Dynamic sensitivity analysis of biological systems

BACKGROUND: A mathematical model to understand, predict, control, or even design a real biological system is a central theme in systems biology. A dynamic biological system is always modeled as a nonlinear ordinary differential equation (ODE) system. How to simulate the dynamic behavior and dynamic parameter sensitivities of systems described by ODEs efficiently and accurately is a critical job. In many practical applications, e.g., the fed-batch fermentation systems, the system admissible input (corresponding to independent variables of the system) can be time-dependent. The main difficulty for investigating the dynamic log gains of these systems is the infinite dimension due to the time-dependent input. The classical dynamic sensitivity analysis does not take into account this case for the dynamic log gains. RESULTS: We present an algorithm with an adaptive step size control that can be used for computing the solution and dynamic sensitivities of an autonomous ODE system simultaneously. Although our algorithm is one of the decouple direct methods in computing dynamic sensitivities of an ODE system, the step size determined by model equations can be used on the computations of the time profile and dynamic sensitivities with moderate accuracy even when sensitivity equations are more stiff than model equations. To show this algorithm can perform the dynamic sensitivity analysis on very stiff ODE systems with moderate accuracy, it is implemented and applied to two sets of chemical reactions: pyrolysis of ethane and oxidation of formaldehyde. The accuracy of this algorithm is demonstrated by comparing the dynamic parameter sensitivities obtained from this new algorithm and from the direct method with Rosenbrock stiff integrator based on the indirect method. The same dynamic sensitivity analysis was performed on an ethanol fed-batch fermentation system with a time-varying feed rate to evaluate the applicability of the algorithm to realistic models with time-dependent admissible input. CONCLUSION: By combining the accuracy we show with the efficiency of being a decouple direct method, our algorithm is an excellent method for computing dynamic parameter sensitivities in stiff problems. We extend the scope of classical dynamic sensitivity analysis to the investigation of dynamic log gains of models with time-dependent admissible input

Narrative-based computational modelling of the Gp130/JAK/STAT signalling pathway.

BACKGROUND: Appropriately formulated quantitative computational models can support researchers in understanding the dynamic behaviour of biological pathways and support hypothesis formulation and selection by "in silico" experimentation. An obstacle to widespread adoption of this approach is the requirement to formulate a biological pathway as machine executable computer code. We have recently proposed a novel, biologically intuitive, narrative-style modelling language for biologists to formulate the pathway which is then automatically translated into an executable format and is, thus, usable for analysis via existing simulation techniques. RESULTS: Here we use a high-level narrative language in designing a computational model of the gp130/JAK/STAT signalling pathway and show that the model reproduces the dynamic behaviour of the pathway derived by biological observation. We then "experiment" on the model by simulation and sensitivity analysis to define those parameters which dominate the dynamic behaviour of the pathway. The model predicts that nuclear compartmentalisation and phosphorylation status of STAT are key determinants of the pathway and that alternative mechanisms of signal attenuation exert their influence on different timescales. CONCLUSION: The described narrative model of the gp130/JAK/STAT pathway represents an interesting case study showing how, by using this approach, researchers can model biological systems without explicitly dealing with formal notations and mathematical expressions (typically used for biochemical modelling), nevertheless being able to obtain simulation and analysis results. We present the model and the sensitivity analysis results we have obtained, that allow us to identify the parameters which are most sensitive to perturbations. The results, which are shown to be in agreement with existing mathematical models of the gp130/JAK/STAT pathway, serve us as a form of validation of the model and of the approach itself

