Mathematical modelling of the MAP kinase pathway using proteomic datasets

Identifying Key Regulatory Genes in Drug Resistance Acquisition: Modeling Pseudotime Trajectories of Breast Cancer Single-Cell Transcriptome

Single-cell RNA-sequencing (scRNA-seq) technology has provided significant insights into cancer drug resistance at the single-cell level. However, understanding dynamic cell transitions at the molecular systems level remains limited, requiring a systems biology approach. We present an approach that combines mathematical modeling with a pseudotime analysis using time-series scRNA-seq data obtained from the breast cancer cell line MCF-7 treated with tamoxifen. Our single-cell analysis identified five distinct subpopulations, including tamoxifen-sensitive and -resistant groups. Using a single-gene mathematical model, we discovered approximately 560-680 genes out of 6000 exhibiting multistable expression states in each subpopulation, including key estrogen-receptor-positive breast cancer cell survival genes, such as RPS6KB1. A bifurcation analysis elucidated their regulatory mechanisms, and we mapped these genes into a molecular network associated with cell survival and metastasis-related pathways. Our modeling approach comprehensively identifies key regulatory genes for drug resistance acquisition, enhancing our understanding of potential drug targets in breast cancer.

Inference of Molecular Regulatory Systems Using Statistical Path-Consistency Algorithm

One of the key challenges in systems biology and molecular sciences is how to infer regulatory relationships between genes and proteins using high-throughout omics datasets. Although a wide range of methods have been designed to reverse engineer the regulatory networks, recent studies show that the inferred network may depend on the variable order in the dataset. In this work, we develop a new algorithm, called the statistical path-consistency algorithm (SPCA), to solve the problem of the dependence of variable order. This method generates a number of different variable orders using random samples, and then infers a network by using the path-consistent algorithm based on each variable order. We propose measures to determine the edge weights using the corresponding edge weights in the inferred networks, and choose the edges with the largest weights as the putative regulations between genes or proteins. The developed method is rigorously assessed by the six benchmark networks in DREAM challenges, the mitogen-activated protein (MAP) kinase pathway, and a cancer-specific gene regulatory network. The inferred networks are compared with those obtained by using two up-to-date inference methods. The accuracy of the inferred networks shows that the developed method is effective for discovering molecular regulatory systems.

From sequence to information

Today massive amounts of sequenced metagenomic and metatranscriptomic data from different ecological niches and environmental locations are available. Scientific progress depends critically on methods that allow extracting useful information from the various types of sequence data. Here, we will first discuss types of information contained in the various flavours of biological sequence data, and how this information can be interpreted to increase our scientific knowledge and understanding. We argue that a mechanistic understanding of biological systems analysed from different perspectives is required to consistently interpret experimental observations, and that this understanding is greatly facilitated by the generation and analysis of dynamic mathematical models. We conclude that, in order to construct mathematical models and to test mechanistic hypotheses, time-series data are of critical importance. We review diverse techniques to analyse time-series data and discuss various approaches by which time-series of biological sequence data have been successfully used to derive and test mechanistic hypotheses. Analysing the bottlenecks of current strategies in the extraction of knowledge and understanding from data, we conclude that combined experimental and theoretical efforts should be implemented as early as possible during the planning phase of individual experiments and scientific research projects.

This article is part of the theme issue ‘Integrative research perspectives on marine conservation’.

Inference of Model Parameters Using Particle Filter Algorithm and Copula Distributions

It is widely accepted that experimental data often include noise because of the limitation in experimental conditions. In addition, biological systems inside the cells also contain uncertainty due to small copy molecular numbers. To address this issue, it was proposed that experimental data include both real system state and a noise term whose variance is a constant. An additional assumption is that the observation data of different variables are independent to each other. However, recent research works showed that noise in experimental data might not be the white noise. In addition, the observed values of different variables may be correlated. This work designs a new algorithm to infer the unknown model parameters based on noisy data. The innovation of this method includes a new noise model, in which the variance of noise is dependent on the system state, and a copula particle filter algorithm that uses the copula density functions to describe the dependence of different variables. The proposed algorithm is evaluated by using two deterministic models for gene networks and a stochastic model. Numerical results show that the accuracy of our proposed method is better than that of the widely used Liu-West filter and copula particle filter algorithms.

