Kolmogorov complexity of epithelial pattern formation: The role of regulatory network configuration

The tissues of multicellular organisms are made of differentiated cells arranged in organized patterns. This organization emerges during development from the coupling of dynamic intra- and intercellular regulatory networks. This work applies the methods of information theory to understand how regulatory network structure both within and between cells relates to the complexity of spatial patterns that emerge as a consequence of network operation. A computational study was performed in which undifferentiated cells were arranged in a two dimensional lattice, with gene expression in each cell regulated by identical intracellular randomly generated Boolean networks. Cell–cell contact signalling between embryonic cells is modeled as coupling among intracellular networks so that gene expression in one cell can influence the expression of genes in adjacent cells. In this system, the initially identical cells differentiate and form patterns of different cell types. The complexity of network structure, temporal dynamics and spatial organization is quantified through the Kolmogorov-based measures of normalized compression distance and set complexity. Results over sets of random networks that operate in the ordered, critical and chaotic domains demonstrate that: (1) ordered and critical networks tend to create the most information-rich patterns; (2) signalling configurations in which cell-to-cell communication is non-directional mostly produce simple patterns irrespective of the internal network domain; and (3) directional signalling configurations, similar to those that function in planar cell polarity, produce the most complex patterns, but only when the intracellular networks function in non-chaotic domains.     

Intracellular signalling as a parallel distributed process

Living cells respond to their environment by means of an interconnected network of receptors, second messengers, protein kinases and other signalling molecules. This article suggests that the performance of cell signalling pathways taken as a whole has similarities to that of the parallel distributed process networks (PDP networks) used in computer-based pattern recognition. Using the response of hepatocytes to glucagon as an example, a procedure is described by which a PDP network could simulate a cell signalling pathway. This procedure involves the following steps: (a) a bounded set of molecules is defined that carry the signals of interest; (b) each of these molecules is represented by a PDP-type of unit, with input and output functions and connection weights corresponding to specific biochemical parameters; (c) a "learning algorithm" is applied in which small random changes are made in the parameters of the cell signalling units and the new network is then tested by a selection procedure in favour of a specific input-output relationship. The analogy with PDP networks shows how living cells can recognize combinations of environmental influences, how cell responses can be stabilized and made resistant to damage, and how novel cell signalling pathways might appear during evolution.     

From individual Wnt pathways towards a Wnt signalling network

Wnt proteins play important roles during vertebrate and invertebrate development. They obviously have the ability to activate different intracellular signalling pathways. Based on the characteristic intracellular mediators used, these are commonly described as the Wnt/beta-catenin, the Wnt/calcium and the Wnt/Jun N-terminal kinase pathways (also called planar cell polarity pathway). In the past, these different signalling events were mainly described as individual and independent signalling branches. Here, we discuss the possibility that Wnt proteins activate a complex intracellular signalling network rather than individual pathways and suggest a graph representation of this network. Furthermore, we discuss different ways of how to predict the specific outcome of an activation of this network in a particular cell type, which will require the use of mathematical models. We point out that the use of deterministic approaches via the application of differential equations is suitable to model only small aspects of the whole network and that more qualitative approaches are possibly a suitable starting point for the prediction of the global behaviour of such large protein interaction networks.     

The apoptosome: signalling platform of cell death

Recent work on the initial switches that trigger cell death has revealed surprising inventions of nature that ensure the ordered suicide of a cell that has been selected for demise. Particularly intriguing is how a signal--the release of cytochrome c from the mitochondria--is translated into the activation of the death cascade, which leads to a point of no return. Now there is new understanding of how this crucial process is delicately handled by a cytosolic signalling platform known as the apoptosome. The formation of the apoptosome and the activation of its effector, caspase-9, reveals a sophisticated mechanism that might be more common than was initially thought.     

