An iterative identification procedure for dynamic modeling of biochemical networks

Mathematical models of complex biological systems, such as metabolic or cell-signalling pathways, usually consist of sets of nonlinear ordinary differential equations which depend on several non-measurable parameters that can be hopefully estimated by fitting the model to experimental data. However, the success of this fitting is largely conditioned by the quantity and quality of data. Optimal experimental design (OED) aims to design the scheme of actuations and measurements which will result in data sets with the maximum amount and/or quality of information for the subsequent model calibration. New methods and computational procedures for OED in the context of biological systems are presented. The OED problem is formulated as a general dynamic optimisation problem where the time-dependent stimuli profiles, the location of sampling times, the duration of the experiments and the initial conditions are regarded as design variables. Its solution is approached using the control vector parameterisation method. Since the resultant nonlinear optimisation problem is in most of the cases non-convex, the use of a robust global nonlinear programming solver is proposed. For the sake of comparing among different experimental schemes, a Monte-Carlo-based identifiability analysis is then suggested. The applicability and advantages of the proposed techniques are illustrated by considering an example related to a cell-signalling pathway.

Optimal measurement design for parameter identification in mechanized tunneling

We consider the problem of A-optimal design of experiment under a Bayesian probabilistic model with both categorical and continuous response variables. The utility function of the local design problem is derived by applying Bayesian experimental design framework. We also develop an efficient optimization algorithm to obtain the local optimal design by combining the particle swarm optimization and the blocked coordinate descent methods. In addition, we discuss two different ways of constructing the global optimal design based on the algorithm for local optimal design. Simulation studies are presented to illustrate the efficiency of our approach.

The need for efficient computational screening of molecular candidates that possess desired properties frequently arises in various scientific and engineering problems, including drug discovery and materials design. However, the large size of the search space containing the candidates and the substantial computational cost of high-fidelity property prediction models makes screening practically challenging. In this work, we propose a general framework for constructing and optimizing a virtual screening (HTVS) pipeline that consists of multi-fidelity models. The central idea is to optimally allocate the computational resources to models with varying costs and accuracy to optimize the return-on-computational-investment (ROCI). Based on both simulated as well as real data, we demonstrate that the proposed optimal HTVS framework can significantly accelerate screening virtually without any degradation in terms of accuracy. Furthermore, it enables an adaptive operational strategy for HTVS, where one can trade accuracy for efficiency.

In environmental and water resource (EWR) engineering, different types of design problems exist, such as operation design, monitoring design, detection design, and remediation design. This chapter is devoted to the subject of experimental design for model calibration and parameter estimation. Experimental design plays a critical role in model construction because the reliability of a model is mainly dependent on the quantity and quality of data used for its calibration. In other words, the experimental design dictates how data should be collected in field campaigns and how many observations are needed. An optimal experimental design (OED), when it is executed, should provide the maximum amount of information with the minimum cost. Basic concepts, theories, and methods of OED are well established in statistics and have been applied to various scientific and engineering disciplines.

Modeling and Analysis Challenges in Systems Biology

Iterative Optimal Experiment Design for Estimation of Microbial Growth Kinetics as Function of Temperature

The Bayesian optimal experimental design (OED) problem seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty. The goal of OED is to find an experiment that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge about expected data. Therefore, within the context of seismic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize the ability to locate seismic events from arrival time data of detected seismic phases. In order to do utilize Bayesian OED we must develop four elements:1. A likelihood function that describes the uncertainty of detection and travel times; 2. A Bayesian solver that takes a prior and likelihood to identify the posterior; 3. An algorithm to compute EIG; and, 4. An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we can explore many relevant questions to monitoring such as: how and what multiphenomenology data can be used to optimally reduce uncertainty, how to trade off sensor fidelity and earth model uncertainty, and how sensor types, number, and locations influence uncertainty

AMIGO: A model identification toolbox based on global optimization and its applications in biosystems

Genotyping costs still preclude analysis of a comprehensive SNP map in thousands of individual subjects in the search for disease susceptibility loci. Allele frequency estimation in DNA pools from cases and controls offers a partial solution, but variance in these estimates will result in some loss of statistical power. However, there has been no systematic attempt to quantify the several sources of error in previous studies. We report an analysis of the magnitude of variance components of each experimental stage in DNA pooling studies, and find that a design based on the formation of numerous small pools of approximately 50 individuals is superior to the formation of fewer, larger pools and the replication of any of the experimental stages. We conclude that this approach may retain an effective sample size greater than 68% of the true sample size, whilst offering a 60-fold reduction in DNA usage and a greater than 30-fold saving in cost, compared to individual genotyping. The possibility of combining pooling with informed selection of haplotype tag SNPs is also considered. In this way further savings in efficiency may be possible by using pooled allele frequency estimates to infer haplotype frequencies and hence, allele frequencies at untyped markers.

