Sensitivity analysis of circadian entrainment in the space of phase response curves

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations.Comment: 22 pages, 8 figures. Correction of a mistake in Definition 2.1. arXiv admin note: text overlap with arXiv:1206.414

Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms

Efficient Uncertainty Quantification for the Periodic Steady State of Forced and Autonomous Circuits

This brief proposes an uncertainty quantification method for the periodic steady-state (PSS) analysis with both Gaussian and non-Gaussian variations. Our stochastic testing formulation for the PSS problem provides superior efficiency over both Monte Carlo methods and existing spectral methods. The numerical implementation of a stochastic shooting Newton solver is presented for both forced and autonomous circuits. Simulation results on some analog/RF circuits are reported to show the effectiveness of our proposed algorithms

Uncertainty quantification for integrated circuits: Stochastic spectral methods

Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the application of conventional stochastic Galerkin and stochastic collocation schemes to nonlinear circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.MIT Masdar Program (196F/002/707/102f/70/9374

Automated analysis, design, and optimization of low noise oscillators

Low noise oscillators are universally needed in digital systems for clock generation and synchronization, and in radio-frequency communication front-ends for frequency up- and down-conversion. Noise in oscillators results in timing jitter, and limits the clock frequency of digital systems. In radio-frequency communication systems, phase noise in oscillators lowers the signal-to-noise ratio of transmitters and receivers, and degrades the overall bit-error-rate. Therefore, accurate simulation and optimization of oscillator noise performance is of utmost importance. The focus of this dissertation is on automated analysis, design and optimization of low noise oscillators. Several advances in oscillator analysis that facilitate automated oscillator design and optimization are presented. These include a new sensitivity analysis for oscillators, a design-oriented circuit analysis technique, and an oscillator design optimization approach. The sensitivity analysis calculates sensitivities of an oscillator's periodic steady-state and perturbation projection vector to design, process, or environmental parameters. In the design-oriented approach to circuit analysis the circuit response is computed together with the values of circuit parameters that result in a desired circuit performance. These analyses form the foundation for an efficient oscillator optimization technique that is general and applicable to all oscillator types.Keywords: simulation, circuit, analysis, sensitivity, optimization, design, oscillato

Relating topology and dynamics in cell signaling networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Biological Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 153-163).Cells are constantly bombarded with stimuli that they must sense, process, and interpret to make decisions. This capability is provided by interconnected signaling pathways. Many of the components and interactions within pathways have been identified, and it is becoming clear that the precise dynamics they generate are necessary for proper system function. However, our understanding of how pathways are interconnected to drive decisions is limited. We must overcoming this limitation to develop interventions that can fine tune a cell decision by modulating specific features of its constituent pathway's dynamics. How can we quantatively map a whole cell decision process? Answering this question requires addressing challenges at three scales: the detailed biochemistry of protein-protein interactions, the complex, interlocked feedback loops of transcriptionally regulated signaling pathways, and the multiple mechanisms of connection that link distinct pathways together into a full cell decision process. In this thesis, we address challenges at each level. We develop new computational approaches for identifying the interactions driving dynamics in protein-protein networks. Applied to the cyanobacterial clock, these approaches identify two coupled motifs that together provide independent control over oscillation phase and period. Using the p53 pathway as a model transcriptional network, we experimentally isolate and characterize dynamics from a core feedback loop in individual cells. A quantitative model of this signaling network predicts and rationalizes the distinct effects on dynamics of additional feedback loops and small molecule inhibitors. Finally, we demonstrated the feasibility of combining individual pathway models to map a whole cell decision: cell cycle arrest elicited by the mammalian DNA damage response. By coupling modeling and experiments, we used this combined perspective to uncover some new biology. We found that multiple arrest mechanisms must work together in a proper cell cycle arrest, and identified a new role for p21 in preventing G2 arrest, paradoxically through its action on G1 cyclins. This thesis demonstrates that we can quantitatively map the logic of cellular decisions, affording new insight and revealing points of control.by Jared E. Toettcher.Ph.D

Sensitivity analysis of oscillating dynamical systems with applications to the mammalian circadian clock

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 227-234).The work presented in this thesis consists of two major parts. In Chapter 2, the theory for sensitivity analysis of oscillatory systems is developed and discussed. Several contributions are made, in particular in the precise definition of phase sensitivities and in the generalization of the theory to all types of autonomous oscillators. All methods rely on the solution of a boundary value problem, which identifies the periodic orbit. The choice of initial condition on the limit cycle has important consequences for phase sensitivity analysis, and its influence is quantified and discussed in detail. The results are exact and efficient to compute compared to existing partial methods. The theory is then applied to different models of the mammalian circadian clock system in the following chapters. First, different types of sensitivities in a pair of smaller models are analyzed. The models have slightly different architectures, with one having an additional negative feedback loop compared to the other. The differences in their behavior with respect to phases, the period and amplitude are discussed in the context of their network architecture. It is found that, contrary to previous assumptions in the literature, the additional negative feedback loop makes the model less "flexible" in at least one sense that was studied here. The theory was also applied to larger, more detailed models of the mammalian circadian clock, based on the original model of Forger and Peskin. Between the original model's publication in 2003 and the present time, several key advances were made in understanding the mechanistic detail of the mammalian circadian clock, and at least one additional clock gene was identified. These advances are incorporated in an extended model, which is then studied using sensitivity analysis. Period sensitivity analysis is performed first and it was found that only one negative feedback loop dominates the setting of the period.(cont.) This was an interesting one-to-one correlation between one topological feature of the network and a single metric of network performance. This led to the question of whether the network architecture is modular, in the sense that each of the several feedback loops might be responsible for a separate network function. A function of particular interest is the ability to separately track "dawn" and "dusk", which is reported to be present in the circadian clock. The ability of the mammalian circadian clock to modify different relative phases --defined by different molecular events -- independently of the period was analyzed. If the model can maintain a perceived day -- defined by the time difference between two phases -- of different lengths, it can be argued that the model can track dawn and dusk separately. This capability is found in all mammalian clock models that were studied in this work, and furthermore, that a network-wide effort is needed to do so. Unlike in the case of the period sensitivities, relative phase sensitivities are distributed throughout several feedback loops. Interestingly, a small number of "key parameters" could be identified in the detailed models that consistently play important roles in the setting of period, amplitude and phases. It appears that most circadian clock features are under shared control by local parameters and by the more global "key parameters". Lastly, it is shown that sensitivity analysis, in particular period sensitivity analysis, can be very useful in parameter estimation for oscillatory systems biology models. In an approach termed "feature-based parameter fitting", the model's parameter values are selected based on their impact on the "features" of an oscillation (period, phases, amplitudes) rather than concentration data points. It is discussed how this approach changes the cost function during the parameter estimation optimization, and when it can be beneficial.(cont.) A minimal model system from circadian biology, the Goodwin oscillator, is taken as an example. Overall, in this thesis it is shown that the contributions made to the theoretical understanding of sensitivities in oscillatory systems are relevant and useful in trying to answer questions that are currently open in circadian biology. In some cases, the theory could indicate exactly which experiments or detailed mechanistic studies are needed in order to perform meaningful mathematical analysis of the system as a whole. It is shown that, provided the biologically relevant quantities are analyzed, a network-wide understanding of the interplay between network function and topology can be gained and differences in performance between models of different size or topology can be quantified.by Anna Katharina Wilkins.Ph.D