Relaxation dynamics and frequency response of a noisy cell signaling network

Abstract

We investigate the dynamics of cell signaling using an experimentally based Boolean model of the human fibroblast signal transduction network. We determine via systematic numerical simulations the relaxation dynamics of the network in response to a constant set of inputs, both in the absence and in the presence of environmental fluctuations. We then study the network's response to periodically modulated signals, uncovering different types of behaviors for different pairs of driven input and output nodes. The phenomena observed include low-pass, high-pass, and band-pass filtering of the input modulations, among other nontrivial responses, at frequencies around the relaxation frequency of the network. The results reveal that the dynamic response to the external modulation of biologically realistic signaling networks is versatile and robust to noise. © 2010 American Institute of Physics. ͓doi:10.1063/1.3524908͔One of the characteristic features of living cells is their ability to continuously monitor their environment and respond appropriately to extracellular signals, which instruct the cells to take decisions such as proliferating, stopping growth, secreting chemicals, or even committing suicide. This behavior is mediated by signal transduction networks, which are composed of large numbers of interacting proteins. These networks have an input layer consisting of receptor proteins on the cell membrane that activate upon binding extracellular signals and an output layer of enzymes and/or transcription factors whose activation produces physiological changes in the cell. Until recently, the structure of these networks was largely unknown, and as a result, their theoretical study had to assume random connectivity between the nodes (proteins). Nowadays, the rise of high-throughput screening techniques allows the mapping of signaling networks with multiple connected pathways, and thus examining the activity of biologically realistic networks has become feasible. Here, we study the dynamical behavior of a signaling network recently identified in human fibroblasts in terms of a Boolean description in which the network elements are either fully active or inactive. Using extensive and systematic numerical simulations, we quantify the response of the network to all its inputs, and especially the relaxation dynamics to the corresponding stationary attractors, both with and without noise in the input signals. We also examine the case of periodically modulated inputs and characterize the frequency response of the network, which is shown to be extremely diverse.

Information Routing Driven by Background Chatter in a Signaling Network

“…The population activity was estimated from cell realizations for each network. After dismissing a transitory period of 160 iterations [26], the temporal average of the population was calculated.…”

“…Figure 1b shows the behavior of the output node p38 (red) for a given realization of the unstructured sequences for all inputs set at chatter level (for clarity, only the input stress is shown, in blue). All simulations below have been made for a duration of 1600 iterations, well beyond the span of any transient behavior [26] (which has been eliminated by removing the first 160 iterations before data analysis). Notice that both nodes show constant activity at the population level (see bottom plot in Figure 1b).…”

“…The dynamics of this network are implemented as a set of logic rules, an approach that, despite its simplicity, represents a good choice when building a detailed kinetic model is unfeasible. Indeed, Boolean networks have successfully been applied to modeling numerous biological processes, including gene regulation [16]–[19], cellular differentiation [20], [21], developmental patterning [22], and signal transduction [23]–[26], evidencing that sequences of cellular events can be reproduced by this type of discrete dynamic models.…”

A Qualitative Model of the Differentiation Network in Chondrocyte Maturation: A Holistic View of Chondrocyte Hypertrophy

“…Depending on the quantity and the form of information that is available, many modelling formalisms have been introduced suited to perform dynamical studies of networks [19–21]. Many formalisms can be categorized as discrete or continuous, deterministic or stochastic, qualitative or quantitative, numerical or analytical, but hybrids falling into neither category are abound [22–27]. Due to the difficulty in establishing a suitable in vitro model and the technological obstacles in obtaining in vivo data in cartilage biology, detailed kinetic data are scarce, necessitating a qualitative approach.…”

Introduction to Focus Issue: Dynamics in Systems Biology

“…In particular, protein interaction networks can be used to understand the many complex interactions between different proteins in a cell, for example, in how a cell responds to extracellular signals. Rué et al 9 studied the signal transduction network found in human fibroblasts; they use a simple Boolean representation of the network with experimentally motivated parameters to show that the relaxation to an attractor is robust to noise. Koseska and Kurths 10 considered network subunits ͑such as switches and oscillators͒ in synthetic biological systems.…”