Robustness properties of apoptosis models with respect to parameter variations and intrinsic noise

Analyses of different robustness aspects for models of the direct signal transduction pathway of receptor-induced apoptosis is presented. Apoptosis is a form of programmed cell death, removing unwanted cells within multicellular organisms to maintain a proper balance between cell reproduction and death. Its signalling pathway includes an activation feedback loop that generates bistable behaviour, where the two steady states can be seen as 'life' and 'death'. Inherent robustness, widely recognised in biological systems, is of major importance in apoptosis signalling, as it guarantees the same cell fate for similar conditions. First, the influence of the stochastic nature of reactions indicating a role for inhibition reactions as noise filters and justifying a deterministic approach in the further analyses is evaluated. Second, the robustness of the bistable threshold with respect to parameter changes is evaluated by statistical methods, showing the need to balance both the forward and the back part of the activation loop. These analyses can also discriminate between the models favouring the model consistent with novel biological findings. The parameter robustness analyses are also applicable to other signal transduction networks, as several have been shown to display bistable behaviour. These methods therefore have a range of possible applications in systems biology not only to measure robustness, but also for model discrimination.     

Regulation of B-cell fate by antigen-receptor signals

Recent evidence indicates that B cells are instructed continuously by B-cell receptor (BCR) signals to make crucial cell-fate decisions at several checkpoints during their development. Targeted disruption of BCR signalling components leads to distinct blocks in B-cell maturation, which indicates that key kinases and adaptors fine-tune BCR signalling to direct appropriate cell fates. Recent progress in unravelling the molecular mechanisms of the BCR signalling pathways has helped to clarify how BCR signals regulate the proliferation, survival and apoptosis of developing B cells.     

Identification of potential targets in biological signalling systems through network perturbation analysis

The network-based representation and analysis of biological systems contributes to a greater understanding of their structures and functions at different levels of complexity. These techniques can also be used to identify potential novel therapeutic targets based on the characterisation of vulnerable or highly influential network components. There is a need to investigate methods for estimating the impact of molecular perturbations. The prediction of high-impact or critical targets can aid in the identification of novel strategies for controlling the level of activation of specific, therapeutically relevant genes or proteins. Here, we report a new computational strategy for the analysis of the vulnerability of cellular signalling networks based on the quantitative assessment of the impact of large-scale, dynamic perturbations. To show the usefulness of this methodology, two complex signalling networks were analysed: the caspase-3 and the adenosine-regulated calcium signalling systems. This allowed us to estimate and rank the perturbation impact of the components defining these networks. Testable hypotheses about how these targets could modify the dynamic operation of the systems are provided. In the case of the caspase-3 system, the predictions and rankings were in line with results obtained from previous experimental validations of computational predictions generated by a relatively more computationally complex technique. In the case of the adenosine-regulated calcium system, we offer new testable predictions on the potential effect of different targets on the control of calcium flux. Unlike previous methods, the proposed approach provides perturbation-specific scores for each network component. The proposed perturbation assessment methodology may be applied to other systems to gain a deeper understanding of their dynamic operation and to assist the discovery of new therapeutic targets and strategies.     

Cell behaviour as a dynamic attractor in the intracellular signalling system

We present a model of the cell signalling network based on the generic properties of interactions between protein kinases (PKs) and protein phosphatases (PPs) inside cells. The model is designed to examine the global properties and intrinsic dynamics of the phosphorylation system. A genetic algorithm (GA) is used to evolve populations of "cells". The GA selects cells and ranks them based on an analysis of the dynamics of the proteins within the networks from a series of different random starting conditions. The fittest cells are taken to be those which can generate a variety of different "behaviours" from a series of different initial conditions. During the GA, intracellular protein interactions evolve via mutation and an analogue of domain shuffling between protein types that is thought to occur during biological evolution. The dynamics of the simulated networks are presented and we discuss the hypothesis that changes in the behaviour of a cell may be interpretable as a switch between attractor basins in the intracellular signalling network.     