Modeling and Analysis of Signal Transduction Networks

Biological pathways, such as signaling networks, are a key component of biological systems of each living cell. In fact, malfunctions of signaling pathways are linked to a number of diseases, and components of signaling pathways are used as potential drug targets. Elucidating the dynamic behavior of the components of pathways, and their interactions, is one of the key research areas of systems biology. Biological signaling networks are characterized by a large number of components and an even larger number of parameters describing the network. Furthermore, investigations of signaling networks are characterized by large uncertainties of the network as well as limited availability of data due to expensive and time-consuming experiments. As such, techniques derived from systems analysis, e.g., sensitivity analysis, experimental design, and parameter estimation, are important tools for elucidating the mechanisms involved in signaling networks. This Special Issue contains papers that investigate a variety of different signaling networks via established, as well as newly developed modeling and analysis techniques

Label-Free Optical Single-Molecule Micro- and Nanosensors

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this recordLabel-free optical sensor systems have emerged that exhibit extraordinary sensitivity for detecting physical, chemical, and biological entities at the micro/nanoscale. Particularly exciting is the detection and analysis of molecules, on miniature optical devices that have many possible applications in health, environment, and security. These micro- and nanosensors have now reached a sensitivity level that allows for the detection and analysis of even single molecules. Their small size enables an exceedingly high sensitivity, and the application of quantum optical measurement techniques can allow the classical limits of detection to be approached or surpassed. The new class of label-free micro- and nanosensors allows dynamic processes at the single-molecule level to be observed directly with light. By virtue of their small interaction length, these micro- and nanosensors probe light–matter interactions over a dynamic range often inaccessible by other optical techniques. For researchers entering this rapidly advancing field of single-molecule micro- and nanosensors, there is an urgent need for a timely review that covers the most recent developments and that identifies the most exciting opportunities. The focus here is to provide a summary of the recent techniques that have either demonstrated label-free single-molecule detection or claim single-molecule sensitivity.Living Systems Institute, University of Exete

Toward quantitative phosphotyrosine profiling in vivo

Tyrosine phosphorylation is a dynamic reversible post-translational modification that regulates many aspects of cell biology. To understand how this modification controls biological function, it is necessary to not only identify the specific sites of phosphorylation, but also to quantify how phosphorylation levels on these sites may be altered under specific physiological conditions. Due to its sensitivity and accuracy, mass spectrometry (MS) has widely been applied to the identification and characterization of phosphotyrosine signaling across biological systems. In this review we highlight the advances in both MS and phosphotyrosine enrichment methods that have been developed to enable the identification of low level tyrosine phosphorylation events. Computational and manual approaches to ensure confident identification of phosphopeptide sequence and determination of phosphorylation site localization are discussed along with methods that have been applied to the relative quantification of large numbers of phosphorylation sites. Finally, we provide an overview of the challenges ahead as we extend these technologies to the characterization of tyrosine phosphorylation signaling in vivo. With these latest developments in analytical and computational techniques, it is now possible to derive biological insight from quantitative MS-based analysis of signaling networks in vitro and in vivo. Application of these approaches to a wide variety of biological systems will define how signal transduction regulates cellular physiology in health and disease

Super-multiplex vibrational imaging

The ability to visualize directly a large number of distinct molecular species inside cells is increasingly essential for understanding complex systems and processes. Even though existing methods have successfully been used to explore structure–function relationships in nervous systems, to profile RNA in situ, to reveal the heterogeneity of tumour microenvironments and to study dynamic macromolecular assembly, it remains challenging to image many species with high selectivity and sensitivity under biological conditions. For instance, fluorescence microscopy faces a ‘colour barrier’, owing to the intrinsically broad (about 1,500 inverse centimetres) and featureless nature of fluorescence spectra that limits the number of resolvable colours to two to five (or seven to nine if using complicated instrumentation and analysis). Spontaneous Raman microscopy probes vibrational transitions with much narrower resonances (peak width of about 10 inverse centimetres) and so does not suffer from this problem, but weak signals make many bio-imaging applications impossible. Although surface-enhanced Raman scattering offers high sensitivity and multiplicity, it cannot be readily used to image specific molecular targets quantitatively inside live cells. Here we use stimulated Raman scattering under electronic pre-resonance conditions to image target molecules inside living cells with very high vibrational selectivity and sensitivity (down to 250 nanomolar with a time constant of 1 millisecond). We create a palette of triple-bond-conjugated near-infrared dyes that each displays a single peak in the cell-silent Raman spectral window; when combined with available fluorescent probes, this palette provides 24 resolvable colours, with the potential for further expansion. Proof-of-principle experiments on neuronal co-cultures and brain tissues reveal cell-type-dependent heterogeneities in DNA and protein metabolism under physiological and pathological conditions, underscoring the potential of this 24-colour (super-multiplex) optical imaging approach for elucidating intricate interactions in complex biological systems