Silver nanoparticles conjugated with Neurotrophin 3 upregulate myelin gene transcription pathway

Mathematical modeling is the art of converting problems from the biological area into handy mathematical formulations whose theoretical and numerical analysis provides understandings about the directions and solutions to the particular problem. Recently, the combination therapy treatments have been revealed exceptionally fruitful by using mathematical modeling technique. The human nervous system is composed of axons, covered by the myelin sheath. Axons carry signals and promote myelin development. The abnormalities in myelination formation due to mutations in myelin gene result in memory disorders and impaired cognitive activities. The ERBb gene family is responsible for causing abnormalities in myelin gene. Using this knowledge, the pathway of mutated myelin gene was retrieved and its model was developed. Modeling and simulation analysis was performed to determine the level of expression of several genes. The Neurotrophin 3 ligand-coated with silver nanoparticle was induced in the model to normalize the transcription of myelin gene. It was observed that the myelin gene expression level increases from 0 after two days of NT3 induction and reaches to the maximum level on the 10th day of drug induction along with an increase in ERBb expression. This research work can be used in the future as a part of drug discovery and formulation.

Effect of STAT3 inhibitor in chronic myeloid leukemia associated signaling pathway: a mathematical modeling, simulation and systems biology study

Chronic myeloid leukemia (CML) is a hematopoietic stem-cell disorder which proliferates due to abnormal growth of basophil cells. Several proangiogenic molecules have been reported to be associated in CML progression, including the hepatocyte growth factor (HGF). However, detail mechanism about the cellular distribution and function of HGF in CML is yet to be revealed. The proliferation of hematopoietic cells are regulated by some of the growth factors like interleukin 3 (IL-3), IL-6, erythropoietin, thrombopoietin, etc. In this study IL-6 pathways have been taken into consideration which induces JAK/STAT and MAPK pathways to decipher the CML progression stages. An attempt has been made to model these pathways with the help of ordinary differential equations (ODEs) and estimating unknown parameters through fminsearch optimization algorithm. Some of the specific component like STAT3, of the pathway has been analyzed in detail and their role in CML progression has been elucidated. The roles of STAT3 inhibitors into the treatment of CML have been thoroughly studied and optimum concentration of the inhibitors have been predicted.

Bioinformatics in protein kinases regulatory network and drug discovery

Protein kinases have been implicated in a number of diseases, where kinases participate many aspects that control cell growth, movement and death. The deregulated kinase activities and the knowledge of these disorders are of great clinical interest of drug discovery. The most critical issue is the development of safe and efficient disease diagnosis and treatment for less cost and in less time. It is critical to develop innovative approaches that aim at the root cause of a disease, not just its symptoms. Bioinformatics including genetic, genomic, mathematics and computational technologies, has become the most promising option for effective drug discovery, and has showed its potential in early stage of drug-target identification and target validation. It is essential that these aspects are understood and integrated into new methods used in drug discovery for diseases arisen from deregulated kinase activity. This article reviews bioinformatics techniques for protein kinase data management and analysis, kinase pathways and drug targets and describes their potential application in pharma ceutical industry.

From proteomes to complexomes in the era of systems biology

Protein complexes carry out almost the entire signaling and functional processes in the cell. The protein complex complement of a cell, and its network of complex-complex interactions, is referred to here as the complexome. Computational methods to predict protein complexes from proteomics data, resulting in network representations of complexomes, have recently being developed. In addition, key advances have been made toward understanding the network and structural organization of complexomes. We review these bioinformatics advances, and their discovery-potential, as well as the merits of integrating proteomics data with emerging methods in systems biology to study protein complex signaling. It is envisioned that improved integration of proteomics and systems biology, incorporating the dynamics of protein complexes in space and time, may lead to more predictive models of cell signaling networks for effective modulation.

Toward a systems-level view of dynamic phosphorylation networks

To better understand how cells sense and respond to their environment, it is important to understand the organization and regulation of the phosphorylation networks that underlie most cellular signal transduction pathways. These networks, which are composed of protein kinases, protein phosphatases and their respective cellular targets, are highly dynamic. Importantly, to achieve signaling specificity, phosphorylation networks must be regulated at several levels, including at the level of protein expression, substrate recognition, and spatiotemporal modulation of enzymatic activity. Here, we briefly summarize some of the traditional methods used to study the phosphorylation status of cellular proteins before focusing our attention on several recent technological advances, such as protein microarrays, quantitative mass spectrometry, and genetically-targetable fluorescent biosensors, that are offering new insights into the organization and regulation of cellular phosphorylation networks. Together, these approaches promise to lead to a systems-level view of dynamic phosphorylation networks.

A continuous optimization approach for inferring parameters in mathematical models of regulatory networks

BACKGROUND

The advances of systems biology have raised a large number of sophisticated mathematical models for describing the dynamic property of complex biological systems. One of the major steps in developing mathematical models is to estimate unknown parameters of the model based on experimentally measured quantities. However, experimental conditions limit the amount of data that is available for mathematical modelling. The number of unknown parameters in mathematical models may be larger than the number of observation data. The imbalance between the number of experimental data and number of unknown parameters makes reverse-engineering problems particularly challenging.

