Mahdi Imani

Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems

We present a framework for the simultaneous estimation of state and parameters of partially observed Boolean dynamical systems (POBDS). Simultaneous state and parameter estimation is achieved through the combined use of the Boolean Kalman filter and Boolean Kalman smoother, which provide the minimum mean-square error state estimators for the POBDS model, and maximum-likelihood (ML) parameter estimation; in the presence of continuous parameters, ML estimation is performed using the expectation-maximization algorithm. The performance of the proposed ML adaptive filter is demonstrated by numerical experiments with a POBDS model of gene regulatory networks observed through noisy next-generation sequencing (RNA-seq) time series data using the well-known p53-MDM2 negative-feedback loop gene regulatory model.

Optimal gene regulatory network inference using the Boolean Kalman filter and multiple model adaptive estimation

We propose a method for the inference of Boolean gene regulatory networks observed through noise. The algorithm is based on the optimal MMSE state estimator for a Boolean dynamical system, known as the Boolean Kalman filter (BKF). In the presence of partial knowledge about the network, a bank of BKFs representing the candidate models is run in parallel in a framework known as Multiple Model Adaptive Estimation (MMAE). Performance is investigated using a model of the p53-MDM2 negative feedback loop network, as well as application to large numbers of random networks in order to estimate average performance.

State-feedback control of Partially-Observed Boolean Dynamical Systems using RNA-seq time series data

External control of a genetic regulatory network is used for the purpose of avoiding undesirable states, such as those associated with disease. This paper proposes a strategy for state-feedback infinite-horizon control of Partially-Observed Boolean Dynamical Systems (POBDS) using a single time series of Next-Generation Sequencing (NGS) RNA-seq data. A separation principle is assumed, whereby first the optimal stationary policy is obtained offline by solving Bellmans equation, and then an optimal MMSE observer, the Boolean Kalman Filter, is employed for online implementation of the policy using the RNA-seq observations of the evolving system. Performance is investigated using a Boolean network model of the mutated mammalian cell cycle and simulated RNA-seq observations.

Particle filters for partially-observed Boolean dynamical systems

Abstract Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we introduce approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method, which are called APF–BKF and APF–BKS, respectively. For joint state and parameter estimation, the APF–BKF is used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the case the unknown parameters are discrete, the proposed ML adaptive filter consists of multiple APF–BKFs running in parallel, in a manner reminiscent of the Multiple Model Adaptive Estimation (MMAE) method in classical linear filtering theory. In the presence of continuous parameters, the proposed ML adaptive filter is based on an efficient particle-based expectation maximization (EM) algorithm for the POBDS model, which is based on a modified Forward Filter Backward Simulation (FFBSi) in combination with the APF–BKS. The performance of the proposed particle-based adaptive filters is assessed through numerical experiments using a POBDS model of the well-known cell cycle gene regulatory network observed through noisy RNA-Seq time series data.

Point-based value iteration for partially-observed Boolean dynamical systems with finite observation space

This paper is concerned with obtaining the infinite-horizon control policy for partially-observed Boolean dynamical systems (POBDS) when measurements take place in a finite observation space, with application to Boolean gene regulatory networks. The goal of control is to reduce the steady-state mass of undesirable states, which might be associated with disease. The idea behind the proposed method is to transfer the partially-observed Boolean states into a continuous observed state space known as belief space, and then employ the well-known value iteration method based on Point-Based Value Iteration (PBVI). The performance of the method is investigated using a Boolean network model constructed from melanoma gene-expression data observed through Bernoulli noise.

Multiple Model Adaptive controller for Partially-Observed Boolean Dynamical Systems

This paper is concerned with developing an adaptive controller for Partially-Observed Boolean Dynamical Systems (POBDS). Assuming that partial knowledge about the system can be modeled by a finite number of candidate models, then simultaneous identification and control of a POBDS is achieved using the combination of a state-feedback controller and a Multiple-Model Adaptive Estimation (MMAE) technique. The proposed method contains two main steps: first, in the offline step, the stationary control policy for the underlying Boolean dynamical system is computed for each candidate model. Then, in the online step, an optimal Bayesian estimator is modeled using a bank of Boolean Kalman Filters (BKFs), each tuned to a candidate model. The result of the offline step along with the estimated state by the bank of BKFs specify the control input that should be applied at each time point. The performance of the proposed adaptive controller is investigated using a Boolean network model constructed from melanoma gene expression data observed through RNA-seq measurements.