Insights into the behaviour of systems biology models from dynamic sensitivity and identifiability analysis: a case study of an NF-kB signaling pathway

Mathematical modelling offers a variety of useful techniques to help in understanding the intrinsic behaviour of complex signal transduction networks. From the system engineering point of view, the dynamics of metabolic and signal transduction models can always be described by nonlinear ordinary differential equations (ODEs) following mass balance principles. Based on the state-space formulation, many methods from the area of automatic control can conveniently be applied to the modelling, analysis and design of cell networks. In the present study, dynamic sensitivity analysis is performed on a model of the IB-NF-B signal pathway system. Univariate analysis of the Euclidean-form overall sensitivities shows that only 8 out of the 64 parameters in the model have major influence on the nuclear NF-B oscillations. The sensitivity matrix is then used to address correlation analysis, identifiability assessment and measurement set selection within the framework of least squares estimation and multivariate analysis. It is shown that certain pairs of parameters are exactly or highly correlated to each other in terms of their effects on the measured variables. The experimental design strategy provides guidance on which proteins should best be considered for measurement such that the unknown parameters can be estimated with the best statistical precision. The whole analysis scheme we describe provides efficient parameter estimation techniques for complex cell networks

Integrated signaling pathway and gene expression regulatory model to dissect dynamics of <em>Escherichia coli </em>challenged mammary epithelial cells

AbstractCells transform external stimuli, through the activation of signaling pathways, which in turn activate gene regulatory networks, in gene expression. As more omics data are generated from experiments, eliciting the integrated relationship between the external stimuli, the signaling process in the cell and the subsequent gene expression is a major challenge in systems biology. The complex system of non-linear dynamic protein interactions in signaling pathways and gene networks regulates gene expression.The complexity and non-linear aspects have resulted in the study of the signaling pathway or the gene network regulation in isolation. However, this limits the analysis of the interaction between the two components and the identification of the source of the mechanism differentiating the gene expression profiles. Here, we present a study of a model of the combined signaling pathway and gene network to highlight the importance of integrated modeling.Based on the experimental findings we developed a compartmental model and conducted several simulation experiments. The model simulates the mRNA expression of three different cytokines (RANTES, IL8 and TNFα) regulated by the transcription factor NFκB in mammary epithelial cells challenged with E. coli. The analysis of the gene network regulation identifies a lack of robustness and therefore sensitivity for the transcription factor regulation. However, analysis of the integrated signaling and gene network regulation model reveals distinctly different underlying mechanisms in the signaling pathway responsible for the variation between the three cytokine's mRNA expression levels. Our key findings reveal the importance of integrating the signaling pathway and gene expression dynamics in modeling. Modeling infers valid research questions which need to be verified experimentally and can assist in the design of future biological experiments

Identification of complex biological network classes using extended correlation analysis

Modeling and analysis of complex biological networks necessitates suitable handling of data on a parallel scale. Using the IkB-NF-kB pathway model and a basis of sensitivity analysis, analytic methods are presented, extending correlation from the network kinetic reaction rates to that of the rate reactions. Alignment of correlated processed components, vastly outperforming correlation of the data source, advanced sets of biological classes possessing similar network activities. Additional construction generated a naturally structured, cardinally based system for component-specific investigation. The computationally driven procedures are described, with results demonstrating viability as mechanisms useful for fundamental oscillatory network activity investigation