B Cell Activation Triggered by the Formation of the Small Receptor Cluster: A Computational Study

We proposed a spatially extended model of early events of B cell receptors (BCR) activation, which is based on mutual kinase-receptor interactions that are characteristic for the immune receptors and the Src family kinases. These interactions lead to the positive feedback which, together with two nonlinearities resulting from the double phosphorylation of receptors and Michaelis-Menten dephosphorylation kinetics, are responsible for the system bistability. We demonstrated that B cell can be activated by a formation of a tiny cluster of receptors or displacement of the nucleus. The receptors and Src kinases are activated, first locally, in the locus of the receptor cluster or the region where the cytoplasm is the thinnest. Then the traveling wave of activation propagates until activity spreads over the whole cell membrane. In the models in which we assume that the kinases are free to diffuse in the cytoplasm, we found that the fraction of aggregated receptors, capable to initiate B cell activation decreases with the decreasing thickness of cytoplasm and decreasing kinase diffusion. When kinases are restricted to the cell membrane - which is the case for most of the Src family kinases - even a cluster consisting of a tiny fraction of total receptors becomes activatory. Interestingly, the system remains insensitive to the modest changes of total receptor level. The model provides a plausible mechanism of B cells activation due to the formation of small receptors clusters collocalized by binding of polyvalent antigens or arising during the immune synapse formation

Model simplification of signal transduction pathway networks via a hybrid inference strategy

A full-scale mathematical model of cellular networks normally involves a large number of variables and parameters. How to effectively develop manageable and reliable models is crucial for effective computation, analysis and design of such systems. The aim of model simplification is to eliminate parts of a model that are unimportant for the properties of interest. In this work, a model reduction strategy via hybrid inference is proposed for signal pathway networks. It integrates multiple techniques including conservation analysis, local sensitivity analysis, principal component analysis and flux analysis to identify the reactions and variables that can be considered to be eliminated from the full-scale model. Using an I·B-NF-·B signalling pathway model as an example, simulation analysis demonstrates that the simplified model quantitatively predicts the dynamic behaviours of the network

Coronavirus: Scientific insights and societal aspects

In December 2019, the first case of infection with a new virus COVID-19 (SARS-CoV-2), named coronavirus, was reported in the city of Wuhan, China. At that time, almost nobody paid any attention to it. The new pathogen, however, fast proved to be extremely infectious and dangerous, resulting in about 3–5% mortality. Over the few months that followed, coronavirus has spread over entire world. At the end of March, the total number of infections is fast approaching the psychological threshold of one million, resulting so far in tens of thousands of deaths. Due to the high number of lives already lost and the virus high potential for further spread, and due to its huge overall impact on the economies and societies, it is widely admitted that coronavirus poses the biggest challenge to the humanity after the second World war. The COVID-19 epidemic is provoking numerous questions at all levels. It also shows that modern society is extremely vulnerable and unprepared to such events. A wide scientific and public discussion becomes urgent. Some possible directions of this discussion are suggested in this article

Dynamical robustness of biological networks with hierarchical distribution of time scales

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First, we obtain the following result for linear networks: for large multiscale systems with hierarchical distribution of time scales the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. We argue that similar phenomena are valid in the nonlinear case as well. As a numerical illustration we use a model of signalling network that can be applied to important transcription factors such as NFkB

Spiky oscillations in NF-kB signalling

The NF-kB signalling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kB transcription factor. How the cell uses the oscillations to differentiate input conditions and send specific signals to downstream genes is an open problem. We shed light on this issue by examining the small core network driving the oscillations, which, we show, is designed to produce periodic spikes in nuclear NF-kB concentration. The oscillations can be used to regulate downstream genes in a variety of ways. In particular, we show that genes to whose operator sites NF-kB binds and dissociates fast can respond very sensitively to changes in the input signal, with effective Hill coefficients in excess of 20.Comment: 11 pages, 13 figure

A family tree of Markov models in systems biology

Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the systems biology literature. As part of this review, we present a novel derivation of the differential Chapman-Kolmogorov equation for a general multidimensional Markov process made up of both continuous and jump processes. We start with the definition of a time-derivative for a probability density but place no restrictions on the probability distribution, in particular, we do not assume it to be confined to a region that has a surface (on which the probability is zero). In our derivation, the master equation gives the jump part of the Markov process while the Fokker-Planck equation gives the continuous part. We thereby sketch a {}``family tree'' for stochastic models in systems biology, providing explicit derivations of their formal relationship and clarifying assumptions involved.Comment: 18 pages, 2 figure

Computation and measurement of cell decision making errors using single cell data

Author summary Cell continuously receives signals from the surrounding environment and is supposed to make correct decisions, i.e., respond properly to various signals and initiate certain cellular functions. Modeling and quantification of decision making processes in a cell have emerged as important areas of research in recent years. Due to signal transduction noise, cells respond differently to similar inputs, which may result in incorrect cell decisions. Here we develop a novel method for characterization of decision making processes in cells, using statistical signal processing and decision theory concepts. To demonstrate the utility of the method, we apply it to an important signaling pathway that regulates molecules which play key roles in cell survival. Our method reveals that cells can make two types of incorrect decisions, namely, false alarm and miss events. We measure the likelihood of these decisions using single cell experimental data, and demonstrate how these incorrect decisions are related to the signal transduction noise or absence of certain molecular functions. Using our method, decision making errors in other molecular systems can be modeled. Such models are useful for understanding and developing treatments for pathological processes such as inflammation, various cancers and autoimmune diseases

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