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In this thesis, we report a novel symmetry breaking system in single-beam optical trap. The breaking of symmetry is observed in Brownian dynamics of a linked pair of beads with substantially differing radii (500nm and 100nm). Such composite beads were originally conceived as a manipulation means to study of Brownian interactions between mesoscopic biological agents of the order of 100 – 200 nm (viruses or bacteria) with cell surfaces. During the initial testing of the composite bead system, we discovered that the system displayed thermally activated transitions and energetics of symmetry breaking. This thesis, while making a brief overview of the biological relevance of the composite bead system, focuses primarily on the analysis and experimentation that reveals the complex dynamics observed in the system. First, we theoretically analyze the origin of the observed symmetry breaking using electromagnetic theory under both Gaussian beam approximation and full Debye-type integral representation. The theory predicts that attachment of a small particle to a trapped microsphere results in creation of a bistable rotational potential with thermally activated transitions. The theoretical results are then verified using optical trapping experiments. We first quantify the top-down symmetry breaking based on measurement of the kinetic transition rates. The rotational potential is then explored using an experiment employing a novel algorithm to track rotational state of the composite bead. The results of the theory and experiments are compared with results of a Brownian dynamics simulation based on Smart Monte Carlo algorithm.

After more than a century, there are no analytical solutions for the Navier-Stokes equations to describe complex fluid behavior, and we often resort to different computational methods to find solutions under specific conditions. In particular, to address many biological questions, we need to use techniques which are accurate at the mesoscale regime and computationally efficient, since atomistic simulations are still incredibly computationally costly, and continuum methods based on Navier-Stokes present challenges with complicated moving boundaries, in the presence of fluctuations. Here, we use a novel particle-based coarse-grained method, known as MPCD, to study ciliated swimmers. Using experimentally measured beating patterns, we show how we recapitulate the emergence of metachronal waves (MCW) on planar surfaces, and present new results on curved surfaces. To quantitatively study these waves, we also analyzed their effect on beating intervals, energy fluctuations, and fluid motion. We then extended our model to realistic cellular geometries, using experimentally obtained Basal Bodies locations.\par In the second part of our study, we focused on the intracellular fluid motion, neglecting hydrodynamic interactions. We developed the Digital Confocal Microscopy Suite (DCMS) that can run on multiple platforms using GPUs and can input realistic cell shapes and optical properties of the confocal microscope. It has this ability to simulate both (Fluorescence Recovery After Photobleaching) FRAP and Fluorescence Correlation Spectroscopy (FCS) experiments, as well as the capability to model photo-switching of fluorophores, acquisition photo-bleaching, and reaction-diffusion systems. With this platform, in collaboration with the Vidali Lab, we were able to elucidate the role of boundaries in interpreting FRAP experiments in \textit{moss} and estimate the binding rates of myosin XI.

After more than a century, there are no analytical solutions for the Navier-Stokes equations to describe complex fluid behavior, and we often resort to different computational methods to find solutions under specific conditions. In particular, to address many biological questions, we need to use techniques which are accurate at the mesoscale regime and computationally efficient, since atomistic simulations are still incredibly computationally costly, and continuum methods based on Navier-Stokes present challenges with complicated moving boundaries, in the presence of fluctuations. Here, we use a novel particle-based coarse-grained method, known as MPCD, to study ciliated swimmers. Using experimentally measured beating patterns, we show how we recapitulate the emergence of metachronal waves (MCW) on planar surfaces, and present new results on curved surfaces. To quantitatively study these waves, we also analyzed their effect on beating intervals, energy fluctuations, and fluid motion. We then extended our model to realistic cellular geometries, using experimentally obtained Basal Bodies locations.\par In the second part of our study, we focused on the intracellular fluid motion, neglecting hydrodynamic interactions. We developed the Digital Confocal Microscopy Suite (DCMS) that can run on multiple platforms using GPUs and can input realistic cell shapes and optical properties of the confocal microscope. It has this ability to simulate both (Fluorescence Recovery After Photobleaching) FRAP and Fluorescence Correlation Spectroscopy (FCS) experiments, as well as the capability to model photo-switching of fluorophores, acquisition photo-bleaching, and reaction-diffusion systems. With this platform, in collaboration with the Vidali Lab, we were able to elucidate the role of boundaries in interpreting FRAP experiments in \textit{moss} and estimate the binding rates of myosin XI.

Every cell contains several millions of diffusing and reacting biological molecules. The interactions between these molecules ultimately manifest themselves in all aspects of life, from the smallest bacterium to the largest whale. One of the greatest open scientific challenges is to understand how the microscopic chemistry determines the macroscopic biology. Key to this challenge is the development of mathematical and computational models of biochemistry with molecule-level detail, but which are sufficiently coarse to enable the study of large systems at the cell or organism scale. Two such models are in common usage: the reaction-diffusion master equation, and Brownian dynamics. These models are utterly different in both their history and in their approaches to chemical reactions and diffusion, but they both seek to address the same reaction-diffusion question. Here we make an in-depth study into the physical validity of these models under various biological conditions, determining when they can reliably be used. Taking each model in turn, we propose modifications to the models to better model the realities of the cellular environment, and to enable more efficient computational implementations. We use the models to make predictions about how and why cells behave the way they do, from mechanisms of self-organisation to noise reduction. We conclude that both models are extremely powerful tools for clarifying the details of the mysterious relationship between chemistry and biology.

