Practicality and time complexity of a sparsified RNA folding algorithm

Commonly used RNA folding programs compute the minimum free energy structure of a sequence under the pseudoknot exclusion constraint. They are based on Zuker's algorithm which runs in time O(n^3). Recently, it has been claimed that RNA folding can be achieved in average time O(n^2) using a sparsification technique. A proof of quadratic time complexity was based on the assumption that computational RNA folding obeys the "polymer-zeta property". Several variants of sparse RNA folding algorithms were later developed. Here, we present our own version, which is readily applicable to existing RNA folding programs, as it is extremely simple and does not require any new data structure. We applied it to the widely used Vienna RNAfold program, to create sibRNAfold, the first public sparsified version of a standard RNA folding program. To gain a better understanding of the time complexity of sparsified RNA folding in general, we carried out a thorough run time analysis with synthetic random sequences, both in the context of energy minimization and base pairing maximization. Contrary to previous claims, the asymptotic time complexity of a sparsified RNA folding algorithm using standard energy parameters remains O(n^3) under a wide variety of conditions. Consistent with our run-time analysis, we found that RNA folding does not obey the "polymer-zeta property" as claimed previously. Yet, a basic version of a sparsified RNA folding algorithm provides 15- to 50-fold speed gain. Surprisingly, the same sparsification technique has a different effect when applied to base pairing optimization. There, its asymptotic running time complexity appears to be either quadratic or cubic depending on the base composition. The code used in this work is available at: http://sibRNAfold.sourceforge.net/

Mesoscale Light-matter Interactions

Mesoscale optical phenomena occur when light interacts with a number of different types of materials, such as biological and chemical systems and fabricated nanostructures. As a framework, mesoscale optics unifies the interpretations of the interaction of light with complex media when the outcome depends significantly upon the scale of the interaction. Most importantly, it guides the process of designing an optical sensing technique by focusing on the nature and amount of information that can be extracted from a measurement. Different aspects of mesoscale optics are addressed in this dissertation which led to the solution of a number of problems in complex media. Dynamical and structural information from complex fluids—such as colloidal suspensions and biological fluids—was obtained by controlling the size of the interaction volume with low coherence interferometry. With this information, material properties such as particle sizes, optical transport coefficients, and viscoelastic characteristics of polymer solutions and blood were determined in natural, realistic conditions that are inaccessible to conventional techniques. The same framework also enabled the development of new, scale-dependent models for several important physical and biological systems. These models were then used to explain the results of some unique measurements. For example, the transport of light in disordered photonic lattices was interpreted as a scale-dependent, diffusive process to explain the anomalous behavior of photon path length distributions through these complex structures. In addition, it was demonstrated how specialized optical measurements and models at the mesoscale enable solutions to fundamental problems in cell biology. Specifically, it was found for the first time that the nature of cell motility changes markedly with the curvature of the substrate that the cells iv move on. This particular work addresses increasingly important questions concerning the nature of cellular responses to external forces and the mechanical properties of their local environment. Besides sensing of properties and modeling behaviors of complex systems, mesoscale optics encompasses the control of material systems as a result of the light-matter interaction. Specific modifications to a material’s structure can occur due to not only an exchange of energy between radiation and a material, but also due to a transfer of momentum. Based on the mechanical action of multiply scattered light on colloidal particles, an optically-controlled active medium that did not require specially tailored particles was demonstrated for the first time. The coupling between the particles and the random electromagnetic field affords new possibilities for controlling mesoscale systems and observing nonequilibrium thermodynamic phenomena

Scalable Probabilistic Model Selection for Network Representation Learning in Biological Network Inference

A biological system is a complex network of heterogeneous molecular entities and their interactions contributing to various biological characteristics of the system. Although the biological networks not only provide an elegant theoretical framework but also offer a mathematical foundation to analyze, understand, and learn from complex biological systems, the reconstruction of biological networks is an important and unsolved problem. Current biological networks are noisy, sparse and incomplete, limiting the ability to create a holistic view of the biological reconstructions and thus fail to provide a system-level understanding of the biological phenomena. Experimental identification of missing interactions is both time-consuming and expensive. Recent advancements in high-throughput data generation and significant improvement in computational power have led to novel computational methods to predict missing interactions. However, these methods still suffer from several unresolved challenges. It is challenging to extract information about interactions and incorporate that information into the computational model. Furthermore, the biological data are not only heterogeneous but also high-dimensional and sparse presenting the difficulty of modeling from indirect measurements. The heterogeneous nature and sparsity of biological data pose significant challenges to the design of deep neural network structures which use essentially either empirical or heuristic model selection methods. These unscalable methods heavily rely on expertise and experimentation, which is a time-consuming and error-prone process and are prone to overfitting. Furthermore, the complex deep networks tend to be poorly calibrated with high confidence on incorrect predictions. In this dissertation, we describe novel algorithms that address these challenges. In Part I, we design novel neural network structures to learn representation for biological entities and further expand the model to integrate heterogeneous biological data for biological interaction prediction. In part II, we develop a novel Bayesian model selection method to infer the most plausible network structures warranted by data. We demonstrate that our methods achieve the state-of-the-art performance on the tasks across various domains including interaction prediction. Experimental studies on various interaction networks show that our method makes accurate and calibrated predictions. Our novel probabilistic model selection approach enables the network structures to dynamically evolve to accommodate incrementally available data. In conclusion, we discuss the limitations and future directions for proposed works

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum