Reverse engineering and identification in systems biology: strategies, perspectives and challenges

EIEPCF: accurate inference of functional gene regulatory networks by eliminating indirect effects from confounding factors

Reconstructing functional gene regulatory networks (GRNs) is a primary prerequisite for understanding pathogenic mechanisms and curing diseases in animals, and it also provides an important foundation for cultivating vegetable and fruit varieties that are resistant to diseases and corrosion in plants. Many computational methods have been developed to infer GRNs, but most of the regulatory relationships between genes obtained by these methods are biased. Eliminating indirect effects in GRNs remains a significant challenge for researchers. In this work, we propose a novel approach for inferring functional GRNs, named EIEPCF (eliminating indirect effects produced by confounding factors), which eliminates indirect effects caused by confounding factors. This method eliminates the influence of confounding factors on regulatory factors and target genes by measuring the similarity between their residuals. The validation results of the EIEPCF method on simulation studies, the gold-standard networks provided by the DREAM3 Challenge and the real gene networks of Escherichia coli demonstrate that it achieves significantly higher accuracy compared to other popular computational methods for inferring GRNs. As a case study, we utilized the EIEPCF method to reconstruct the cold-resistant specific GRN from gene expression data of cold-resistant in Arabidopsis thaliana. The source code and data are available at https://github.com/zhanglab-wbgcas/EIEPCF.

Inferring upstream regulatory genes of FOXP3 in human regulatory T cells from time-series transcriptomic data

The discovery of upstream regulatory genes of a gene of interest still remains challenging. Here we applied a scalable computational method to unbiasedly predict candidate regulatory genes of critical transcription factors by searching the whole genome. We illustrated our approach with a case study on the master regulator FOXP3 of human primary regulatory T cells (Tregs). While target genes of FOXP3 have been identified, its upstream regulatory machinery still remains elusive. Our methodology selected five top-ranked candidates that were tested via proof-of-concept experiments. Following knockdown, three out of five candidates showed significant effects on the mRNA expression of FOXP3 across multiple donors. This provides insights into the regulatory mechanisms modulating FOXP3 transcriptional expression in Tregs. Overall, at the genome level this represents a high level of accuracy in predicting upstream regulatory genes of key genes of interest.

Inference of gene regulatory networks based on directed graph convolutional networks

Inferring gene regulatory network (GRN) is one of the important challenges in systems biology, and many outstanding computational methods have been proposed; however there remains some challenges especially in real datasets. In this study, we propose Directed Graph Convolutional neural network-based method for GRN inference (DGCGRN). To better understand and process the directed graph structure data of GRN, a directed graph convolutional neural network is conducted which retains the structural information of the directed graph while also making full use of neighbor node features. The local augmentation strategy is adopted in graph neural network to solve the problem of poor prediction accuracy caused by a large number of low-degree nodes in GRN. In addition, for real data such as E.coli, sequence features are obtained by extracting hidden features using Bi-GRU and calculating the statistical physicochemical characteristics of gene sequence. At the training stage, a dynamic update strategy is used to convert the obtained edge prediction scores into edge weights to guide the subsequent training process of the model. The results on synthetic benchmark datasets and real datasets show that the prediction performance of DGCGRN is significantly better than existing models. Furthermore, the case studies on bladder uroepithelial carcinoma and lung cancer cells also illustrate the performance of the proposed model.

Evolving Improved Sampling Protocols for Dose-Response Modelling Using Genetic Algorithms with a Profile-Likelihood Metric

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Mathematical modeling of transdermal delivery of topical drug formulations in a dynamic microfluidic diffusion chamber in health and disease

Mathematical models of epidermal and dermal transport are essential for optimization and development of products for percutaneous delivery both for local and systemic indication and for evaluation of dermal exposure to chemicals for assessing their toxicity. These models often help directly by providing information on the rate of drug penetration through the skin and thus on the dermal or systemic concentration of drugs which is the base of their pharmacological effect. The simulations are also helpful in analyzing experimental data, reducing the number of experiments and translating the in vitro investigations to an in-vivo setting. In this study skin penetration of topically administered caffeine cream was investigated in a skin-on-a-chip microfluidic diffusion chamber at room temperature and at 32°C. Also the transdermal penetration of caffeine in healthy and diseased conditions was compared in mouse skins from intact, psoriatic and allergic animals. In the last experimental setup dexamethasone, indomethacin, piroxicam and diclofenac were examined as a cream formulation for absorption across the dermal barrier. All the measured data were used for making mathematical simulation in a three-compartmental model. The calculated and measured results showed a good match, which findings indicate that our mathematical model might be applied for prediction of drug delivery through the skin under different circumstances and for various drugs in the novel, miniaturized diffusion chamber.

Analytical challenges in omics research on asthma and allergy: A National Institute of Allergy and Infectious Diseases workshop

Studies of asthma and allergy are generating increasing volumes of omics data for analysis and interpretation. The National Institute of Allergy and Infectious Diseases (NIAID) assembled a workshop comprising investigators studying asthma and allergic diseases using omics approaches, omics investigators from outside the field, and NIAID medical and scientific officers to discuss the following areas in asthma and allergy research: genomics, epigenomics, transcriptomics, microbiomics, metabolomics, proteomics, lipidomics, integrative omics, systems biology, and causal inference. Current states of the art, present challenges, novel and emerging strategies, and priorities for progress were presented and discussed for each area. This workshop report summarizes the major points and conclusions from this NIAID workshop. As a group, the investigators underscored the imperatives for rigorous analytic frameworks, integration of different omics data types, cross-disciplinary interaction, strategies for overcoming current limitations, and the overarching goal to improve scientific understanding and care of asthma and allergic diseases.