Boolean Kalman Filter with correlated observation noise

This paper is concerned with optimal estimation of the state of a Boolean dynamical systems observed through correlated noisy Boolean measurements. The optimal Minimum Mean-Square Error (MMSE) state estimator for general Partially-Observed Boolean Dynamical Systems (POBDS) can be computed via the Boolean Kalman Filter (BKF). However, thus far in the literature only the case of white observation noise has been considered. In this paper, we develop the optimal MMSE filter for a class of POBDS with correlated Boolean measurements. The performance of the proposed method is subsequently investigated using the p53-MDM2 negative feedback loop genetic network model.

BoolFilter: an R package for estimation and identification of partially-observed Boolean dynamical systems

BackgroundGene regulatory networks govern the function of key cellular processes, such as control of the cell cycle, response to stress, DNA repair mechanisms, and more. Boolean networks have been used successfully in modeling gene regulatory networks. In the Boolean network model, the transcriptional state of each gene is represented by 0 (inactive) or 1 (active), and the relationship among genes is represented by logical gates updated at discrete time points. However, the Boolean gene states are never observed directly, but only indirectly and incompletely through noisy measurements based on expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays. The Partially-Observed Boolean Dynamical System (POBDS) signal model is distinct from other deterministic and stochastic Boolean network models in removing the requirement of a directly observable Boolean state vector and allowing uncertainty in the measurement process, addressing the scenario encountered in practice in transcriptomic analysis.ResultsBoolFilter is an R package that implements the POBDS model and associated algorithms for state and parameter estimation. It allows the user to estimate the Boolean states, network topology, and measurement parameters from time series of transcriptomic data using exact and approximated (particle) filters, as well as simulate the transcriptomic data for a given Boolean network model. Some of its infrastructure, such as the network interface, is the same as in the previously published R package for Boolean Networks BoolNet, which enhances compatibility and user accessibility to the new package.ConclusionsWe introduce the R package BoolFilter for Partially-Observed Boolean Dynamical Systems (POBDS). The BoolFilter package provides a useful toolbox for the bioinformatics community, with state-of-the-art algorithms for simulation of time series transcriptomic data as well as the inverse process of system identification from data obtained with various expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays.

Finite-horizon LQR controller for partially-observed Boolean dynamical systems

Abstract This paper proposes an approach for finite-horizon control of partially-observed Boolean dynamical systems (POBDS) with uncertain continuous control input and infinite observation space. To cope with the partial observability of states, the proposed method first maps the POBDS to an unnormalized belief space. The nonlinear dynamics in this continuous belief space are linearized over a nominal trajectory. Then, the optimal feedback controller is derived, based on the well-known linear quadratic regulator (LQR), to push the system to follow the nominal trajectory. This nominal trajectory is computed in a planning stage before starting execution, and updated efficiently during execution, whenever the system is found to deviate from the nominal trajectory. We prove that, under mild regularization conditions, the proposed controller approaches the cost of the nominal trajectory as the linearization error approaches zero. The performance of the proposed controller is demonstrated by numerical experiments with a Melanoma gene regulatory network observed through noisy gene expression measurements.

Scalable Optimal Bayesian Classification of Single-Cell Trajectories under Regulatory Model Uncertainty

Single-cell gene expression measurements offer opportunities in deriving mechanistic understanding of complex diseases, including cancer. However, due to the complex regulatory machinery of the cell, gene regulatory network (GRN) model inference based on such data still manifests significant uncertainty. The goal of this paper is to develop optimal classification of single-cell trajectories accounting for potential model uncertainty. Partially-observed Boolean dynamical systems (POBDS) are used for modeling gene regulatory networks observed through noisy gene-expression data. We derive the exact optimal Bayesian classifier (OBC) for binary classification of single-cell trajectories. The application of the OBC becomes impractical for large GRNs, due to computational and memory requirements. To address this, we introduce a particle-based single-cell classification method that is highly scalable for large GRNs with much lower complexity than the optimal solution. The performance of the proposed particle-based method is demonstrated through numerical experiments using a POBDS model of the well-known T-cell large granular lymphocyte (T-LGL) leukemia network with noisy time-series gene-expression data.