Evaluation of stochastic effects on biomolecular networks using the generalised Nyquist stability criterion

Abstract—Stochastic differential equations are now commonly used to model biomolecular networks in systems biology, and much recent research has been devoted to the development of methods to analyse their stability properties. Stability analysis of such systems may be performed using the Laplace transform, which requires the calculation of the exponential matrix involving time symbolically. However, the calculation of the symbolic exponential matrix is not feasible for problems of even moderate size, as the required computation time increases exponentially with the matrix order. To address this issue, we present a novel method for approximating the Laplace transform which does not require the exponential matrix to be calculated explicitly. The calculation time associated with the proposed method does not increase exponentially with the size of the system, and the approximation error is shown to be of the same order as existing methods. Using this approximation method, we show how a straightforward application of the generalized Nyquist stability criterion provides necessary and sufficient conditions for the stability of stochastic biomolecular networks. The usefulness and computational efficiency of the proposed method is illustrated through its application to the problem of analysing a model for limit-cycle oscillations in cAMP during aggregation of Dictyostelium cells

Complex-Coefficient Frequency Domain Stability Analysis Method for a Class of Cross-Coupled Antisymmetrical Systems and Its Extension in MSR Systems

This paper develops a complex-coefficient frequency domain stability analysis method for a class of cross-coupled two-dimensional antisymmetrical systems, which can greatly simplify the stability analysis of the multiple-input multiple-output (MIMO) system. Through variable reconstruction, the multiple-input multiple-output (MIMO) system is converted into a single-input single-output (SISO) system with complex coefficients. The pole locations law of the closed-loop system after the variable reconstruction has been revealed, and the controllability as well as observability of the controlled plants before and after the variable reconstruction has been studied too, and then the classical Nyquist stability criterion is extended to the complex-coefficient frequency domain. Combined with the rigid magnetically suspended rotor (MSR) system with heavy gyroscopic effects, corresponding stability criterion has been further developed. Compared with the existing methods, the developed criterion for the rigid MSR system not only accurately predicts the absolute stability of the different whirling modes, but also directly demonstrates their relative stability, which greatly simplifies the analysis, design, and debugging of the control system

Investigating High Speed Localization Microscopy Through Experimental Methods, Data Processing Methods, and Applications of Localization Microscopy to Biological Questions

Fluorescence Photoactivation Localization Microscopy(FPALM) and other super resolution localization microscopy techniques can resolve structures with nanoscale resolution. Unlike techniques of electron microscopy, they are also compatible with live cell and live animal studies, making FPALM and related techniques ideal for answering questions about the dynamic nature of molecular biology in living systems. Many processes in biology occur on rapid sub second time scales requiring the imaging technique to be capable of resolving these processes not just with a high enough spatial resolution, but with an appropriate temporal resolution. To that end, this Dissertation in part investigates high speed FPALM as an experimental technique showing images can be reconstructed with effective temporal resolutions of 0.1s. Using fluorescent proteins attached to an influenza viral protein, hemagglutinin(HA), questions of protein clustering and cluster dynamics on the host cell membrane are explored. The results indicate that these HA clusters may be more dynamic than previously thought. The principle disadvantage of the increased speed of imaging is the reduction in information that comes through collecting fewer photons to localize each molecule, and fewer molecules overall. As the molecules become dimmer, they also become harder to identify using conventional identification algorithms. Tools from machine learning and computer vision such as artificial neural networks(ANNs) have been shown to be adept at object identification. Here a method for repeatedly training an ANN is investigated. This method is shown to have exceptional performance on simulations indicating that it can be regarded as a method of high fidelity, even in the presence of weakly fluorescent molecules. Development of this technique can be used to recover more molecules from data sets with weaker molecular fluorescence, such as those obtained with high speed imaging, allowing for higher sampling, and overall higher spatial resolution of the final image. The combination of a high speed experimental technique coupled with a sensitive and robust identification algorithm allow FPALM and related techniques to probe questions of fast biological processes while limiting the sacrifice to spatial resolution inherent in high speed techniques

Active Wavelength Selection for Chemical Identification Using Tunable Spectroscopy

Spectrometers are the cornerstone of analytical chemistry. Recent advances in microoptics manufacturing provide lightweight and portable alternatives to traditional spectrometers. In this dissertation, we developed a spectrometer based on Fabry-Perot interferometers (FPIs). A FPI is a tunable (it can only scan one wavelength at a time) optical filter. However, compared to its traditional counterparts such as FTIR (Fourier transform infrared spectroscopy), FPIs provide lower resolution and lower signal-noiseratio (SNR). Wavelength selection can help alleviate these drawbacks. Eliminating uninformative wavelengths not only speeds up the sensing process but also helps improve accuracy by avoiding nonlinearity and noise. Traditional wavelength selection algorithms follow a training-validation process, and thus they are only optimal for the target analyte. However, for chemical identification, the identities are unknown. To address the above issue, this dissertation proposes active sensing algorithms that select wavelengths online while sensing. These algorithms are able to generate analytedependent wavelengths. We envision this algorithm deployed on a portable chemical gas platform that has low-cost sensors and limited computation resources. We develop three algorithms focusing on three different aspects of the chemical identification problems. First, we consider the problem of single chemical identification. We formulate the problem as a typical classification problem where each chemical is considered as a distinct class. We use Bayesian risk as the utility function for wavelength selection, which calculates the misclassification cost between classes (chemicals), and we select the wavelength with the maximum reduction in the risk. We evaluate this approach on both synthesized and experimental data. The results suggest that active sensing outperforms the passive method, especially in a noisy environment. Second, we consider the problem of chemical mixture identification. Since the number of potential chemical mixtures grows exponentially as the number of components increases, it is intractable to formulate all potential mixtures as classes. To circumvent combinatorial explosion, we developed a multi-modal non-negative least squares (MMNNLS) method that searches multiple near-optimal solutions as an approximation of all the solutions. We project the solutions onto spectral space, calculate the variance of the projected spectra at each wavelength, and select the next wavelength using the variance as the guidance. We validate this approach on synthesized and experimental data. The results suggest that active approaches are superior to their passive counterparts especially when the condition number of the mixture grows larger (the analytes consist of more components, or the constituent spectra are very similar to each other). Third, we consider improving the computational speed for chemical mixture identification. MM-NNLS scales poorly as the chemical mixture becomes more complex. Therefore, we develop a wavelength selection method based on Gaussian process regression (GPR). GPR aims to reconstruct the spectrum rather than solving the mixture problem, thus, its computational cost is a function of the number of wavelengths. We evaluate the approach on both synthesized and experimental data. The results again demonstrate more accurate and robust performance in contrast to passive algorithms

Investigation of the Regulatory Roles of Micrornas by Systems Biology Approaches

Ph.DDOCTOR OF PHILOSOPH

Impedance Spectroscopy

This book covers new advances in the field of impedance spectroscopy including fundamentals, methods and applications. It releases selected extended and peer reviewed scientific contributions from the International Workshop on Impedance Spectroscopy (IWIS 2017) focussing on detailed information about recent scientific research results in electrochemistry and battery research, bioimpedance measurement, sensors, system design, signal processing

College of Engineering

Cornell University Courses of Study Vol. 96 2004/200