Balancing competing effects of tissue growth and cytoskeletal regulation during Drosophila wing disc development

How a developing organ robustly coordinates the cellular mechanics and growth to reach a final size and shape remains poorly understood. Through iterations between experiments and model simulations that include a mechanistic description of interkinetic nuclear migration, we show that the local curvature, height, and nuclear positioning of cells in the Drosophila wing imaginal disc are defined by the concurrent patterning of actomyosin contractility, cell-ECM adhesion, ECM stiffness, and interfacial membrane tension. We show that increasing cell proliferation via different growth-promoting pathways results in two distinct phenotypes. Triggering proliferation through insulin signaling increases basal curvature, but an increase in growth through Dpp signaling and Myc causes tissue flattening. These distinct phenotypic outcomes arise from differences in how each growth pathway regulates the cellular cytoskeleton, including contractility and cell-ECM adhesion. The coupled regulation of proliferation and cytoskeletal regulators is a general strategy to meet the multiple context-dependent criteria defining tissue morphogenesis.

Information integration during bioelectric regulation of morphogenesis of the embryonic frog brain

Spatiotemporal patterns of cellular resting potential regulate several aspects of development. One key aspect of the bioelectric code is that transcriptional and morphogenetic states are determined not by local, single-cell, voltage levels but by specific distributions of voltage across cell sheets. We constructed and analyzed a minimal dynamical model of collective gene expression in cells based on inputs of multicellular voltage patterns. Causal integration analysis revealed a higher-order mechanism by which information about the voltage pattern was spatiotemporally integrated into gene activity, as well as a division of labor among and between the bioelectric and genetic components. We tested and confirmed predictions of this model in a system in which bioelectric control of morphogenesis regulates gene expression and organogenesis: the embryonic brain of the frog Xenopus laevis. This study demonstrates that machine learning and computational integration approaches can advance our understanding of the information-processing underlying morphogenetic decision-making, with a potential for other applications in developmental biology and regenerative medicine.

Distilling identifiable and interpretable dynamic models from biological data

Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam's razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

Inferring gene regulatory networks using transcriptional profiles as dynamical attractors

Genetic regulatory networks (GRNs) regulate the flow of genetic information from the genome to expressed messenger RNAs (mRNAs) and thus are critical to controlling the phenotypic characteristics of cells. Numerous methods exist for profiling mRNA transcript levels and identifying protein-DNA binding interactions at the genome-wide scale. These enable researchers to determine the structure and output of transcriptional regulatory networks, but uncovering the complete structure and regulatory logic of GRNs remains a challenge. The field of GRN inference aims to meet this challenge using computational modeling to derive the structure and logic of GRNs from experimental data and to encode this knowledge in Boolean networks, Bayesian networks, ordinary differential equation (ODE) models, or other modeling frameworks. However, most existing models do not incorporate dynamic transcriptional data since it has historically been less widely available in comparison to "static" transcriptional data. We report the development of an evolutionary algorithm-based ODE modeling approach (named EA) that integrates kinetic transcription data and the theory of attractor matching to infer GRN architecture and regulatory logic. Our method outperformed six leading GRN inference methods, none of which incorporate kinetic transcriptional data, in predicting regulatory connections among TFs when applied to a small-scale engineered synthetic GRN in Saccharomyces cerevisiae. Moreover, we demonstrate the potential of our method to predict unknown transcriptional profiles that would be produced upon genetic perturbation of the GRN governing a two-state cellular phenotypic switch in Candida albicans. We established an iterative refinement strategy to facilitate candidate selection for experimentation; the experimental results in turn provide validation or improvement for the model. In this way, our GRN inference approach can expedite the development of a sophisticated mathematical model that can accurately describe the structure and dynamics of the in vivo GRN.

The SunBEAm birth cohort: Protocol design

Background

Food allergy (FA) and atopic dermatitis (AD) are common conditions that often present in the first year of life. Identification of underlying mechanisms and environmental determinants of FA and AD is essential to develop and implement effective prevention and treatment strategies. Objectives: We sought to describe the design of the Systems Biology of Early Atopy (SunBEAm) birth cohort.

Methods

Funded by the National Institute of Allergy and Infectious Diseases (NIAID) and administered through the Consortium for Food Allergy Research (CoFAR), SunBEAm is a US population-based, multicenter birth cohort that enrolls pregnant mothers, fathers, and their newborns and follows them to 3 years. Questionnaire and biosampling strategies were developed to apply a systems biology approach to identify environmental, immunologic, and multiomic determinants of AD, FA, and other allergic outcomes.

Results

Enrollment is currently underway. On the basis of an estimated FA prevalence of 6%, the enrollment goal is 2500 infants. AD is defined on the basis of questionnaire and assessment, and FA is defined by an algorithm combining history and testing. Although any FA will be recorded, we focus on the diagnosis of egg, milk, and peanut at 5 months, adding wheat, soy, cashew, hazelnut, walnut, codfish, shrimp, and sesame starting at 12 months. Sampling includes blood, hair, stool, dust, water, tape strips, skin swabs, nasal secretions, nasal swabs, saliva, urine, functional aspects of the skin, and maternal breast milk and vaginal swabs.

