolation threshold. Close to the critical concentration, DMSO molecules start forming a spanning cluster which gives rise to a bi-continuous phase (of water-rich region and DMSO-rich region) beyond the threshold of xDMSO ≈ 0.15. This percolation transition might be responsible for composition-dependent anomalies of the binary mixture in this low concentration regime. Similar phenomenon is observed for another amphiphilic molecule – ethanol, as discussed in Chapter 4. We again find composition dependent anomalies in several thermophysical properties, such as local composition fluctuation, radial distribution function of ethyl groups and self-diffusion co-efficient of ethanol. Earlier experiments often suggested distinct structural regimes in water-ethanol mixture at different concentrations. Using the statistical mechanical techniques introduced in the previous chapter, we show that ethanol clusters undergo a percolation transition in the anomalous concentration range. Despite the lack of a precise determination of the percolation threshold, estimate lies in the ethanol mole fraction range xEtOH ≈ 0.075 - 0.10. This difficulty is probably due to transient nature of the clusters (as will be discussed in Chapter 6) and finite size of the system. The scaling of ethanol cluster size distribution and the fractal behavior of ethanol clusters, however, conclusively demonstrate their “spanning” nature. To develop a unified understanding, we further study the composition-dependent anomalies and structural transformations in another amphiphilic molecule, tertiary butyl alcohol (TBA) in Chapter 5. Similar to the above-mentioned aqueous binary mixtures of DMSO and ethanol, we demonstrate here that the anomalies occur due to local structural changes involving self-aggregation of TBA molecules and percolation transition of TBA clusters at xTBA ≈ 0.05. At this percolation threshold, we observe a lambda-type divergence in the fluctuation of the size of the largest TBA cluster, reminiscent of a critical point. Interestingly, water molecules themselves exhibit a reverse percolation transition at higher TBA concentration ≈ 0.45, where large spanning water clusters now break-up into small clusters. This is accompanied by significant divergence of the fluctuations in the size of the largest water cluster. This second transition gives rise to another set of anomalies around. We conclude this part of the thesis with Chapter 6, where we introduce a novel method for understanding the stability of fluctuating clusters of DMSO, ethanol and TBA in their respective aqueous binary mixtures. We find that TBA clusters are the most stable, whereas ethanol clusters are the most transient among the three representative amphiphilic co-solvents. This correlates well with the amplitude of anomalies observed in these three binary mixtures. Part II deals with the topic of hydrophobic force law in water. In the introductory Chapter 7 of this part, we briefly discuss the concept of hydrophobicity which is believed to be of importance in understanding / explaining the initial processes involved in protein folding. We also discuss the experimental observations of Israelachvili (on the force between hydrophobic plates) and the empirical hydrophobic force law. We briefly touch upon the theoretical back-ground, including Lum-Chandler-Weeks theory. We conclude this chapter with a brief account of relevant and important in silico studies so far. In Chapter 8, we present our studies on Mercedes-Benz (MB) model – a two dimensional model system where circular disks interact with an anisotropic potential. This model was introduced by Ben-Naim and was later parametrized by Dill and co-workers to reproduce many of the anomalous properties of water. Using molecular dynamics simulation, we show that hydrophobic force law is indeed observed in MB model, with a correlation length of ξ=3.79. The simplicity of the model enables us to unravel the underlying physics that leads to this long range force between hydrophobic plates. In accordance with Lum-Chandler-Weeks theory, density fluctuation of MB particles (leading to cavitation) between the hydrophobic rods is clearly distinguishable – but it is not sufficiently long ranged, with density correlation extending only up to ζ=2.45. We find that relative orientation of MB molecules plays an important role in the origin of the hydrophobic force in long range. We define appropriate order parameters to capture the role of orientation, and briefly discuss a plausible approach of an orientation-dependent theory to explain this phenomenon. Part III consists of two chapters and focuses on the diffusion of a Brownian particle on a Gaussian random energy landscape. We articulate the rich history of the problem in the introductory Chapter 9. Despite broad applicability and historical importance of the problem, we have little knowledge about the effect of ruggedness on diffusion at a quantitative level. Every study seems to use the expression of Zwanzig [Proc. Natl. Acad. U.S.A, 85, 2029 (1988)] who derived the effective diffusion coefficient, Deff =D0 exp (-β2ε2 )for a Gaussian random surface with variance ε, but validity of the same has never been tested rigorously. In Chapter 10, we introduce two models of Gaussian random energy surface – a discrete lattice and a continuous field. Using computer simulation and theoretical analyses, we explore many different aspects of the diffusion process. We show that the elegant expression of Zwanzig can be reproduced ex-actly by Rosenfeld diffusion-entropy scaling relationship. Our simulations show that Zwanzig’s expression overestimates diffusion in the uncorrelated Gaussian random lattice – differing even by more than an order of magnitude at moderately high ruggedness (ε>3.0). The disparity originates from the presence of “three-site traps” (TST) on the landscape – which are formed by deep minima flanked by high barriers on either side. Using mean first passage time (MFPT) formalism, we derive an expression for the effective diffusion coefficient, Deff =D0 exp ( -β2ε2)[1 +erf (βε/2)]−1 in the presence of TSTs. This modified expression reproduces the simulation results accurately. Further, in presence of spatial correlation we derive a general expression, which reduces to Zwanzig’s form in the limit of infinite spatial correlation and to the above-mentioned equation in absence of correlation. The Gaussian random field has an inherent spatial correlation. Diffusion coefficient obtained from the Gaussian field – both by simulations and analytical methods – establish the effect of spatial correlation on random walk. We make special note of the fact that presence of TSTs at large ruggedness gives rise to an apparent breakdown of ergodicity of the type often encountered in glassy liquids. We characterize the same using non-Gaussian order parameter, and show that this “breakdown” scales with ruggedness following an asymptotic power law. We have discussed the scope of future work at the end of each chapter when-ever appropriate.