The use of computational simulation to study the dynamics and interactions of macromolecules has become an important tool in the field of biochemistry. A common method to perform these simulations is to use all-atom explicit-solvent molecular dynamics (MD). However, due to the limitations in computational power currently available, this method is not practical for simulating large-scale biomolecular systems on long timescales. An alternative is to perform implicit-solvent Brownian dynamics (BD) simulations using a coarse grained (CG) model that allows for increased computational efficiency. However, if simulations using the CG model are not realistic, then the gain in computational efficiency from using a CG model is not worthwhile. This thesis describes the derivation of a set of bonded and nonbonded CG potential functions for use in implicit-solvent BD simulations of proteins derived from all-atom explicit-solvent MD simulations of amino acids. To determine which force field and water model to use in the MD simulations, Chapter II describes 1 Μs all-atom explicit-solvent MD simulations of glycine, asparagine, phenylalanine, and valine solutions at 50, 100, 200 and 300 mg/ml concentrations performed using eight different force field and water model combinations. To evaluate the accuracy of the force fields at high solute concentrations, the density, viscosity, and dielectric increments of the four amino acids were calculated from the simulations and compared to experimental results. Additionally, the change in the strength of hydrophobic and electrostatic interactions with increasing solute concentration was calculated for each force field and water model combination. As a result of this study, the Amber ff99SB-ILDN force field and TIP4P-Ew explicit-solvent water model were chosen for all subsequent MD simulations. Chapter III describes the derivation of CG bonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of each of the twenty amino acids, including a separate simulation for protonated histidine. The angle and dihedral probability distributions sampled during the MD simulations were used to optimize the bonded potential functions using the iterative Boltzmann inversion (IBI) method. Chapter IV describes the derivation of CG nonbonded potential functions from 1 Μs all-atom explicit-solvent MD simulations of every possible pairing of the amino acids (231 different systems). The radial distribution functions calculated from these MD simulations were used to optimize a set of nonbonded CG potential functions using the IBI method. The optimized set of bonded and nonbonded potential functions, which is termed COFFDROP (COarse-grained Force Field for Dynamic Representation Of Proteins), quantitatively reproduced all of the calculated MD distributions. To determine if COFFDROP would be useful for simulations of bimolecular systems, Chapter V describes the testing of the transferability of the force field. First, COFFDROP was used to simulate concentrated amino acid solutions. The clustering of the solutes in these simulations was directly compared with results from corresponding all-atom explicit-solvent MD simulations and found to be in excellent agreement. Next, BD simulations of 9.2 mM solutions of the small protein villin headpiece were performed. The proteins aggregated during these simulations, which is in agreement with results from MD simulation but in disagreement with experiment. After scaling the strength of COFFDROP's nonbonded potential functions by a factor of 0.8 and rerunning the BD simulations, the amount of aggregation was comparable to experimental observations. Based on these results, COFFDROP is likely to be applicable in CG BD simulations of large, highly concentrated, biomolecular systems.

Brownian dynamics (BD) simulation method has been widely used for studying problems in dispersed systems, such as polymer solutions, colloidal suspensions and more recently, complex (dusty) plasmas. The main problem addressed with this simulation technique is that of time scale separation, which occurs when one form of motion in the system is much faster than the other. This can be a serious problem in Molecular dynamics (MD) simulation where very short time steps are needed to handle the fast motions and thus, requiring very long time runs for the proper evolution of slower modes making the simulation very expensive. More importantly, the fast motions may not be of much interest within themselves, as will be the case in a dusty plasma. The motion of neutral atoms or molecules comprising the plasma occurs at a very fast time scale with respect to the motion of dust particles, and is usually of very little interest, though a large number of such neutrals are present. In such cases, an approximate method is usually adopted, whereby the neutral particles are omitted from the simulation and their effect upon the dynamics of dust particles modeled by a combination of random forces and frictional terms. This leads to a recasting of the Newton's Equation of motion solved in MD, to a Langevin equation, solved in BD. Adopting this approach, we simulate a system of charged dust particles interacting via Yukawa potential in a 2-Dimensional layer, and extract relevant equilibrium statistical features such as the radial distribution function, static structure factor and the low frequency dust wave modes. We then propose the use of a Generalized Hydrodynamical (GH) approach to provide a semi-analytical model for the dust collective modes, which not only provides us with good predictions of the wave dispersion but also provides reasonable estimates for wave-number dependent wave damping, both of which will be compared against the results obtained from BD simulation. Finally, through our simulations, we also observe the equilibrium configuration of dust particles in the presence of cold ions streaming perpendicularly into the 2-Dimensional layer of dust particles. This provides us with novel results in the regime of sub-sonic ion flow speeds.