Conclusions

The SunBEAm birth cohort will provide a rich repository of data and specimens to interrogate mechanisms and determinants of early allergic outcomes, with an emphasis on FA, AD, and systems biology.

Nonlinear expression patterns and multiple shifts in gene network interactions underlie robust phenotypic change in Drosophila melanogaster selected for night sleep duration

All but the simplest phenotypes are believed to result from interactions between two or more genes forming complex networks of gene regulation. Sleep is a complex trait known to depend on the system of feedback loops of the circadian clock, and on many other genes; however, the main components regulating the phenotype and how they interact remain an unsolved puzzle. Genomic and transcriptomic data may well provide part of the answer, but a full account requires a suitable quantitative framework. Here we conducted an artificial selection experiment for sleep duration with RNA-seq data acquired each generation. The phenotypic results are robust across replicates and previous experiments, and the transcription data provides a high-resolution, time-course data set for the evolution of sleep-related gene expression. In addition to a Hierarchical Generalized Linear Model analysis of differential expression that accounts for experimental replicates we develop a flexible Gaussian Process model that estimates interactions between genes. 145 gene pairs are found to have interactions that are different from controls. Our method appears to be not only more specific than standard correlation metrics but also more sensitive, finding correlations not significant by other methods. Statistical predictions were compared to experimental data from public databases on gene interactions. Mutations of candidate genes implicated by our results affected night sleep, and gene expression profiles largely met predicted gene-gene interactions.

Predictive power of non-identifiable models

Resolving practical non-identifiability of computational models typically requires either additional data or non-algorithmic model reduction, which frequently results in models containing parameters lacking direct interpretation. Here, instead of reducing models, we explore an alternative, Bayesian approach, and quantify the predictive power of non-identifiable models. We considered an example biochemical signalling cascade model as well as its mechanical analogue. For these models, we demonstrated that by measuring a single variable in response to a properly chosen stimulation protocol, the dimensionality of the parameter space is reduced, which allows for predicting the measured variable's trajectory in response to different stimulation protocols even if all model parameters remain unidentified. Moreover, one can predict how such a trajectory will transform in the case of a multiplicative change of an arbitrary model parameter. Successive measurements of remaining variables further reduce the dimensionality of the parameter space and enable new predictions. We analysed potential pitfalls of the proposed approach that can arise when the investigated model is oversimplified, incorrect, or when the training protocol is inadequate. The main advantage of the suggested iterative approach is that the predictive power of the model can be assessed and practically utilised at each step.

Cancer cachexia as a blueprint for treating obesity

Effective pharmacological treatments to achieve significant and sustained weight loss in obese individuals remain limited. Here, we apply a 'reverse engineering' approach to cancer cachexia, an extreme form of dysregulated energy balance resulting in net catabolism. We discuss three phenotypic features of the disease, summarize the underlying molecular checkpoints, and explore their translation to obesity research. We then provide examples for established pharmaceuticals, which follow a reverse engineering logic, and propose additional targets that may be of relevance for future studies. Finally, we argue that approaching diseases from this perspective may prove useful as a generic strategy to fuel the development of innovative therapies.

Cracking the Code of Neuronal Cell Fate

Transcriptional regulation is fundamental to most biological processes and reverse-engineering programs can be used to decipher the underlying programs. In this review, we describe how genomics is offering a systems biology-based perspective of the intricate and temporally coordinated transcriptional programs that control neuronal apoptosis and survival. In addition to providing a new standpoint in human pathology focused on the regulatory program, cracking the code of neuronal cell fate may offer innovative therapeutic approaches focused on downstream targets and regulatory networks. Similar to computers, where faults often arise from a software bug, neuronal fate may critically depend on its transcription program. Thus, cracking the code of neuronal life or death may help finding a patch for neurodegeneration and cancer.

Sloppiness: Fundamental study, new formalism and its application in model assessment

Computational modelling of biological processes poses multiple challenges in each stage of the modelling exercise. Some significant challenges include identifiability, precisely estimating parameters from limited data, informative experiments and anisotropic sensitivity in the parameter space. One of these challenges' crucial but inconspicuous sources is the possible presence of large regions in the parameter space over which model predictions are nearly identical. This property, known as sloppiness, has been reasonably well-addressed in the past decade, studying its possible impacts and remedies. However, certain critical unanswered questions concerning sloppiness, particularly related to its quantification and practical implications in various stages of system identification, still prevail. In this work, we systematically examine sloppiness at a fundamental level and formalise two new theoretical definitions of sloppiness. Using the proposed definitions, we establish a mathematical relationship between the parameter estimates' precision and sloppiness in linear predictors. Further, we develop a novel computational method and a visual tool to assess the goodness of a model around a point in parameter space by identifying local structural identifiability and sloppiness and finding the most sensitive and least sensitive parameters for non-infinitesimal perturbations. We demonstrate the working of our method in benchmark systems biology models of various complexities. The pharmacokinetic HIV infection model analysis identified a new set of biologically relevant parameters that can be used to control the free virus in an active HIV infection.

