The implicit-solvent model uses continuum electrostatic theory to represent the salt solution around dissolved biomolecules, leading to a coupled system of the Poisson-Boltzmann and Poisson equations. This thesis uses the implicit-solvent model to study solvation, binding and adsorption of proteins. We developed an implicit-solvent model solver that uses the boundary element method (BEM), called PyGBe. BEM numerically solves integral equations along the biomolecule-solvent interface only, therefore, it does not need to discretize the entire domain. PyGBe accelerates the BEM with a treecode algorithm and runs on graphic processing units. We performed extensive verification and validation of the code, comparing it with experimental observations, analytical solutions, and other numerical tools. Our results suggest that a BEM approach is more appropriate than volumetric based methods, like finite-difference or finite-element, for high accuracy calculations. We also discussed the effect of features like solvent-filled cavities and Stern layers in the implicit-solvent model, and realized that they become relevant in binding energy calculations. The application that drove this work was nano-scale biosensors-- devices designed to detect biomolecules. Biosensors are built with a functionalized layer of ligand molecules, to which the target molecule binds when it is detected. With our code, we performed a study of the orientation of proteins near charged surfaces, and investigated the ideal conditions for ligand molecule adsorption. Using immunoglobulin G as a test case, we found out that low salt concentration in the solvent and high positive surface charge density leads to favorable orientations of the ligand molecule for biosensing applications. We also studied the plasmonic response of localized surface plasmon resonance (LSPR) biosensors. LSPR biosensors monitor the plasmon resonance frequency of metallic nanoparticles, which shifts when a target molecule binds to a ligand molecule. Electrostatics is a valid approximation to the LSPR biosensor optical phenomenon in the long-wavelength limit, and BEM was able to reproduce the shift in the plasmon resonance frequency as proteins approach the nanoparticle.

The folding mechanism of several β-structures (e.g., β-hairpins and β-sheets) was studied using newly developed enhanced sampling methods along with MD simulations in all implicit solvent environments. The influence of different implicit solvent models on the folding simulation of β-structure was also tested. Through the analysis of the free energy landscape as the function of several suitable reaction coordinates, we observed that the folding of β-hairpins is actually a two-state transition. In addition, the folding free energy landscapes for those related hairpins indicate the apparent sequence dependence, which demonstrates different folding mechanisms of similar β-structures of varied sequence. We also found that the stability of backbone hydrogen bonds is determined by the turn sequence and the composition of hydrophobic core cluster in β-structures. Neither of these findings was reported before. The processive movement of kinesin was also studied at the mesoscopic level. We developed a simple physical model to understand the asymmetric hand-over-hand mechanism of the kinesin walking on the microtubule. The hand-over-hand motion of the conventional kinesin is reproduced in our model and good agreement is achieved between calculated and experimental results. The experimentally observed limping of the truncated kinesin is also perfectly described by our model. The global conformational change of kinesin heads (e.g., the power stroke of neck-linkers which works as lever-arms during the kinesin walking, the transition between open and closed states of the switch region of the nucleotide binding domain in each head induced by the nucleotide binding and release) was studied for both dimeric and monomeric kinesins using a coarse-grained model, anisotropic network model (ANM). At the same time Langevin mode analysis was used to study the solvent influence on the motions of the kinesin head mimicked by ANM. Additionally, the correlation between the neck-linker and the nucleotide binding site was also studied for dimeric and monomeric kinesins. The former shows the apparent correlation between two subdomains whereas the latter does not, which may explain the experimental observation that only the dimeric kinesin is capable of walking processively on the microtubule.

