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DNA sequencing via nanopore translocation was a pipedream two decades ago. Today, biotech companies are releasing commercial devices. Yet many challenges still hover around the simple concept of threading a long DNA molecule through a small nanoscopic pore with the aim of extracting the DNA’s sequence along the process. In this thesis I use computer simulations to create what are in essence virtual pro- totypes for testing design ideas for the improvement of nanopore translocation devices. These ideas are based on the general concept of modifying the average shape of the initial DNA conformations. This is done, for example, by introducing new geometrical features to the nanopore’s surrounding or by the means of some external force. The goal of these simulations is not just to test design improvements, but also to systematically deconstruct the physical mechanisms involved in the translocation process. The roles of pore friction, initial polymer conformations, monomer crowding on the trans- side of the membrane, Brownian fluctuations, and polymer rigidity can, with careful consideration, be essentially muted at will. Computer simulations in this sense play the role of a sandbox in which the physics can be tinkered with, in order to assess and evaluate the magnitude of certain approximations found in theoretical modelling of translocation. This enables me to construct theoretical models that contain the necessary features pertaining to the different designs tested by simulations. The work presented here is thus constituted of both Langevin Dynamics simulations and adaptations of the Tension-Propagation theory of polymer translocation when the polymer is subject to the various test conditions.

Molecular dynamics (MD) computations aim to simulate materials at the atomic level by approximating molecular interactions classically, relying on the Born-Oppenheimer approximation and semi-empirical potential energy functions as an alternative to solving the difficult time-dependent Schrodinger equation. An approximate solution is obtained by discretization in time, with an appropriate algorithm used to advance the state of the system between successive timesteps. Modern MD simulations simulate complex systems with as many as a trillion individual atoms in three spatial dimensions. Many applications use MD to compute ensemble averages of molecular systems at constant temperature. Langevin dynamics approximates the effects of weakly coupling an external energy reservoir to a system of interest, by adding the stochastic Ornstein-Uhlenbeck process to the system momenta, where the resulting trajectories are ergodic with respect to the canonical (Boltzmann-Gibbs) distribution. By solving the resulting stochastic differential equations (SDEs), we can compute trajectories that sample the accessible states of a system at a constant temperature by evolving the dynamics in time. The complexity of the classical potential energy function requires the use of efficient discretization schemes to evolve the dynamics. In this thesis we provide a systematic evaluation of splitting-based methods for the integration of Langevin dynamics. We focus on the weak properties of methods for confiurational sampling in MD, given as the accuracy of averages computed via numerical discretization. Our emphasis is on the application of discretization algorithms to high performance computing (HPC) simulations of a wide variety of phenomena, where configurational sampling is the goal. Our first contribution is to give a framework for the analysis of stochastic splitting methods in the spirit of backward error analysis, which provides, in certain cases, explicit formulae required to correct the errors in observed averages. A second contribution of this thesis is the investigation of the performance of schemes in the overdamped limit of Langevin dynamics (Brownian or Smoluchowski dynamics), showing the inconsistency of some numerical schemes in this limit. A new method is given that is second-order accurate (in law) but requires only one force evaluation per timestep. Finally we compare the performance of our derived schemes against those in common use in MD codes, by comparing the observed errors introduced by each algorithm when sampling a solvated alanine dipeptide molecule, based on our implementation of the schemes in state-of-the-art molecular simulation software. One scheme is found to give exceptional results for the computed averages of functions purely of position.

We develop a cluster expansion in space-time for an infinite-dimensional system of interacting diffusions where the drift term of each diffusion depends on the whole past of the trajectory; these interacting diffusions arise when considering the Langevin dynamics of a ferromagnetic system submitted to a disordered external magnetic field.