Automated model calibration with parallel MCMC: Applications for a cardiovascular system model

Computational physiological models continue to increase in complexity, however, the task of efficiently calibrating the model to available clinical data remains a significant challenge. One part of this challenge is associated with long calibration times, which present a barrier for the routine application of model-based prediction in clinical practice. Another aspect of this challenge is the limited available data for the unique calibration of complex models. Therefore, to calibrate a patient-specific model, it may be beneficial to verify that task-specific model predictions have acceptable uncertainty, rather than requiring all parameters to be uniquely identified. We have developed a pipeline that reduces the set of fitting parameters to make them structurally identifiable and to improve the efficiency of a subsequent Markov Chain Monte Carlo (MCMC) analysis. MCMC was used to find the optimal parameter values and to determine the confidence interval of a task-specific prediction. This approach was demonstrated on numerical experiments where a lumped parameter model of the cardiovascular system was calibrated to brachial artery cuff pressure, echocardiogram volume measurements, and synthetic cerebral blood flow data that approximates what can be obtained from 4D-flow MRI data. This pipeline provides a cerebral arterial pressure prediction that may be useful for determining the risk of hemorrhagic stroke. For a set of three patients, this pipeline successfully reduced the parameter set of a cardiovascular system model from 12 parameters to 8–10 structurally identifiable parameters. This enabled a significant (>4×) efficiency improvement in determining confidence intervals on predictions of pressure compared to performing a naive MCMC analysis with the full parameter set. This demonstrates the potential that the proposed pipeline has in helping address one of the key challenges preventing clinical application of such models. Additionally, for each patient, the MCMC approach yielded a 95% confidence interval on systolic blood pressure prediction in the middle cerebral artery smaller than ±10 mmHg (±1.3 kPa). The proposed pipeline exploits available high-performance computing parallelism to allow straightforward automation for general models and arbitrary data sets, enabling automated calibration of a parameter set that is specific to the available clinical data with minimal user interaction.

Analysis of sloppiness in model simulations: Unveiling parameter uncertainty when mathematical models are fitted to data

This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.

Impact of Particle Size on Toxicity, Tissue Distribution and Excretion Kinetics of Subchronic Intratracheal Instilled Silver Nanoparticles in Mice

The unique physicochemical properties of silver nanoparticles (AgNPs) make them useful in a wide range of sectors, increasing their propensity for human exposure, as well as the need for thorough toxicological assessment. The biodistribution of silver, hematological parameters and GSH/GSSG levels in the lung and liver were studied in mice that were intratracheally instilled with AgNP (5 and 50 nm) and AgNO₃ once a week for 5 weeks, followed by a recovery period of up to 28 days (dpi). Data was gathered to build a PBPK model after the entry of AgNPs into the lungs. AgNPs could be absorbed into the blood and might cross the physiological barriers and be distributed extensively in mice. Similar to AgNO₃, AgNP5 induced longer-lasting toxicity toward blood cells and increased GSH levels in the lung. The exposure to AgNP50 increased the GSH from 1 dpi onward in the liver and silver was distributed to the organs after exposure, but its concentration decreased over time. In AgNP5 treated mice, silver levels were highest in the spleen, kidney, liver and blood, persisting for at least 28 days, suggesting accumulation. The major route for excretion seemed to be through the urine, despite a high concentration of AgNP5 also being found in feces. The modeled silver concentration was in line with the in vivo data for the heart and liver.

A protocol for dynamic model calibration

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

Mechanical properties and clamping behaviors of snow crab claw

The high-performing biomimetic behaviors of crustaceans are the optimal results of long-time wise adaption to their living environment. One outstanding prototype is crab claw, which has the combining advantages of lightweight and high strength. To promote relevant engineering applications, it is imperative to explore its mechanical behaviors and structural characteristics. In this work, mechanical test and finite element analysis (FEA) are performed to reveal the fundamental mechanical properties and clamping behaviors of snow crab (Chionoecetes opilio) claw, respectively. A lightweight modeling method, parametric lofting modeling, for the 3D modeling of the claw is employed, which is compared with the traditional reverse engineering modeling method based on tomography image. Our results demonstrated that the hardness and modulus of the regions near the top of the claw are larger than those of the regions near of bottom of the claw. Moisture is a critical factor in controlling the tensile behavior of the claw and the wet specimens exhibit higher modulus and strength under tensile loading. Besides, The parametric lofting method is highly flexible and efficient in generating 3D geometrical model. The investigation of clamping behaviors provides not only insights into mechanical behaviors and intrinsic mechanisms but also a practical guide for their potential applications, such as designing high-performing artificial clamping muscles for clinical operations, aerospace applications, and robotics.

Improvement of multisource localization of magnetic particles in an animal

In this simulation work, the linearized Bregman iterative algorithm was applied to solve the magnetic source distribution problem of a magnetic particle imaging (MPI) system for small animals. MPI system can apply an excitation magnetic field, and the induced magnetic field from the magnetic nanoparticles (MNPs) can be detected by the sensors of MPI system. With a gaussian distribution source at the upper side of the mouse brain, sensors set above the mouse brain and the constant excitation magnetic field, the average deviation of the calculated source distribution from the multiplane scanning along the axis away from the mouse brain and the closest plane scanning are 2.78 × 10^–3 and 2.84 × 10^–3 respectively. The simulated result showed that combination of multiplane scanning hardly improves the accuracy of the source localization. In addition, a gradient scan method was developed that uses gradient magnetic field to scan the mouse brain. The position of the maximum of the lead field matrix will be controlled by the gradient field. With a set up gaussian distribution source at the bottom of the mouse brain, the average deviation of the calculated source distribution from the gradient scan method and the constant field are 4.42 × 10^–2 and 5.05 × 10^–2. The location error from the two method are 2.24 × 10^–1 cm and 3.61 × 10^–1 cm. The simulation showed that this method can improve the accuracy compared to constant field when the source is away from the sensor and having a potential for application.

