At very early embryonic stages, when embryos are composed of just a few cells, establishing the correct packing arrangements (contacts) between cells is essential for proper development of the organism. As early as the 4-cell stage, the observed blastomere packings in different species are different and, in many cases, differ from the equilibrium packings expected for simple adherent and deformable particles.

We use a novel 3D Voronoi-augnemted Langevin simulator to systematically study how the forces between blastomeres, their division rates, orientation of cell division, and embryonic confinement influence the final packing configurations. In the absence of physical confinement of the embryo, we find that blastomere packings are not robust, with multiple packing configurations simultaneously possible (degeneracy) and are very sensitive to parameter changes. Our results indicate that the geometry of the embryonic confining shell determines the packing configurations at the 4-cell stage, removing degeneracy in the possible packing configurations and overriding division rules in most cases.

Furthermore, we use our simulator to study the robustness of the C. elegans early embryo to noise in division timing and angle. We find that there exists a range of timing and angular noise that the embryo is fully robust to and categorize the errors outside this regime as coming from mistimed divisions or misplaced cells. We also study how robust the embryo is to overall shifts in the timing offset between the AB and P1 divisions and find that even large changes can be non-lethal. Finally, we systematically investigate how robust the embryo is to deterministic shifts in division directions from the wildtype rules and find that the major source of lethal error is from offsets of more than 90 degrees to the P2-EMS division axis. Overall, our results demonstrate how confinement, division timing and division rules all contribute to ensuring robust development with confinement setting the overall packing topology and division timings and rules specifying where individual cells will go within that shape.

The strong negative charge of nucleic acids adds additional complexity to their behavior, beyond what would be expected for neutral polymers, through the addition of long-range self-repulsive interactions and through the screening of those interactions by ions in solution. Among the techniques that can probe the electrostatic behavior of a charged polymer are single-molecule force spectroscopy, which reports on the elasticity of the polymer (i.e., extension as a function of applied force), and ion counting, which reports on the stoichiometry of positive and negative ions constituting the polymer’s “ion atmosphere”. While extensive studies of both types have been made of double-stranded DNA, a strongly charged and moderately stiff polymer, less is known about the single-stranded nucleic acids (ssNAs), which are also strongly charged but are comparatively flexible.

In my dissertation, I use single-molecule magnetic tweezers to measure the elasticity of ssRNA as a function of monovalent and divalent salt concentration under 0.1–10 pN applied force and observe behavior characteristic of flexible polyelectrolytes. I then extend the measurements up to 100 pN to probe the intermediate-force domain connecting behavior dominated by electrostatics and by the chemical structure of the backbone. These new data allow the critical testing of a wormlike chain-derived model treating electrostatics through a mean-field, salt-dependent tension. This model is shown to quantitatively account for the data and to bridge the established behaviors at lower and higher force. I also quantify the ion atmosphere stoichiometry of both ssDNA and ssRNA using three complementary experimental techniques, including both bulk and single-molecule approaches. These results are compared with Poisson-Boltzmann models incorporating varying degrees of structural complexity, demonstrating the inherently short-ranged (i.e., sub-Debye screening length) nature of nucleic acid-ion interactions.

This dissertation is primarily a survey of the zero-temperature string method, a minimum energy path search algorithm, applied to novel barrier-crossing problems in polymer field theory. I apply the method to both self-consistent field theory (SCFT) and a phase-field model (the Landau-Brazovskii model). In the case of SCFT, the focus is on defect annealing problems in homo+copolymer melts; in the case of the Landau-Brazovskii model, the focus is on finding critical nuclei for the disorder-to-lamellar transition, which is known to be a fluctuation-induced first-order phase transition.

In SCFT, applying the string method is computationally demanding in both processing time and memory, especially for fully 3-dimensional simulations at industrially relevant system sizes. I successfully address these challenges on state-of-the-art massively parallel computing architectures (NVIDIA graphics processing units). As a result our group is able to identify free energy barriers and transition mechanisms for a wide variety of defect annealing problems relevant to industrial directed self-assembly (DSA).

Nucleation in the Landau-Brazovskii model presents its own challenges. The string method as originally formulated is inefficient for nucleation problems, since many images are wasted tracing out unphysical configurations once the nucleus grows to the edges of the simulation cell. I devise a new truncation-based energy weighting (TBEW) scheme that resolves this issue, and will prove valuable to future researchers using the string method to find critical nuclei.

Since the bare Landau-Brazovskii model predicts a second-order transition between disorder and lamellae at a mean-field level, naive application of the zero-temperature string method to this model fails to find a barrier. To circumvent this, I instead apply the string method to a renormalized model that incorporates fluctuations at a mean-field level. Using TBEW and the renormalized model, I investigate nucleation pathways for the disorder-to-lamellar transition, finding anisotropic nuclei in agreement with previous predictions and experimental observations. I also conduct a comprehensive search for experimentally observed nuclei containing various exotic defect structures.

Finally, I evaluate the validity of the nucleation pathways obtained from the renormalized model by numerically simulating the bare model with explicit fluctuations. I find that the renormalized model makes good predictions for certain quantities, including the location of the order-disorder transition. However, due to sharp dependence of critical nucleus size on proximity to the order-disorder transition, even slight errors in the predicted ODT lead to large errors in predicted nucleus size. I conclude that the renormalized Landau-Brazovskii model is a poor tool for predicting critical nuclei in the fully fluctuating bare theory at experimentally accessible parameters, and recommend that future studies work with the fluctuating bare theory directly. I recommend several strategies to extract barriers and rates.