The generalized Langevin equation (GLE) has been used to describe the dynamics of particles in a stationary environment. To better understand the dynamics of polymerization, the GLE has been generalized to the irreversible generalized Langevin equation (iGLE) so as to incorporate the non-stationary response of the solvent. This non-stationary response is manifested in the friction kernel and the behavior of the projected (stochastic) force. A particular polymerizing system, such as living polymerization, is specified both through the parameters of the friction kernel and the potential of mean force (PMF). Equilibrium properties such as extent of polymerization have been obtained and are consistent with Flory-Huggin¡¯s theory. In addition, time-dependent non-equilibrium observables such as polymer length, the polymer length distribution, and polydispersity index (PDI) of living polymerization have been obtained. These have been compared to several experiments so as to validate the models, and to provide additional insight into the thermodynamic and kinetic properties of these systems. In addition to the iGLE, a stochastic model has been used to study the effect of nonequilibrium reactivity on living polymerization. This model can be used to determine whether the reaction is controlled by kinetics or diffusion. A combination of the iGLE and stochastic models may help us obtain more information about living polymerization.

Orientador: René Alfonso Nome Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-26T04:23:53Z (GMT). No. of bitstreams: 1 Zornio_BrunoFedosse_M.pdf: 1493558 bytes, checksum: 07565e7077eefa5f9f91f03dc9cc90d4 (MD5) Previous issue date: 2014 / Resumo: No final do século XIX Van¿tHoff empiricamente estabeleceu que a constante de velocidade de uma reação química é função exponencial da razão entre energia de ativação da reação pela energia térmica do ambiente (e portanto função da temperatura). Há uma variada ordem nas escalas de tempos reacionais, em especial, a constante de velocidade de reações lentas (por exemplo, reações bioquímicas não catalisadas) é difícil de determinar. Uma partícula difundindo em um meio viscoso que apresenta movimento aleatório ¿ com posição média (em um intervalo de tempo suficientemente grande) nula, e a variância da posição linearmente dependente em função do tempo ¿ é dita browniana, e quando submetida a um potencial bi quadrático é um bom modelo para descrição de reações químicas. A partir da dinâmica de Langevin (que serve para descrever a dinâmica de uma partícula browniana) é derivada a teoria de Kramers para meio viscosos - que relaciona o formato da curva potencial com a constante de taxa de reações químicas -. Experimentalmente pode-se recriar esse modelo utilizando pinças ópticas. Pinças ópticas são capazes de aprisionar partículas da ordem micrométricas em suspensão, pode-se recriar um potencial bi estávelutilizando uma pinça óptica dupla (com dois pontos de aprisionamento). Este estudo tem como objetivo avaliar a constante de taxa de um processo de transição entre poços de potencial de partículas brownianas teoricamente utilizando uma simulação de dinâmica de Langevin para sistemas em equilíbrio tanto quanto para sistemas antes de atingir o equilíbrio, assim como determinar experimentalmente utilizando microscopia ocoeficiente de difusão a partir da trajetória temporal de uma única partícula. Os resultados teóricos obtidos são bastante condizentes com os resultados experimentais descritos na literatura, assim como as predições da constante de taxa para tempos antes do equilíbrio apresentam correlação com o sistema em equilíbrio. Com relação à estimativa do coeficiente de difusão apresenta um erro sistemático associado ao tamanho da trajetória temporal de uma única partícula / Abstract: By the end of the XIX century, Van¿t¿ Hoff has empirically established that the rate constant of some chemical reaction is exponentially dependent by the ratio between the reaction activation energy and the environment thermal energy (and so on function of temperature). There is a wide variety in the reaction time scales, in particular, the rate constant of slow reactions (such as uncatalysed biochemical reactions) is difficult to determine. A diffusing particle in a viscous media which exhibit random motion ¿ with mean position (in a sufficiently large time series) is zero, and the position variance is linearly time dependent ¿ is called Brownian, and when is submitted in a biquadratic potential it¿s a good model to describe chemical reactions. By the Langevin dynamics (which serves to describe the Brownian particle motion) the Kramers theory for viscous media is derived ¿ that theory connects the potential energy shape with the chemical rate constant -. Experimentally it is possible to create this model using optical tweezes. Optical tweezers where capable to trap micrometrical beads in suspension, it can generate a bi-stable using a double optical tweezers (that is with two trapping points). The main objective of this essay is evaluate the rate constant a Brownian particles jumping between potential wells theoretically using Langevin dynamics simulations for the system at equilibrium and before reach the equilibrium, as determinate experimentally the diffusion coefficient of single particle time path using microscopy. The theoretical results is very consistent with experimental results described in literature, as well as the prediction of the rate constant for the system before reaches equilibrium are correlated with the rate constant for the system at equilibrium. For the diffusion coefficient estimative it was observed that there is a systematical source of errors, and its is related with the length of the time series of the single particle path / Mestrado / Físico-Química / Mestre em Química

The ratchet effect can be exploited in many types of research, yet few researchers pay attention to it. In this thesis, I investigate two examples of such effects in microfluidic devices, under the guidance of computational simulations. The first chapter provides a brief introduction to ratchet effects, electrophoresis, and swimming cells, topics directly related to the following chapters. The second chapter of this thesis studies the separation of charged spherical particles in various microfluidic devices. My work shows how to manipulate those particles with modified temporal asymmetric electric potentials. The rectification of randomly swimming bacteria in microfluidic devices has been extensively studied. However, there have been few attempts to optimize such rectification devices. Mapping such motion onto a lattice Monte Carlo model may suggest some new mathematical methods, which might be useful for optimizing the similar systems. Such a mapping process is introduced in chapter four.

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The transport of a biomolecule through a nanopore occurs in many biological functions such as, DNA or RNA transport across nuclear pores and the translocation of proteins across the eukaryotic endoplasmic reticulum. In addition to the biological processes, it has potential applications in technology such as, drug delivery, gene therapy, and single molecule sensing. The DNA translocation through a synthetic nanopore device is considered as the basis for cheap and fast sequencing technology. Motivated by the experimental advances, many theoretical models have been developed. In this thesis, we explore the dynamics of driven translocation of a semiflexible polymer through a nanopore in two dimensions (2D) using Langevin dynamics (LD) simulation. By carrying out extensive simulation as a function of different parameters such as, driving force, length and rigidity of the chain, viscosity of the solvent, and diameter of the nanopore, we provide a detailed description of the translocation process. Our studies are relevant for fundamental understanding of the translocation process which is essential for making accurate nano-pore based devices.

This thesis investigates the integration of Stein Variational Gradient Descent (SVGD) with Joint Energy Models (JEMs), comparing its performance to Stochastic Gradient Langevin Dynamics (SGLD). We incorporated a generative loss term with an entropy component to enhance diversity and a smoothing factor to mitigate numerical instability issues commonly associated with the energy function in energy-based models. Experiments on the CIFAR-10 dataset demonstrate that SGLD, particularly with Sharpness-Aware Minimization (SAM), outperforms SVGD in classification accuracy. However, SVGD without SAM, despite its lower classification accuracy, exhibits lower calibration error underscoring its potential for developing well-calibrated classifiers required in safety-critical applications. Our results emphasize the importance of adaptive tuning of the SVGD smoothing factor ($alpha$) to balance generative and classification objectives. This thesis highlights the trade-offs between computational cost and performance, with SVGD demanding significant resources. Our findings stress the need for adaptive scaling and robust optimization techniques to enhance the stability and efficacy of JEMs. This thesis lays the groundwork for exploring more efficient and robust sampling techniques within the JEM framework, offering insights into the integration of SVGD with JEMs. / Master of Science / This thesis explores advanced techniques for improving machine learning models with a focus on developing well-calibrated and robust classifiers. We concentrated on two methods, Stein Variational Gradient Descent (SVGD) and Stochastic Gradient Langevin Dynamics (SGLD), to evaluate their effectiveness in enhancing classification accuracy and reliability. Our research introduced a new mathematical approach to improve the stability and performance of Joint Energy Models (JEMs). By leveraging the generative capabilities of SVGD, the model is guided to learn better data representations, which are crucial for robust classification. Using the CIFAR-10 image dataset, we confirmed prior research indicating that SGLD, particularly when combined with an optimization method called Sharpness-Aware Minimization (SAM), delivered the best results in terms of accuracy and stability. Notably, SVGD without SAM, despite yielding slightly lower classification accuracy, exhibited significantly lower calibration error, making it particularly valuable for safety-critical applications. However, SVGD required careful tuning of hyperparameters and substantial computational resources. This study lays the groundwork for future efforts to enhance the efficiency and reliability of these advanced sampling techniques, with the overarching goal of improving classifier calibration and robustness with JEMs.