Daniel N. Mohsenizadeh

Dynamical modeling of uncertain interaction-based genomic networks

BackgroundMost dynamical models for genomic networks are built upon two current methodologies, one process-based and the other based on Boolean-type networks. Both are problematic when it comes to experimental design purposes in the laboratory. The first approach requires a comprehensive knowledge of the parameters involved in all biological processes a priori, whereas the results from the second method may not have a biological correspondence and thus cannot be tested in the laboratory. Moreover, the current methods cannot readily utilize existing curated knowledge databases and do not consider uncertainty in the knowledge. Therefore, a new methodology is needed that can generate a dynamical model based on available biological data, assuming uncertainty, while the results from experimental design can be examined in the laboratory.ResultsWe propose a new methodology for dynamical modeling of genomic networks that can utilize the interaction knowledge provided in public databases. The model assigns discrete states for physical entities, sets priorities among interactions based on information provided in the database, and updates each interaction based on associated node states. Whenever uncertainty in dynamics arises, it explores all possible outcomes. By using the proposed model, biologists can study regulation networks that are too complex for manual analysis.ConclusionsThe proposed approach can be effectively used for constructing dynamical models of interaction-based genomic networks without requiring a complete knowledge of all parameters affecting the network dynamics, and thus based on a small set of available data.

Optimal Objective-Based Experimental Design for Uncertain Dynamical Gene Networks with Experimental Error

In systems biology, network models are often used to study interactions among cellular components, a salient aim being to develop drugs and therapeutic mechanisms to change the dynamical behavior of the network to avoid undesirable phenotypes. Owing to limited knowledge, model uncertainty is commonplace and network dynamics can be updated in different ways, thereby giving multiple dynamic trajectories, that is, dynamics uncertainty. In this manuscript, we propose an experimental design method that can effectively reduce the dynamics uncertainty and improve performance in an interaction-based network. Both dynamics uncertainty and experimental error are quantified with respect to the modeling objective, herein, therapeutic intervention. The aim of experimental design is to select among a set of candidate experiments the experiment whose outcome, when applied to the network model, maximally reduces the dynamics uncertainty pertinent to the intervention objective.

Multivariable controller synthesis using SISO design methods

This paper proposes a new method to design multivariable controllers for linear Multi-Input Multi-Output (MIMO) control systems using the Smith-McMillan form. The Smith-McMillan form of the transfer function matrix of a MIMO plant is an equivalent diagonal transfer function matrix using which the problem of multivariable controller synthesis can be reduced to multiple Single-Input Single-Output (SISO) controller designs. If the designed SISO controllers satisfy certain relative degree conditions, then the corresponding multivariable controller, to be connected to the MIMO plant, will be proper. In this paper we show how such multivariable controllers can be designed to satisfy closed loop stability and reference tracking. We also provide some illustrative examples.

Extremal Results for Algebraic Linear Interval Systems

This chapter explores some important characteristics of algebraic linear systems containing interval parameters. Applying the Cramer’s rule, a parametrized solution of a linear system can be expressed as the ratio of two determinants. We show that these determinants can be expanded as multivariate polynomial functions of the parameters. In many practical problems, the parameters in the system characteristic matrix appear with rank one, resulting in a rational multilinear form for the parametrized solutions. These rational multilinear functions are monotonic with respect to each parameter. This monotonic characteristic plays an important role in the analysis and design of algebraic linear interval systems in which the parameters appear with rank one. In particular, the extremal values of the parametrized solutions over the box of interval parameters occur at the vertices of the box.

An Equivalent Plant Representation for Unknown Control Systems

This paper proposes a new method to the design of a controller to be embedded at a prescribed location in an otherwise unknown complex and multiple-loop Linear Time-Invariant (LTI) control system. The questions that arise naturally are: Will a controller proposed for this location stabilizes the overall system and, if so, what stability margins and response can be obtained? We address these questions by constructing an equivalent single-loop frequency domain representation of the original unknown complex system. This equivalent plant construction can be accomplished by a small set of frequency response measurements.Copyright

An Extremal Result for Unknown Interval Linear Systems

Abstract This paper explores some important characteristics of a system of linear equations containing parameters. Such a system of equations arises in many branches of engineering including electrical circuits, hydraulic networks and truss structures. A parametrized solution of a set of linear equations can be obtained by applying Cramers rule. In many practically important cases the parameters appear with rank one dependency, resulting in parametrized solutions to be of a rational multilinear form, which will be monotonic in each parameter. This monotonic characteristic has practical importance in the analysis and design of linear systems with parameters having interval uncertainties. In particular, extremal values of system variables occur at the vertices of the parameter boxes.

Optimal dynamics uncertainty reduction in gene networks in the presence of experimental error

We present an experimental design method for choosing optimal experiments to reduce dynamics uncertainty in dynamical gene networks. The method, takes into account both the modeling objective and the experimental error.

An experimental design to reduce dynamics uncertainty in genomic networks

In systems biology, network models are often used as a promising tool to study interactions among cellular components (e.g., genes or proteins). However, these models are typically too complex and biological data is very limited which leads to model uncertainty. Network dynamics involves the evolution of entities over time which is central in developing cancer drugs whose aim is to change the dynamical behavior of the network to avoid cancerous phenotypes. In the presence of uncertainty, network dynamics can be updated in different ways giving multiple dynamic trajectories. In this paper, we propose an experimental design method that can effectively reduces the dynamics uncertainty and improve the performance of the interventions. We use the concept of mean objective cost of uncertainty (MOCU) to quantify dynamics uncertainty. We also incorporate the error of the potential experiments in such a way that the objective from the experimental design is taken into account. As a byproduct of the proposed objective-based experimental design method, we also develop a mathematical framework for applying interventions to interaction-based genomic networks. Furthermore, our proposed approach is well-suited for laboratory tests as the results have biological correspondence. A software package is also programmed based on the proposed experimental design method.

A new measurement based approach to the study of biological systems

This paper proposes a new approach to the analysis and design of biological systems. It will be shown that, upon an application of Time-Scale Separation Principle to a nonlinear biochemical system at steady-state, a rational polynomial function relates the chemical characteristics of slow-rate substances. This functional dependency can be determined by a small set of measurements. With the functional dependency in hand, one can impose design constraints, such as limiting values for concentration of product substances, and extract corresponding values for the design parameters. Some important characteristics of this rational polynomial form will be also explored.

Experimental PID Controller Design: A New Frequency Domain Approach Based on Desired Performance

This paper presents an alternative approach to design PID controllers based on frequency response measurements. The proposed method does not require any mathematical model of the system and can handle the design process directly from a small set of frequency domain data. It is shown that for the class of Linear Time-Invariant (LTI) control systems, there exists a rational multilinear function for the frequency response between any two arbitrary breaking points in terms of the design controller. This function can be determined by conducting a small set of frequency response measurements and then will be used to synthesize a controller that guarantee a set of desired frequency-domain specifications. In this paper, we use this result to design a PID controller for a servomechanism control system. In particular, we show that such desirable PID controller can be calculated by solving an optimization problem.Copyright