RESULTS

To address the issue of inadequate experimental data, we propose a continuous optimization approach for making reliable inference of model parameters. This approach first uses a spline interpolation to generate continuous functions of system dynamics as well as the first and second order derivatives of continuous functions. The expanded dataset is the basis to infer unknown model parameters using various continuous optimization criteria, including the error of simulation only, error of both simulation and the first derivative, or error of simulation as well as the first and second derivatives. We use three case studies to demonstrate the accuracy and reliability of the proposed new approach. Compared with the corresponding discrete criteria using experimental data at the measurement time points only, numerical results of the ERK kinase activation module show that the continuous absolute-error criteria using both function and high order derivatives generate estimates with better accuracy. This result is also supported by the second and third case studies for the G1/S transition network and the MAP kinase pathway, respectively. This suggests that the continuous absolute-error criteria lead to more accurate estimates than the corresponding discrete criteria. We also study the robustness property of these three models to examine the reliability of estimates. Simulation results show that the models with estimated parameters using continuous fitness functions have better robustness properties than those using the corresponding discrete fitness functions.

CONCLUSIONS

The inference studies and robustness analysis suggest that the proposed continuous optimization criteria are effective and robust for estimating unknown parameters in mathematical models.

Conserved residues at the MAPKs binding interfaces that regulate transcriptional machinery

Signaling through c-Raf downstream pathways is the crucial subject of extensive studies because over expressed or mutated genes in this pathway lead to a variety of human cancers. On the basis of cellular localization, this pathway has been sub-divided into two cascades. The first RAF1-MEK1-ERK2 cascade which remains in the cytosol, whereas the second MEK1-ERK2-RSKs transduces into the nucleus and regulates the transactivation function. But how a few amino acids critically regulate the transcriptional function remains unclear. In this paper, we have performed in silico studies to unravel how atomic complexities at the MEK1-ERK2-RSKs pathways intercedes different functional responses. The secondary structure of the ERK, RSKs have been modeled using Jpred3, PSI-PHRED, protein modeler, and Integrated sequence analyzer from Discovery Studio software. Peptides of RSKs isozymes (RSK1/2/3/4) were built and docked on ERK2 structure using ZDOCK module. The hydropathy index for the RSKs molecules was determined using the KYTE-DOOLITTLE plot. The simulations of complex molecules were carried out using a CHARMM force field. The protein-protein interactions (PPIs) in different cascade of MAP kinase (MAPK) have been shown to be similar to those predicted in vivo. PPIs elucidate that the amino acids located at the conserved domains of MAPK pathways are responsible for transactivation functions.

Modelling pathways to Rubisco degradation: a structural equation network modelling approach

'Omics analysis (transcriptomics, proteomics) quantifies changes in gene/protein expression, providing a snapshot of changes in biochemical pathways over time. Although tools such as modelling that are needed to investigate the relationships between genes/proteins already exist, they are rarely utilised. We consider the potential for using Structural Equation Modelling to investigate protein-protein interactions in a proposed Rubisco protein degradation pathway using previously published data from 2D electrophoresis and mass spectrometry proteome analysis. These informed the development of a prior model that hypothesised a pathway of Rubisco Large Subunit and Small Subunit degradation, producing both primary and secondary degradation products. While some of the putative pathways were confirmed by the modelling approach, the model also demonstrated features that had not been originally hypothesised. We used Bayesian analysis based on Markov Chain Monte Carlo simulation to generate output statistics suggesting that the model had replicated the variation in the observed data due to protein-protein interactions. This study represents an early step in the development of approaches that seek to enable the full utilisation of information regarding the dynamics of biochemical pathways contained within proteomics data. As these approaches gain attention, they will guide the design and conduct of experiments that enable 'Omics modelling to become a common place practice within molecular biology.

Modeling of the MAPK machinery activation in response to various abiotic and biotic stresses in plants by a system biology approach

Mitogen-Activated Protein Kinases (MAPKs) cascade plays an important role in regulating plant growth and development, generating cellular responses to the extracellular stimuli. MAPKs cascade mainly consist of three sub-families i.e. mitogen-activated protein kinase kinase kinase (MAPKKK), mitogen-activated protein kinase kinase (MAPKK) and mitogen activated protein kinase (MAPK), several cascades of which are activated by various abiotic and biotic stresses. In this work we have modeled the holistic molecular mechanisms essential to MAPKs activation in response to several abiotic and biotic stresses through a system biology approach and performed its simulation studies. As extent of abiotic and biotic stresses goes on increasing, the process of cell division, cell growth and cell differentiation slow down in time dependent manner. The models developed depict the combinatorial and multicomponent signaling triggered in response to several abiotic and biotic factors. These models can be used to predict behavior of cells in event of various stresses depending on their time and exposure through activation of complex signaling cascades.