Cancer immune control dynamics: a clinical data driven model of systemic immunity in patients with metastatic melanoma

Background

Recent clinical advances in cancer immuno-therapeutics underscore the need for improved understanding of the complex relationship between cancer and the multiple, multi-functional, inter-dependent, cellular and humoral mediators/regulators of the human immune system. This interdisciplinary effort exploits engineering analysis methods utilized to investigate anomalous physical system behaviors to explore immune system behaviors. Cancer Immune Control Dynamics (CICD), a systems analysis approach, attempts to identify differences between systemic immune homeostasis of 27 healthy volunteers versus 14 patients with metastatic malignant melanoma based on daily serial measurements of conventional peripheral blood biomarkers (15 cell subsets, 35 cytokines). The modeling strategy applies engineering control theory to analyze an individual’s immune system based on the biomarkers’ dynamic non-linear oscillatory behaviors. The reverse engineering analysis uses a Singular Value Decomposition (SVD) algorithm to solve the inverse problem and identify a solution profile of the active biomarker relationships. Herein, 28,605 biologically possible biomarker interactions are modeled by a set of matrix equations creating a system interaction model. CICD quantifies the model with a participant’s biomarker data then computationally solves it to measure each relationship’s activity allowing a visualization of the individual’s current state of immunity.

Results

CICD results provide initial evidence that this model-based analysis is consistent with identified roles of biomarkers in systemic immunity of cancer patients versus that of healthy volunteers. The mathematical computations alone identified a plausible network of immune cells, including T cells, natural killer (NK) cells, monocytes, and dendritic cells (DC) with cytokines MCP-1 [CXCL2], IP-10 [CXCL10], and IL-8 that play a role in sustaining the state of immunity in advanced cancer.

Conclusions

With CICD modeling capabilities, the complexity of the immune system is mathematically quantified through thousands of possible interactions between multiple biomarkers. Therefore, the overall state of an individual’s immune system regardless of clinical status, is modeled as reflected in their blood samples. It is anticipated that CICD-based capabilities will provide tools to specifically address cancer and treatment modulated (immune checkpoint inhibitors) parameters of human immunity, revealing clinically relevant biological interactions.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-021-04025-7.

Topological clustering of regulatory genes confers pathogenic tolerance to cassava brown streak virus (CBSV) in cassava

Robustness, a naïve property of biological systems, enables organisms to maintain functions during perturbation and is crucial for improving the resilience of crops to prevailing stress conditions and diseases, guaranteeing food security. Most studies of robustness in crops have focused on genetic superiority based upon individual genes, overlooking the collaborative actions of multiple responsive genes and the regulatory network topology. This research aims to uncover patterns of gene cooperation leading to organismal robustness by studying the topology of gene co-expression networks (GCNs) of both CBSV virus resistant and susceptible cassava cultivars. The resulting GCNs show higher topological clustering of cooperative genes in the resistant cultivar, suggesting that the network architecture is central to attaining robustness. Despite a reduction in the number of hub genes in the resistant cultivar following the perturbation, essential biological functions contained in the network were maintained through neighboring genes that withstood the shock. The susceptible cultivar seemingly coped by inducing more gene actions in the network but could not maintain the functions required for plant growth. These findings underscore the importance of regulatory network architecture in ensuring phenotypic robustness and deepen our understanding of transcriptional regulation.

Qualitative Modeling, Analysis and Control of Synthetic Regulatory Circuits

Qualitative modeling approaches are promising and still underexploited tools for the analysis and design of synthetic circuits. They can make predictions of circuit behavior in the absence of precise, quantitative information. Moreover, they provide direct insight into the relation between the feedback structure and the dynamical properties of a network. We review qualitative modeling approaches by focusing on two specific formalisms, Boolean networks and piecewise-linear differential equations, and illustrate their application by means of three well-known synthetic circuits. We describe various methods for the analysis of state transition graphs, discrete representations of the network dynamics that are generated in both modeling frameworks. We also briefly present the problem of controlling synthetic circuits, an emerging topic that could profit from the capacity of qualitative modeling approaches to rapidly scan a space of design alternatives.

A comprehensive overview and critical evaluation of gene regulatory network inference technologies

Gene regulatory network (GRN) is the important mechanism of maintaining life process, controlling biochemical reaction and regulating compound level, which plays an important role in various organisms and systems. Reconstructing GRN can help us to understand the molecular mechanism of organisms and to reveal the essential rules of a large number of biological processes and reactions in organisms. Various outstanding network reconstruction algorithms use specific assumptions that affect prediction accuracy, in order to deal with the uncertainty of processing. In order to study why a certain method is more suitable for specific research problem or experimental data, we conduct research from model-based, information-based and machine learning-based method classifications. There are obviously different types of computational tools that can be generated to distinguish GRNs. Furthermore, we discuss several classical, representative and latest methods in each category to analyze core ideas, general steps, characteristics, etc. We compare the performance of state-of-the-art GRN reconstruction technologies on simulated networks and real networks under different scaling conditions. Through standardized performance metrics and common benchmarks, we quantitatively evaluate the stability of various methods and the sensitivity of the same algorithm applying to different scaling networks. The aim of this study is to explore the most appropriate method for a specific GRN, which helps biologists and medical scientists in discovering potential drug targets and identifying cancer biomarkers.