Brownian dynamics (BD) simulation method has been widely used for studying problems in dispersed systems, such as polymer solutions, colloidal suspensions and more recently, complex (dusty) plasmas. The main problem addressed with this simulation technique is that of time scale separation, which occurs when one form of motion in the system is much faster than the other. This can be a serious problem in Molecular dynamics (MD) simulation where very short time steps are needed to handle the fast motions and thus, requiring very long time runs for the proper evolution of slower modes making the simulation very expensive. More importantly, the fast motions may not be of much interest within themselves, as will be the case in a dusty plasma. The motion of neutral atoms or molecules comprising the plasma occurs at a very fast time scale with respect to the motion of dust particles, and is usually of very little interest, though a large number of such neutrals are present. In such cases, an approximate method is usually adopted, whereby the neutral particles are omitted from the simulation and their effect upon the dynamics of dust particles modeled by a combination of random forces and frictional terms. This leads to a recasting of the Newton's Equation of motion solved in MD, to a Langevin equation, solved in BD. Adopting this approach, we simulate a system of charged dust particles interacting via Yukawa potential in a 2-Dimensional layer, and extract relevant equilibrium statistical features such as the radial distribution function, static structure factor and the low frequency dust wave modes. We then propose the use of a Generalized Hydrodynamical (GH) approach to provide a semi-analytical model for the dust collective modes, which not only provides us with good predictions of the wave dispersion but also provides reasonable estimates for wave-number dependent wave damping, both of which will be compared against the results obtained from BD simulation. Finally, through our simulations, we also observe the equilibrium configuration of dust particles in the presence of cold ions streaming perpendicularly into the 2-Dimensional layer of dust particles. This provides us with novel results in the regime of sub-sonic ion flow speeds.

Multiple lines of evidence suggest that RNA performed all of the biological functions in the first life forms on earth. These functions included cleavage, ligation, polymerization, recognition, binding, and replication. In order to perform these functions, populations of RNA molecules with unevolved sequences must have been able to fold into compact three dimensional shapes, in unregulated environments, and without the help of proteins. Folding into compact tertiary structures is difficult because of the high charge density of RNA. Consequently, the ranges of temperature, salinity, pH, and pressure that allow RNA to fold into functional shapes is very restricted. We use thermodynamic arguments and Brownian dynamics simulations to compute the range of these environmental parameters that will allow RNA to fold. This is a non-trivial calculation due to the formation of an ion atmosphere around RNA that reduces its electric field. The results can be used to clarify the environments in which the transition to life is possible. Our preliminary calculations suggest that environments with low temperatures ($0-50^\circ C$) and high salt concentrations (greater than 100mM) are the most favorable for unassisted RNA folding and thus the transition to RNA-based life. Applications of our results include determining the environments on early earth where life formed, assesing the habitability of Europa, Titan, and (using modeled parameters) extrasolar planets. / text

This thesis investigates DNA dynamics and translocation through nanopores using Brownian dynamics (BD) simulations, offering insights into sequencing technologies, DNA marker detection, and accurate barcoding utilizing solid-state nanopore platforms. First, we in silico study the intricate process of capture and translocation in a single nanopore. Our simulation reveals a high probability of hairpin loop formation during the capture process. However, attaching a charged tag to one end of DNA improves multi-scan rates and enhances unidirectional translocations. We use modulating voltage biases to multi-scan a lambda-phage dsDNA with oligonucleotide flap markers (tags) through a single and double nanopore system. Our study shows that the bulkier tags introduce velocity variations along the chain length that lead to potential inaccuracies in genetic distance (barcode) estimations. We introduce an interpolation scheme that incorporates both the tag velocities and the average velocity of the chain to improve barcode precision. Subsequently, we include bead and side-chain tags to explain asymmetric dwell time distributions as observed in double nanopore experiments. Our findings indicate that local charge interactions between tags and the nanopore's electric field introduce dwell time asymmetries that can be used for discriminating tags based on their net charges. Finally, we obtain the current blockades of the molecular motifs attached to a dsDNA using electrokinetic Brownian dynamics (EKBD) simulation. Our simulation demonstrates that divalent salt reduces the translocation speed, facilitating precise measurement of the motif's dwell time. Finally, we formulate a volumetric ansatz to construct current blockade diagrams from the ordinary BD simulation in a computationally efficient way and show that using simple scale factors, these volumetric blockades can be mapped accurately to the ionic current blockades obtained from more expensive EKBD simulation. Our studies present comprehensive explorations of DNA translocation and barcoding methods in solid-state nanopores, demonstrating their utility in nanopore sequencing and nanobiotechnology