Atomistic modeling and simulation methods enable a modern molecular approach to bio-medical research. Issues addressed range from structure-function relationships to structure-based drug design. The ability of these methods to address biologically relevant problems is largely determined by their accurate treatment of electrostatic interactions in the target biomolecular structure. In practical molecular simulations, the electrostatic charge density of molecules is approximated by an arrangement of fractional "point charges" throughout the molecule. While chemically intuitive and straightforward in technical implementation, models based exclusively on atom-centered charge placement, a major workhorse of the biomolecular simulations, do not necessarily provide a sufficiently detailed description of the molecular electrostatic potentials for small systems, and can become prohibitively expensive for large systems with thousands to millions of atoms. In this work, we propose a rigorous and generally applicable approach, Optimal Point Charge Approximation (OPCA), for approximating electrostatic charge distributions of biomolecules with a small number of point charges to best represent the underlying electrostatic potential, regardless of the distance to the charge distribution. OPCA places a given number of point charges so that the lowest order multipole moments of the reference charge distribution are optimally reproduced. We provide a general framework for calculating OPCAs to any order, and introduce closed-form analytical expressions for the 1-charge, 2-charge and 3-charge OPCA. We demonstrate the advantage of OPCA by applying it to a wide range of biomolecules of varied sizes. We use the concept of OPCA to develop a different, novel approach of constructing accurate and simple point charge water models. The proposed approach permits a virtually exhaustive search for optimal model parameters in the sub-space most relevant to electrostatic properties of the water molecule in liquid phase. A novel rigid 4-point Optimal Point Charge (OPC) water model constructed based on the new approach is substantially more accurate than commonly used models in terms of bulk water properties, and delivers critical accuracy improvement in practical atomistic simulations, such as RNA simulations, protein folding, protein-ligand binding and small molecule hydration. We also apply our new approach to construct a 3-point version of the Optimal Point Charge water model, referred to as OPC3. OPCA can be employed to represent large charge distributions with only a few point charges. We use this capability of OPCA to develop a multi-scale, yet fully atomistic, generalized Born approach (GB-HCPO) that can deliver up to 2 orders of magnitude speedup compared to the reference MD simulation. As a practical demonstration, we exploit the new multi-scale approach to gain insight into the structure of million-atom 30-nm chromatin fiber. Our results suggest important structural details consistent with experiment: the linker DNA fills the core region and the H3 histone tails interact with the linker DNA. OPC, OPC3 and GB-HCPO are implemented in AMBER molecular dynamics software package. / Ph. D.

En sjukdom kan många gånger härledas till en kaskadereaktion mellan proteiner, co-faktorer och substrat. Denna kaskadreaktion blir många gånger målet för att behandla sjukdomen med läkemedel. För att designa nya läkemedelsmoleyler används vanligen datorbaserade verktyg. Denna design av läkemedelsmolekyler drar stor nytta av att målproteinet är känt och då framförallt dess tredimensionella (3D) struktur. Är 3D-strukturen känd kan man utföra så kallad struktur- och datorbaserad molekyldesign, 3D-geometrin (f.f.a. för inbindningsplatsen) blir en vägledning för designen av en ny molekyl. Många faktorer avgör interaktionen mellan en molekyl och bindningsplatsen, till exempel fysikalisk-kemiska egenskaper hos molekylen och bindningsplatsen, flexibiliteten i molekylen och målproteinet, och det omgivande lösningsmedlet. För att strukturbaserad molekyldesign ska fungera väl måste två viktiga steg utföras: i) 3D anpassning av molekyler till bindningsplatsen i ett målprotein (s.k. dockning) och ii) prediktion av molekylers affinitet för bindningsplatsen. Huvudsyftena med arbetet i denna avhandling var som följer: i) skapa modeler för att prediktera affiniteten mellan en molekyl och bindningsplatsen i ett målprotein; ii) förfina molekyl-protein-geometrin som skapas vid 3D-anpassning mellan en molekyl och bindningsplatsen i ett målprotein (s.k. dockning); iii) karaktärisera proteiner och framför allt deras sekundärstruktur; iv) bedöma effekten av olika matematiska beskrivningar av lösningsmedlet för