Plant tropisms as a window on plant computational processes

Plants are living information-processing organisms with highly adaptive behavior, allowing them to prosper in a harsh and fluctuating environment in spite of being sessile. Lacking a central nervous system, plants are distributed systems orchestrating complex computational processes performed at the tissue level. Here I consider plant tropisms as a useful input-output system boasting a robust mathematical description, naturally permitting a dialogue between mathematical modeling and biological observations. I propose tropisms as an ideal framework for the study of plant computational processes, allowing us to infer the relationship between observed tropic responses and known stimuli. I concentrate on macroscopic models, and elucidate this approach by presenting recent examples focusing on computational processes involved at different hierarchical levels of interactions: a plant's interaction with itself and its internal state, with the abiotic environment, and with neighboring plants.

The effect of tissue composition on gene co-expression

Variable cellular composition of tissue samples represents a significant challenge for the interpretation of genomic profiling studies. Substantial effort has been devoted to modeling and adjusting for compositional differences when estimating differential expression between sample types. However, relatively little attention has been given to the effect of tissue composition on co-expression estimates. In this study, we illustrate the effect of variable cell-type composition on correlation-based network estimation and provide a mathematical decomposition of the tissue-level correlation. We show that a class of deconvolution methods developed to separate tumor and stromal signatures can be applied to two component cell-type mixtures. In simulated and real data, we identify conditions in which a deconvolution approach would be beneficial. Our results suggest that uncorrelated cell-type-specific markers are ideally suited to deconvolute both the expression and co-expression patterns of an individual cell type. We provide a Shiny application for users to interactively explore the effect of cell-type composition on correlation-based co-expression estimation for any cell types of interest.

A motion compensation treadmill for untethered wood ants (Formica rufa): evidence for transfer of orientation memories from free-walking training

The natural scale of insect navigation during foraging makes it challenging to study under controlled conditions. Virtual reality and trackball setups have offered experimental control over visual environments while studying tethered insects, but potential limitations and confounds introduced by tethering motivates the development of alternative untethered solutions. In this paper, we validate the use of a motion compensator (or ‘treadmill’) to study visually driven behaviour of freely moving wood ants (Formica rufa). We show how this setup allows naturalistic walking behaviour and preserves foraging motivation over long time frames. Furthermore, we show that ants are able to transfer associative and navigational memories from classical maze and arena contexts to our treadmill. Thus, we demonstrate the possibility to study navigational behaviour over ecologically relevant durations (and virtual distances) in precisely controlled environments, bridging the gap between natural and highly controlled laboratory experiments.

Summary: We have developed and validated a motion compensating treadmill for wood ants which opens new perspectives to study insect navigation behaviour in a fully controlled manner over ecologically relevant durations.

Identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

Robust Jet Classifiers through Distance Correlation

While deep learning has proven to be extremely successful at supervised classification tasks at the LHC and beyond, for practical applications, raw classification accuracy is often not the only consideration. One crucial issue is the stability of network predictions, either versus changes of individual features of the input data or against systematic perturbations. We present a new method based on a novel application of "distance correlation," a measure quantifying nonlinear correlations, that achieves equal performance to state-of-the-art adversarial decorrelation networks but is much simpler and more stable to train. To demonstrate the effectiveness of our method, we carefully recast a recent ATLAS study of decorrelation methods as applied to boosted, hadronic W tagging. We also show the feasibility of regularization with distance correlation for more powerful convolutional neural networks, as well as for the problem of hadronic top tagging.

Modeling the Control of TGF-β/Smad Nuclear Accumulation by the Hippo Pathway Effectors, Taz/Yap

Integration of transforming growth factor β (TGF-β) signals with those of other pathways allows for precise temporal and spatial control of gene expression patterns that drive development and homeostasis. The Hippo pathway nuclear effectors, Taz/Yap, interact with the TGF-β transcriptional mediators, Smads, to control Smad activity. Key to TGF-β signaling is the nuclear localization of Smads. Thus, to investigate the role of Taz/Yap in Smad nuclear accumulation, we developed mathematical models of Hippo and TGF-β cross talk. The models were based on experimental measurements of TGF-β-induced changes in Taz/Yap and Smad subcellular localization obtained using high-throughput immunofluorescence (IF) imaging in the mouse mammary epithelial cell line, EpH4. Bayesian MCMC DREAM parameter estimation was used to quantify the uncertainty in estimates of the kinetic parameters. Variation of the model parameters and statistical analysis show that our modeling predicts that Taz/Yap can alter TGF-β receptor activity and directly or indirectly act as nuclear retention factors.

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Taz/Yap modulate TGF-β-induced nuclear accumulation of Smad2/3 and Smad4

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TGF-β does not affect Taz/Yap localization when Hippo activity is constant

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Taz/Yap loss may alter activity of both Receptor and Smad nuclear retention factors

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The mediator complex regulates Smad nuclear accumulation

Explaining biosimilars and how reverse engineering plays a critical role in their development

INTRODUCTION

Biologicals are protein-based therapeutics consisting of larger and more complex structures than small molecule medicines. As the patents for originator biological therapeutics expire, biosimilar products are licensed for the same indications as their marketed reference biologics across different specialities. Owing to the complex nature of the manufacturing process for a biological therapy compared to conventional chemically synthetized medicines, the development of biosimilars is more complicated and costly than the manufacture of generic small molecules.