Finite-time Lyapunov exponents and metabolic control coefficients for threshold detection of stimulus–response curves

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus–response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus–response curves with sigmoidal shape.     

Control of death receptor and mitochondrial-dependent apoptosis by c-Jun N-terminal kinase in hippocampal CA1 neurones following global transient ischaemia

c-Jun N-terminal kinase (JNK), a member of the mitogen-activated protein kinase family, is activated in response to a number of extracellular stimuli, including inflammatory cytokines, UV irradiation and ischaemia. A large body of evidence supports a role for JNK signalling in stress-induced apoptosis. It has been hypothesized that JNK may contribute to the apoptotic response by regulating the intrinsic cell death pathway involving the mitochondria. Here, we examined the role of the JNK signalling pathway in hippocampal CA1 apoptotic neurones following transient ischaemia in gerbils. We showed early activation of death receptor-dependent apoptosis (caspase-8 activation 2 days after ischaemia) and a biphasic activation of caspase-3 and caspase-9 after ischaemia. Activation of the mitochondrial pathway, as measured by cytochrome c release, appeared as a late event (5-7 days after ischaemia). AS601245, a novel JNK inhibitor, antagonized activation of both pathways and significantly protected CA1 neurones from cell death. Our results suggest a key role of JNK in the control of death receptor and mitochondrial-dependent apoptosis after transient ischaemia.     

Dynamical analysis of cellular networks based on the Green's function matrix

The complexity of cellular networks often limits human intuition in understanding functional regulations in a cell from static network diagrams. To this end, mathematical models of ordinary differential equations (ODEs) have commonly been used to simulate dynamical behavior of cellular networks, to which a quantitative model analysis can be applied in order to gain biological insights. In this paper, we introduce a dynamical analysis based on the use of Green's function matrix (GFM) as sensitivity coefficients with respect to initial concentrations. In contrast to the classical (parametric) sensitivity analysis, the GFM analysis gives a dynamical, molecule-by-molecule insight on how system behavior is accomplished and complementarily how (impulse) signal propagates through the network. The knowledge gained will have application from model reduction and validation to drug discovery research in identifying potential drug targets, studying drug efficacy and specificity, and optimizing drug dosing and timing. The efficacy of the method is demonstrated through applications to common network motifs and a Fas-induced programmed cell death model in Jurkat T cell line.     

Multiple roles of Activin/Nodal,bone morphogenetic protein,fibroblast growth factor and Wnt/β-catenin signalling in the anterior neural patterning of adherent human embryonic stem cell cultures

Several studies have successfully produced a variety of neural cell types from human embryonic stem cells (hESCs), but there has been limited systematic analysis of how different regional identities are established using well-defined differentiation conditions. We have used adherent, chemically defined cultures to analyse the roles of Activin/Nodal, bone morphogenetic protein (BMP), fibroblast growth factor (FGF) and Wnt/β-catenin signalling in neural induction, anteroposterior patterning and eye field specification in hESCs. We show that either BMP inhibition or activation of FGF signalling is required for effective neural induction, but these two pathways have distinct outcomes on rostrocaudal patterning. While BMP inhibition leads to specification of forebrain/midbrain positional identities, FGF-dependent neural induction is associated with strong posteriorization towards hindbrain/spinal cord fates. We also demonstrate that Wnt/β-catenin signalling is activated during neural induction and promotes acquisition of neural fates posterior to forebrain. Therefore, inhibition of this pathway is needed for efficient forebrain specification. Finally, we provide evidence that the levels of Activin/Nodal and BMP signalling have a marked influence on further forebrain patterning and that constitutive inhibition of these pathways represses expression of eye field genes. These results show that the key mechanisms controlling neural patterning in model vertebrate species are preserved in adherent, chemically defined hESC cultures and reveal new insights into the signals regulating eye field specification.     