förfining av 3D molekyl-protein-geometrin skapad vid dockning och prediktion av molekylers affinitet för proteiners bindningsfickor. Ett övergripande syfte var att använda kemometriska metoder för modellering och dataanalys på de ovan nämnda punkterna. För att sammanfatta så presenterar denna avhandling metoder och resultat som är användbara för strukturbaserad molekyldesign. De rapporterade resultaten visar att det är möjligt att skapa kemometriska modeler för prediktion av molekylers affinitet för bindningsplatsen i ett protein och att dessa presterade lika bra som andra vanliga metoder. Dessutom kunde kemometriska modeller skapas för att beskriva effekten av hur inställningarna för olika parametrar i dockningsprogram påverkade den 3D molekyl-protein-geometrin som dockingsprogram skapade. Vidare kunde kemometriska modeller andvändas för att öka förståelsen för deskriptorer som beskrev sekundärstrukturen i proteiner. Förfining av molekyl-protein-geometrin skapad genom dockning gav liknande och ickesignifikanta resultat oberoende av vilken matematisk modell för lösningsmedlet som användes, förutom för ett fåtal (sex av 30) fall. Däremot visade det sig att användandet av en förfinad geometri var värdefullt för prediktion av molekylers affinitet för bindningsplatsen i ett protein. Förbättringen av prediktion av affintitet var markant då en Poisson-Boltzmann beskrivning av lösningsmedlet användes; jämfört med prediktionerna gjorda med ett dockningsprogram förbättrades korrelationen mellan beräknad affintiet och uppmätt affinitet med 0,7 (R2). / A disease is often associated with a cascade reaction pathway involving proteins, co-factors and substrates. Hence to treat the disease, elements of this pathway are often targeted using a therapeutic agent, a drug. Designing new drug molecules for use as therapeutic agents involves the application of methods collectively known as computer-aided molecular design, CAMD. When the three dimensional (3D) geometry of a macromolecular target (usually a protein) is known, structure-based CAMD is undertaken and structural information of the target guides the design of new molecules and their interactions with the binding sites in targeted proteins. Many factors influence the interactions between the designed molecules and the binding sites of the target proteins, such as the physico-chemical properties of the molecule and the binding site, the flexibility of the protein and the ligand, and the surrounding solvent. In order for structure-based CAMD to be successful, two important aspects must be considered that take the abovementioned factors into account. These are; i) 3D fitting of molecules to the binding site of the target protein (like fitting pieces of a jigsaw puzzle), and ii) predicting the affinity of molecules to the protein binding site. The main objectives of the work underlying this thesis were: to create models for predicting the affinity between a molecule and a protein binding site; to refine the geometry of the molecule-protein complex derived by or in 3D fitting (also known as docking); to characterize the proteins and their secondary structure; and to evaluate the effects of different generalized-Born (GB) and Poisson-Boltzmann (PB) implicit solvent models on the refinement of the molecule-protein complex geometry created in the docking and the prediction of the molecule-to-protein binding site affinity. A further objective was to apply chemometric methodologies for modeling and data analysis to all of the above. To summarize, this thesis presents methodologies and results applicable to structure-based CAMD. Results show that predictive chemometric models for molecule-to-protein binding site affinity could be created that yield comparable results to similar, commonly used methods. In addition, chemometric models could be created to model the effects of software settings on the molecule-protein complex geometry using software for molecule-to-binding site docking. Furthermore, the use of chemometric models provided a more profound understanding of protein secondary structure descriptors. Refining the geometry of molecule-protein complexes created through molecule-to-binding site docking gave similar results for all investigated implicit solvent models, but the geometry was significantly improved in only a few examined cases (six of 30). However, using the geometry-refined molecule-protein complexes was highly valuable for the prediction of molecule-to-binding site affinity. Indeed, using the PB solvent model it yielded improvements of 0.7 in correlation coefficients (R2) for binding affinity parameters of a set of Factor Xa protein drug molecules, relative to those obtained using the fitting software.