AREAS COVERED

The manufacturing process of the originator biologic is in most cases largely unknown to biosimilar developers and therefore reverse engineering through extensive analysis of the originator is a fundamental and critical step for successful biosimilar development. In this review, the authors examine the abbreviated roadmap for biosimilar approval which must be underpinned by the same rigorous standards that apply to all biological medicines. They discuss various aspects of biosimilar manufacturing with a focus on reverse engineering.

EXPERT OPINION

The biosimilar approval pathway places a greater emphasis on preclinical assessments in comparison to the development of originator biologics. Multiple comparative clinical studies add little to the confirmation of the efficacy of the molecule under study whilst adding considerably to the cost and time of bringing a biosimilar into clinical use. A successful demonstration of biosimilarity to the reference product is therefore essential at a structural and functional level but this could not be achieved without well-designed and quality-driven reverse engineering of the originator production process.

A dual-parameter identification approach for data-based predictive modeling of hybrid gene regulatory network-growth kinetics in Pseudomonas putida mt-2

Data integration to model-based description of biological systems incorporating gene dynamics improves the performance of microbial systems. Bioprocess performance, typically predicted using empirical Monod-type models, is essential for a sustainable bioeconomy. To replace empirical models, we updated a hybrid gene regulatory network-growth kinetic model, predicting aromatic pollutants degradation and biomass growth in Pseudomonas putida mt-2. We modeled a complex biological system including extensive information to understand the role of the regulatory elements in toluene biodegradation and biomass growth. The updated model exhibited extra complications such as the existence of oscillations and discontinuities. As parameter estimation of complex biological models remains a key challenge, we used the updated model to present a dual-parameter identification approach (the 'dual approach') combining two independent methodologies. Approach I handled the complexity by incorporation of demonstrated biological knowledge in the model-development process and combination of global sensitivity analysis and optimisation. Approach II complemented Approach I handling multimodality, ill-conditioning and overfitting through regularisation estimation, global optimisation, and identifiability analysis. To systematically quantify the biological system, we used a vast amount of high-quality time-course data. The dual approach resulted in an accurately calibrated kinetic model (NRMSE: 0.17055) efficiently handling the additional model complexity. We tested model validation using three independent experimental data sets, achieving greater predictive power (NRMSE: 0.18776) than the individual approaches (NRMSE I: 0.25322, II: 0.25227) and increasing model robustness. These results demonstrated data-driven predictive modeling potentially leading to bioprocess' model-based control and optimisation.

TopoFilter: a MATLAB package for mechanistic model identification in systems biology

Background

To develop mechanistic dynamic models in systems biology, one often needs to identify all (or minimal) representations of the biological processes that are consistent with experimental data, out of a potentially large set of hypothetical mechanisms. However, a simple enumeration of all alternatives becomes quickly intractable when the number of model parameters grows. Selecting appropriate dynamic models out of a large ensemble of models, taking the uncertainty in our biological knowledge and in the experimental data into account, is therefore a key current problem in systems biology.

Results

The TopoFilter package addresses this problem in a heuristic and automated fashion by implementing the previously described topological filtering method for Bayesian model selection. It includes a core heuristic for searching the space of submodels of a parametrized model, coupled with a sampling-based exploration of the parameter space. Recent developments of the method allow to balance exhaustiveness and speed of the model space search, to efficiently re-sample parameters, to parallelize the search, and to use custom scoring functions. We use a theoretical example to motivate these features and then demonstrate TopoFilter’s applicability for a yeast signaling network with more than 250’000 possible model structures.

Conclusions

TopoFilter is a flexible software framework that makes Bayesian model selection and reduction efficient and scalable to network models of a complexity that represents contemporary problems in, for example, cell signaling. TopoFilter is open-source, available under the GPL-3.0 license at https://gitlab.com/csb.ethz/TopoFilter. It includes installation instructions, a quickstart guide, a description of all package options, and multiple examples.

Benchmarking optimization methods for parameter estimation in large kinetic models

Motivation

Kinetic models contain unknown parameters that are estimated by optimizing the fit to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to surmount these issues, it is difficult to choose the best one for a given problem a priori. A systematic comparison of parameter estimation methods for problems with tens to hundreds of optimization variables is currently missing, and smaller studies provided contradictory findings.

Results

We use a collection of benchmarks to evaluate the performance of two families of optimization methods: (i) multi-starts of deterministic local searches and (ii) stochastic global optimization metaheuristics; the latter may be combined with deterministic local searches, leading to hybrid methods. A fair comparison is ensured through a collaborative evaluation and a consideration of multiple performance metrics. We discuss possible evaluation criteria to assess the trade-off between computational efficiency and robustness. Our results show that, thanks to recent advances in the calculation of parametric sensitivities, a multi-start of gradient-based local methods is often a successful strategy, but a better performance can be obtained with a hybrid metaheuristic. The best performer combines a global scatter search metaheuristic with an interior point local method, provided with gradients estimated with adjoint-based sensitivities. We provide an implementation of this method to render it available to the scientific community.

