Control of Gene Regulatory Networks With Noisy Measurements and Uncertain Inputs

Imani, Mahdi; Braga-Neto, Ulisses

doi:10.1109/tcns.2017.2746341

“…Partially-observed Boolean dynamical systems consist of a Boolean state process, also known as a Boolean network, observed through an arbitrary noisy mapping to a measurement space [1][2][3][4][5][6][7][8][9][10][11]. Instances of POBDSs abound in fields such as genomics [12], robotics [13], digital communication systems [14], and more.…”

Section: Introductionmentioning

confidence: 99%

Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems

Imani

¹

,

Braga-Neto

²

2017

IEEE Trans. Signal Process.

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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 propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model.

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“…In this section, the state estimation performance of the APF-BKF and APF-BKS is compared to that of the exact BKF and BKS, respectively. Given that the cellcycle network comprises 10 genes, the size of the transition and update matrices required by both the BKF and BKS is 2 10 × 2 10 . As a result, the computational cost of the BKF and BKS is high.…”

Section: Experiments 1: State Estimationmentioning

confidence: 99%

Particle filters for partially-observed Boolean dynamical systems

Imani

¹

,

Braga-Neto

²

2018

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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 propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model. (Mahdi Imani), ulisses@ece.tamu.edu (Ulisses Braga-Neto).becomes impractical due to large computational and memory requirements. In [3], an approximate sequential Monte-Carlo (SMC) algorithm was proposed to compute the BKF using sequential importance resampling (SIR). By contrast, we develop here SMC algorithms for both the BKF and fixed-interval BKS based on the more efficient auxiliary particle filter (APF) algorithm [17].The BKF and BKS require for their application that all system parameters be known. In the case where noise intensities, the network topology, or observational parameters are not known or only partially known, an adaptive scheme to simultaneously estimate the state and parameters of the system is required. An exact adaptive filtering framework to accomplish that task was proposed recently in [18], which is based on the BKF and BKS in conjunction with maximum-likelihood estimation of the parameters. In this paper, we develop an accurate and efficient particle filtering implementation of the adaptive filtering framework in [18], which is suitable for large systems.In the case where the parameter space is discrete (finite), the adaptive filter corresponds to a bank of particle filters in parallel, which is reminiscent of the multiple

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“…A basic problem in genomic signal processing is to derive intervention strategies for gene regulatory networks (GRNs) to avoid undesirable states, in particular, cancerous phenotypes. The problem goes back to the early days of genomics when 2 paradigms were introduced to force dynamical GRNs away from carcinogenic states, dynamical intervention 1 – 3 and structural intervention . 4 Substantial work has been done since then (see the work by Dougherty et al 5 for reviews).…”

Section: Introductionmentioning

confidence: 99%

Sequential Experimental Design for Optimal Structural Intervention in Gene Regulatory Networks Based on the Mean Objective Cost of Uncertainty

Imani

¹

,

Dehghannasiri

²

,

Braga-Neto

³

et al. 2018

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Scientists are attempting to use models of ever-increasing complexity, especially in medicine, where gene-based diseases such as cancer require better modeling of cell regulation. Complex models suffer from uncertainty and experiments are needed to reduce this uncertainty. Because experiments can be costly and time-consuming, it is desirable to determine experiments providing the most useful information. If a sequence of experiments is to be performed, experimental design is needed to determine the order. A classical approach is to maximally reduce the overall uncertainty in the model, meaning maximal entropy reduction. A recently proposed method takes into account both model uncertainty and the translational objective, for instance, optimal structural intervention in gene regulatory networks, where the aim is to alter the regulatory logic to maximally reduce the long-run likelihood of being in a cancerous state. The mean objective cost of uncertainty (MOCU) quantifies uncertainty based on the degree to which model uncertainty affects the objective. Experimental design involves choosing the experiment that yields the greatest reduction in MOCU. This article introduces finite-horizon dynamic programming for MOCU-based sequential experimental design and compares it with the greedy approach, which selects one experiment at a time without consideration of the full horizon of experiments. A salient aspect of the article is that it demonstrates the advantage of MOCU-based design over the widely used entropy-based design for both greedy and dynamic programming strategies and investigates the effect of model conditions on the comparative performances.

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Control of Gene Regulatory Networks With Noisy Measurements and Uncertain Inputs

Cited by 41 publications

References 45 publications

Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems

Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems

Particle filters for partially-observed Boolean dynamical systems

Sequential Experimental Design for Optimal Structural Intervention in Gene Regulatory Networks Based on the Mean Objective Cost of Uncertainty

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