Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determing unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiability analysis, practical identifiability analysis and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV, influenza and hepatitis viruses are given to illustrate how to apply these identifiability analysis methods in practice.

Seasonal and pandemic influenza A virus (IAV) continues to be a public health threat. However, we lack a detailed and quantitative understanding of the immune response kinetics to IAV infection and which biological parameters most strongly influence infection outcomes. To address these issues, we use modeling approaches combined with experimental data to quantitatively investigate the innate and adaptive immune responses to primary IAV infection. Mathematical models were developed to describe the dynamic interactions between target (epithelial) cells, influenza virus, cytotoxic T lymphocytes (CTLs), and virus-specific IgG and IgM. IAV and immune kinetic parameters were estimated by fitting models to a large data set obtained from primary H3N2 IAV infection of 340 mice. Prior to a detectable virus-specific immune response (before day 5), the estimated half-life of infected epithelial cells is ϳ1.2 days, and the half-life of free infectious IAV is ϳ4 h. During the adaptive immune response (after day 5), the average half-life of infected epithelial cells is ϳ0.5 days, and the average half-life of free infectious virus is ϳ1.8 min. During the adaptive phase, model fitting confirms that CD8 ؉ CTLs are crucial for limiting infected cells, while virus-specific IgM regulates free IAV levels. This may imply that CD4 T cells and class-switched IgG antibodies are more relevant for generating IAV-specific memory and preventing future infection via a more rapid secondary immune response. Also, simulation studies were performed to understand the relative contributions of biological parameters to IAV clearance. This study provides a basis to better understand and predict influenza virus immunity.

Transcriptional and post-transcriptional regulation of gene expression is of fundamental importance to numerous biological processes. Nowadays, an increasing amount of gene regulatory relationships have been documented in various databases and literature. However, to more efficiently exploit such knowledge for biomedical research and applications, it is necessary to construct a genome-wide regulatory network database to integrate the information on gene regulatory relationships that are widely scattered in many different places. Therefore, in this work, we build a knowledge-based database, named ‘RegNetwork’, of gene regulatory networks for human and mouse by collecting and integrating the documented regulatory interactions among transcription factors (TFs), microRNAs (miRNAs) and target genes from 25 selected databases. Moreover, we also inferred and incorporated potential regulatory relationships based on transcription factor binding site (TFBS) motifs into RegNetwork. As a result, RegNetwork contains a comprehensive set of experimentally observed or predicted transcriptional and post-transcriptional regulatory relationships, and the database framework is flexibly designed for potential extensions to include gene regulatory networks for other organisms in the future. Based on RegNetwork, we characterized the statistical and topological properties of genome-wide regulatory networks for human and mouse, we also extracted and interpreted simple yet important network motifs that involve the interplays between TF-miRNA and their targets. In summary, RegNetwork provides an integrated resource on the prior information for gene regulatory relationships, and it enables us to further investigate context-specific transcriptional and post-transcriptional regulatory interactions based on domain-specific experimental data.Database URL: http://www.regnetworkweb.org

The cellular immune response to primary influenza virus infection is complex, involving multiple cell types and anatomical compartments, and is difficult to measure directly. Here we develop a two-compartment model that quantifies the interplay between viral replication and adaptive immunity. The fidelity of the model is demonstrated by accurately confirming the role of CD4 help for antibody persistence and the consequences of immune depletion experiments. The model predicts that drugs to limit viral infection and/or production must be administered within 2 days of infection, with a benefit of combination therapy when administered early, and cytotoxic CD8 T cells in the lung are as effective for viral clearance as neutralizing antibodies when present at the time of challenge. The model can be used to investigate explicit biological scenarios and generate experimentally testable hypotheses. For example, when the adaptive response depends on cellular immune cell priming, regulation of antigen presentation has greater influence on the kinetics of viral clearance than the efficiency of virus neutralization or cellular cytotoxicity. These findings suggest that the modulation of antigen presentation or the number of lung resident cytotoxic cells and the combination drug intervention are strategies to combat highly virulent influenza viruses. We further compared alternative model structures, for example, B-cell activation directly by the virus versus that through professional antigen-presenting cells or dendritic cell licensing of CD8 T cells.

Motor imagery classification is an important topic in brain-computer interface (BCI) research that enables the recognition of a subject's intension to, e.g., implement prosthesis control. The brain dynamics of motor imagery are usually measured by electroencephalography (EEG) as nonstationary time series of low signal-to-noise ratio. Although a variety of methods have been previously developed to learn EEG signal features, the deep learning idea has rarely been explored to generate new representation of EEG features and achieve further performance improvement for motor imagery classification. In this study, a novel deep learning scheme based on restricted Boltzmann machine (RBM) is proposed. Specifically, frequency domain representations of EEG signals obtained via fast Fourier transform (FFT) and wavelet package decomposition (WPD) are obtained to train three RBMs. These RBMs are then stacked up with an extra output layer to form a four-layer neural network, which is named the frequential deep belief network (FDBN). The output layer employs the softmax regression to accomplish the classification task. Also, the conjugate gradient method and backpropagation are used to fine tune the FDBN. Extensive and systematic experiments have been performed on public benchmark datasets, and the results show that the performance improvement of FDBN over other selected state-of-the-art methods is statistically significant. Also, several findings that may be of significant interest to the BCI community are presented in this article.