Availability and implementation

The code to reproduce the results is provided as Supplementary Material and is available at Zenodo https://doi.org/10.5281/zenodo.1304034.

Supplementary information

Supplementary data are available at Bioinformatics online.

Inference-based assessment of parameter identifiability in nonlinear biological models

As systems approaches to the development of biological models become more mature, attention is increasingly focusing on the problem of inferring parameter values within those models from experimental data. However, particularly for nonlinear models, it is not obvious, either from inspection of the model or from the experimental data, that the inverse problem of parameter fitting will have a unique solution, or even a non-unique solution that constrains the parameters to lie within a plausible physiological range. Where parameters cannot be constrained they are termed 'unidentifiable'. We focus on gaining insight into the causes of unidentifiability using inference-based methods, and compare a recently developed measure-theoretic approach to inverse sensitivity analysis to the popular Markov chain Monte Carlo and approximate Bayesian computation techniques for Bayesian inference. All three approaches map the uncertainty in quantities of interest in the output space to the probability of sets of parameters in the input space. The geometry of these sets demonstrates how unidentifiability can be caused by parameter compensation and provides an intuitive approach to inference-based experimental design.

Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models

In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.

Gene Regulatory Network Inference from Single-Cell Data Using Multivariate Information Measures

While single-cell gene expression experiments present new challenges for data processing, the cell-to-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data.

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PIDC infers gene regulatory networks from single-cell transcriptomic data

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Multivariate information measures and context in PIDC improve network inference

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Heterogeneity in single-cell data carries information about gene-gene interactions

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Fast, efficient, open-source software is made freely available

Computational Approaches in Theranostics: Mining and Predicting Cancer Data

The ability to understand the complexity of cancer-related data has been prompted by the applications of (1) computer and data sciences, including data mining, predictive analytics, machine learning, and artificial intelligence, and (2) advances in imaging technology and probe development. Computational modelling and simulation are systematic and cost-effective tools able to identify important temporal/spatial patterns (and relationships), characterize distinct molecular features of cancer states, and address other relevant aspects, including tumor detection and heterogeneity, progression and metastasis, and drug resistance. These approaches have provided invaluable insights for improving the experimental design of therapeutic delivery systems and for increasing the translational value of the results obtained from early and preclinical studies. The big question is: Could cancer theranostics be determined and controlled in silico? This review describes the recent progress in the development of computational models and methods used to facilitate research on the molecular basis of cancer and on the respective diagnosis and optimized treatment, with particular emphasis on the design and optimization of theranostic systems. The current role of computational approaches is providing innovative, incremental, and complementary data-driven solutions for the prediction, simplification, and characterization of cancer and intrinsic mechanisms, and to promote new data-intensive, accurate diagnostics and therapeutics.

Metabolic kinetic modeling provides insight into complex biological questions, but hurdles remain

Metabolic models containing kinetic information can answer unique questions about cellular metabolism that are useful to metabolic engineering. Several kinetic modeling frameworks have recently been developed or improved. In addition, techniques for systematic identification of model structure, including regulatory interactions, have been reported. Each framework has advantages and limitations, which can make it difficult to choose the most appropriate framework. Common limitations are data availability and computational time, especially in large-scale modeling efforts. However, recently developed experimental techniques, parameter identification algorithms, as well as model reduction techniques help alleviate these computational bottlenecks. Opportunities for additional improvements may come from the rich literature in catalysis and chemical networks. In all, kinetic models are positioned to make significant impact in cellular engineering.

Parameter estimation in models of biological oscillators: an automated regularised estimation approach

BACKGROUND

Dynamic modelling is a core element in the systems biology approach to understanding complex biosystems. Here, we consider the problem of parameter estimation in models of biological oscillators described by deterministic nonlinear differential equations. These problems can be extremely challenging due to several common pitfalls: (i) a lack of prior knowledge about parameters (i.e. massive search spaces), (ii) convergence to local optima (due to multimodality of the cost function), (iii) overfitting (fitting the noise instead of the signal) and (iv) a lack of identifiability. As a consequence, the use of standard estimation methods (such as gradient-based local ones) will often result in wrong solutions. Overfitting can be particularly problematic, since it produces very good calibrations, giving the impression of an excellent result. However, overfitted models exhibit poor predictive power. Here, we present a novel automated approach to overcome these pitfalls. Its workflow makes use of two sequential optimisation steps incorporating three key algorithms: (1) sampling strategies to systematically tighten the parameter bounds reducing the search space, (2) efficient global optimisation to avoid convergence to local solutions, (3) an advanced regularisation technique to fight overfitting. In addition, this workflow incorporates tests for structural and practical identifiability.

RESULTS

We successfully evaluate this novel approach considering four difficult case studies regarding the calibration of well-known biological oscillators (Goodwin, FitzHugh-Nagumo, Repressilator and a metabolic oscillator). In contrast, we show how local gradient-based approaches, even if used in multi-start fashion, are unable to avoid the above-mentioned pitfalls.

CONCLUSIONS

Our approach results in more efficient estimations (thanks to the bounding strategy) which are able to escape convergence to local optima (thanks to the global optimisation approach). Further, the use of regularisation allows us to avoid overfitting, resulting in more generalisable calibrated models (i.e. models with greater predictive power).

Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ - (0 - 4 Hz) and α - (8 - 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.