Sequential and combinatorial inputs from Nodal, Delta2/Notch and FGF/MEK/ERK signalling pathways establish a grid-like organisation of distinct cell identities in the ascidian neural plate

The ascidian neural plate has a grid-like organisation, with six rows and eight columns of aligned cells, generated by a series of stereotypical cell divisions. We have defined unique molecular signatures for each of the eight cells in the posterior-most two rows of the neural plate - rows I and II. Using a combination of morpholino gene knockdown, dominant-negative forms and pharmacological inhibitors, we tested the role of three signalling pathways in defining these distinct cell identities. Nodal signalling at the 64-cell stage was found to be required to define two different neural plate domains - medial and lateral - with Nodal inducing lateral and repressing medial identities. Delta2, an early Nodal target, was found to then subdivide each of the lateral and medial domains to generate four columns. Finally, a separate signalling system along the anteroposterior axis, involving restricted ERK1/2 activation, was found to promote row I fates and repress row II fates. Our results reveal how the sequential integration of three signalling pathways - Nodal, Delta2/Notch and FGF/MEK/ERK - defines eight different sub-domains that characterise the ascidian caudal neural plate. Most remarkably, the distinct fates of the eight neural precursors are each determined by a unique combination of inputs from these three signalling pathways.     

RA and FGF Signalling Are Required in the Zebrafish Otic Vesicle to Pattern and Maintain Ventral Otic Identities

During development of the zebrafish inner ear, regional patterning in the ventral half of the otic vesicle establishes zones of gene expression that correspond to neurogenic, sensory and non-neural cell fates. FGF and Retinoic acid (RA) signalling from surrounding tissues are known to have an early role in otic placode induction and otic axial patterning, but how external signalling cues are translated into intrinsic patterning during otic vesicle (OV) stages is not yet understood. FGF and RA signalling pathway members are expressed in and around the OV, suggesting important roles in later patterning or maintenance events. We have analysed the temporal requirement of FGF and RA signalling for otic development at stages after initial anteroposterior patterning has occurred. We show that high level FGF signalling acts to restrict sensory fates, whereas low levels favour sensory hair cell development; in addition, FGF is both required and sufficient to promote the expression of the non-neural marker otx1b in the OV. RA signalling has opposite roles: it promotes sensory fates, and restricts otx1b expression and the development of non-neural fates. This is surprisingly different from the earlier requirement for RA signalling in specification of non-neural fates via tbx1 expression, and highlights the shift in regulation that takes place between otic placode and vesicle stages in zebrafish. Both FGF and RA signalling are required for the development of the otic neurogenic domain and the generation of otic neuroblasts. In addition, our results indicate that FGF and RA signalling act in a feedback loop in the anterior OV, crucial for pattern refinement.     

Mathematical Modelling of Cell-Fate Decision in Response to Death Receptor Engagement

Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we present a mathematical model of cell fate decision recapitulating and integrating the most consistent facts extracted from the literature. This model provides a generic high-level view of the interplays between NFκB pro-survival pathway, RIP1-dependent necrosis, and the apoptosis pathway in response to death receptor-mediated signals. Wild type simulations demonstrate robust segregation of cellular responses to receptor engagement. Model simulations recapitulate documented phenotypes of protein knockdowns and enable the prediction of the effects of novel knockdowns. In silico experiments simulate the outcomes following ligand removal at different stages, and suggest experimental approaches to further validate and specialise the model for particular cell types. We also propose a reduced conceptual model implementing the logic of the decision process. This analysis gives specific predictions regarding cross-talks between the three pathways, as well as the transient role of RIP1 protein in necrosis, and confirms the phenotypes of novel perturbations. Our wild type and mutant simulations provide novel insights to restore apoptosis in defective cells. The model analysis expands our understanding of how cell fate decision is made. Moreover, our current model can be used to assess contradictory or controversial data from the literature. Ultimately, it constitutes a valuable reasoning tool to delineate novel experiments.