The demand for 3D models that represent real-world objects such as structures and buildings has increased in recent years. It is becoming increasingly important that the reconstructions are not only visually convincing but also feature high geometric accuracy. This includes, for example, the fields of civil engineering, terrestrial surveying and archeology, where precise measurements are made in the models for documentation and analysis purposes. There are different approaches to create such a reconstruction. The photogrammetric method Structure from Motion and laser scanning are among the most widely used methods here, as they do not require a complicated setup and can be used for scenarios at small to large scale. Recent developments are enabling unmanned robotic systems, especially sensor mounted UAVs, to assist in the recording of areas which are otherwise difficult to observe. The demand for a high geometric accuracy, however, comes at the expense of high computational complexity of up to several days. Hence, especially real-time reconstructions are unfeasible, such that recording and reconstruction procedure must be executed consecutively. The resulting model quality, i.e. completeness and accuracy, is only assessable afterwards. Since it is often difficult or even impossible to improve these models with additional measurements afterwards, methods that ensure a reliable acquisition of sufficient data is required.
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\nIn this thesis we develop new methods and theory that address this problem for the mentioned sensor types. For both, a probabilistic description of the expected surface reconstruction error is maintained cost-efficiently as an estimate for the model quality during the recording procedure. For image sensors this is realized by incrementally constructing confidence ellipsoids that describe the information obtained from all views. With depth sensors the surface quality is described by the variance of a Gaussian process implicit surface regression fit to point cloud data using polyharmonic kernel functions. Sensor poses are then assessed by the information they add to the subsequent reconstruction up to a desired geometric accuracy using a formulation that is motivated from Optimal Experimental Design. This quantity is further used in an iterative next-best-view selection framework as a subproblem of a coverage path planning problem.
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\nThe general formulations presented in this thesis enables a wide range of applications, such as offline and online view planning or various autonomous robot systems under consideration of dynamic and geometric constraints. We present the first multi-view coverage path planning approach, specifically targeted at autonomous Structure from Motion data acquisition. Its correctness is validated in simulation using the physics simulator Gazebo. Furthermore, we lay a foundation for similar applications with depth sensors. All presented algorithms were developed with scalability in mind and show promising results regarding real-time usability.

To introduce a computationally efficient approach to optimizing the data acquisition parameters of MR Fingerprinting experiments with the Cramér-Rao bound. This paper presents a new approach to the optimal experimental design (OED) problem for MR Fingerprinting, which leverages an early observation that the optimized data acquisition parameters of MR Fingerprinting experiments are highly structured. Specifically, the proposed approach captures the desired structure by representing the sequences of data acquisition parameters with a special class of piecewise polynomials known as B-splines. This incorporates low-dimensional spline subspace constraints into the OED problem, which significantly reduces the search space of the problem, thereby improving the computational efficiency. With the rich B-spline representations, the proposed approach also allows for incorporating prior knowledge on the structure of different acquisition parameters, which facilitates the experimental design. The effectiveness of the proposed approach was evaluated using numerical simulations, phantom experiments, and in vivo experiments. The proposed approach achieves a two-order-of-magnitude improvement of the computational efficiency over the state-of-the-art approaches, while providing a comparable signal-to-noise ratio efficiency benefit. It enables an optimal experimental design problem for MR Fingerprinting with a typical acquisition length to be solved in approximately 1 min. The proposed approach significantly improves the computational efficiency of the optimal experimental design for MR Fingerprinting, which enhances its practical utility for a variety of quantitative MRI applications.

Mathematical modeling is one of the fundamental techniques for understanding biophysical mechanisms in developmental biology. It helps researchers to analyze complex physiological processes and connect like a bridge between theoretical and experimental observations. Various groups of mathematical models have been studied to analyze these processes, and the nonlocal models are one of them. Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances (e.g., cell-cell, cell-tissue adhesions, neural networks, the spread of diseases, intra-specific competition, nanobeams, etc.). This review illustrates different nonlocal mathematical models applied to biology and life sciences. The major focus has been given to sources, developments, and applications of such models. Among other things, a systematic discussion has been provided for the conditions of pattern formations in biological systems of population dynamics. Special attention has also been given to nonlocal interactions on networks, network coupling and integration, including brain dynamics models that provide an important tool to understand neurodegenerative diseases better. In addition, we have discussed nonlocal modeling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. Furthermore, the discussed nonlocal continuum models can go sufficiently smaller scales, including nanotechnology, where classical local models often fail to capture the complexities of nanoscale interactions, applied to build biosensors to sense biomaterial and its concentration. Piezoelectric and other smart materials are among them, and these devices are becoming increasingly important in the digital and physical world that is intrinsically interconnected with biological systems. Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue growth and shrinkage, and other areas increasingly important in biomedical and bioengineering applications. Finally, we provided a comprehensive summary of emerging trends and highlighted future directions in this rapidly expanding field.

The problem under consideration is to obtain a measurement schedule for training neural networks. This task is perceived as an experimental design in a given design space that is obtained in such a way as to minimize the difference between the neural network and the system being considered. This difference can be expressed in many different ways and one of them, namely, the D-optimality criterion is used in this paper. In particular, the paper presents a unified and comprehensive treatment of this problem by discussing the existing and previously unpublished properties of the optimum experimental design (OED) for neural networks. The consequences of the above properties are discussed as well. A hybrid algorithm that can be used for both the training and data development of neural networks is another important contribution of this paper. A careful analysis of the algorithm is presented and its comprehensive convergence analysis with the help of the Lyapunov method are given. The paper contains a number of numerical examples that justify the application of the OED theory for neural networks. Moreover, an industrial application example is given that deals with the valve actuator.

A hybrid approach for efficient and robust parameter estimation in biochemical pathways