Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK.

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest that two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. However, eliminating positive feedback by fixing vri expression altered the oscillation period. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations, of per overexpression, and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. Temperature compensation of oscillation period could be simulated if temperature elevation slowed PER nuclear entry or PER phosphorylation. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Symmetric inverse consistent nonlinear registration driven by mutual information.

A nonlinear viscoelastic image registration algorithm based on the demons paradigm and incorporating inverse consistent constraint (ICC) is implemented. An inverse consistent and symmetric cost function using mutual information (MI) as a similarity measure is employed. The cost function also includes regularization of transformation and inverse consistent error (ICE). The uncertainties in balancing various terms in the cost function are avoided by alternatively minimizing the similarity measure, the regularization of the transformation, and the ICE terms. The diffeomorphism of registration for preventing folding and/or tearing in the deformation is achieved by the composition scheme. The quality of image registration is first demonstrated by constructing brain atlas from 20 adult brains (age range 30-60). It is shown that with this registration technique: (1) the Jacobian determinant is positive for all voxels and (2) the average ICE is around 0.004 voxels with a maximum value below 0.1 voxels. Further, the deformation-based segmentation on Internet Brain Segmentation Repository, a publicly available dataset, has yielded high Dice similarity index (DSI) of 94.7% for the cerebellum and 74.7% for the hippocampus, attesting to the quality of our registration method.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^