Coronavirus disease 2019 (COVID-19), an infectious disease caused by the infection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is spreading and causing the global coronavirus pandemic. The viral dynamics of SARS-CoV-2 infection have not been quantitatively investigated. In this paper, we use mathematical models to study the pathogenic features of SARS-CoV-2 infection by examining the interaction between the virus, cells and immune responses. Models are fit to the data of SARS-CoV-2 infection in patients and non-human primates. Data fitting and numerical simulation show that viral dynamics of SARS-CoV-2 infection have a few distinct stages. In the initial stage, viral load increases rapidly and reaches the peak, followed by a plateau phase possibly generated by lymphocytes as a secondary target of infection. In the last stage, viral load declines due to the emergence of adaptive immune responses. When the initiation of seroconversion is late or slow, the model predicts viral rebound and prolonged viral persistence, consistent with the observation in non-human primates. Using the model we also evaluate the effect of several potential therapeutic interventions for SARS-CoV-2 infection. Model simulation shows that anti-inflammatory treatments or antiviral drugs combined with interferon are effective in reducing the duration of the viral plateau phase and diminishing the time to recovery. These results provide insights for understanding the infection dynamics and might help develop treatment strategies against COVID-19.

Background Molecular descriptors and fingerprints have been routinely used in QSAR/SAR analysis, virtual drug screening, compound search/ranking, drug ADME/T prediction and other drug discovery processes. Since the calculation of such quantitative representations of molecules may require substantial computational skills and efforts, several tools have been previously developed to make an attempt to ease the process. However, there are still several hurdles for users to overcome to fully harness the power of these tools. First, most of the tools are distributed as standalone software or packages that require necessary configuration or programming efforts of users. Second, many of the tools can only calculate a subset of molecular descriptors, and the results from multiple tools need to be manually merged to generate a comprehensive set of descriptors. Third, some packages only provide application programming interfaces and are implemented in different computer languages, which pose additional challenges to the integration of these tools.Results A freely available web-based platform, named ChemDes, is developed in this study. It integrates multiple state-of-the-art packages (i.e., Pybel, CDK, RDKit, BlueDesc, Chemopy, PaDEL and jCompoundMapper) for computing molecular descriptors and fingerprints. ChemDes not only provides friendly web interfaces to relieve users from burdensome programming work, but also offers three useful and convenient auxiliary tools for format converting, MOPAC optimization and fingerprint similarity calculation. Currently, ChemDes has the capability of computing 3679 molecular descriptors and 59 types of molecular fingerprints.ConclusionChemDes provides users an integrated and friendly tool to calculate various molecular descriptors and fingerprints. It is freely available at http://www.scbdd.com/chemdes. The source code of the project is also available as a supplementary file.Graphical abstract:An overview of ChemDes. A platform for computing various molecular descriptors and fingerprints

We use a technique from engineering (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330-336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005) to investigate the algebraic identifiability of a popular three-dimensional HIV/AIDS dynamic model containing six unknown parameters. We find that not all six parameters in the model can be identified if only the viral load is measured, instead only four parameters and the product of two parameters (N and lambda) are identifiable. We introduce the concepts of an identification function and an identification equation and propose the multiple time point (MTP) method to form the identification function which is an alternative to the previously developed higher-order derivative (HOD) method (Xia and Moog, in IEEE Trans. Autom. Contr. 48(2):330-336, 2003; Jeffrey and Xia, in Tan, W.Y., Wu, H. (Eds.), Deterministic and Stochastic Models of AIDS Epidemics and HIV Infections with Intervention, 2005). We show that the newly proposed MTP method has advantages over the HOD method in the practical implementation. We also discuss the effect of the initial values of state variables on the identifiability of unknown parameters. We conclude that the initial values of output (observable) variables are part of the data that can be used to estimate the unknown parameters, but the identifiability of unknown parameters is not affected by these initial values if the exact initial values are measured with error. These noisy initial values only increase the estimation error of the unknown parameters. However, having the initial values of the latent (unobservable) state variables exactly known may help to identify more parameters. In order to validate the identifiability results, simulation studies are performed to estimate the unknown parameters and initial values from simulated noisy data. We also apply the proposed methods to a clinical data set to estimate HIV dynamic parameters. Although we have developed the identifiability methods based on an HIV dynamic model, the proposed methodologies are generally applicable to any ordinary differential equation systems.