Mechanistic simulations of inflammation: current state and future prospects

Inflammation is a normal, robust physiological process. It can also be viewed as a complex system that senses and attempts to resolve homeostatic perturbations initiated from within the body (for example, in autoimmune disease) or from the outside (for example, in infections). Virtually all acute and chronic diseases are either driven or modulated by inflammation. The complex interplay between beneficial and harmful arms of the inflammatory response may underlie the lack of fully effective therapies for many diseases. Mathematical modeling is emerging as a frontline tool for understanding the complexity of the inflammatory response. A series of articles in this issue highlights various modeling approaches to inflammation in the larger context of health and disease, from intracellular signaling to whole-animal physiology. Here we discuss the state of this emerging field. We note several common features of inflammation models, as well as challenges and prospects for future studies.     

Kinetic Buffering of Cross Talk between Bacterial Two-Component Sensors

Two-component systems are a class of sensors that enable bacteria to respond to environmental and cell-state signals. The canonical system consists of a membrane-bound sensor histidine kinase that autophosphorylates in response to a signal and transfers the phosphate to an intracellular response regulator. Bacteria typically have dozens of two-component systems. The key questions are whether these systems are linear and, if they are, how cross talk between systems is buffered. In this work, we studied the EnvZ/OmpR and CpxA/CpxR systems from Escherichia coli, which have been shown previously to exhibit slow cross talk in vitro. Using in vitro radiolabeling and a rapid quenched-flow apparatus, we experimentally measured 10 biochemical parameters capturing the cognate and non-cognate phosphotransfer reactions between the systems. These data were used to parameterize a mathematical model that was used to predict how cross talk is affected as different genes are knocked out. It was predicted that significant cross talk between EnvZ and CpxR only occurs for the triple mutant ΔompR ΔcpxA ΔactA-pta. All seven combinations of these knockouts were made to test this prediction and only the triple mutant demonstrated significant cross talk, where the cpxP promoter was induced 280-fold upon the activation of EnvZ. Furthermore, the behavior of the other knockouts agrees with the model predictions. These results support a kinetic model of buffering where both the cognate bifunctional phosphatase activity and the competition between regulator proteins for phosphate prevent cross talk in vivo.     

Inferring biomolecular regulatory networks from phase portraits of time-series expression profiles

Reverse engineering of biomolecular regulatory networks such as gene regulatory networks, protein interaction networks, and metabolic networks has received an increasing attention as more high-throughput time-series measurements become available. In spite of various approaches developed from this motivation, it still remains as a challenging subject to develop a new reverse engineering scheme that can effectively uncover the functional interaction structure of a biomolecular network from given time-series expression profiles (TSEPs). We propose a new reverse engineering scheme that makes use of phase portraits constructed by projection of every two TSEPs into respective phase planes. We introduce two measures of a slope index (SI) and a winding index (WI) to quantify the interaction properties embedded in the phase portrait. Based on the SI and WI, we can reconstruct the functional interaction network in a very efficient and systematic way with better inference results compared to previous approaches. By using the SI, we can also estimate the time-lag accompanied with the interaction between molecular components of a network.     

Coupled positive feedbacks provoke slow induction plus fast switching in apoptosis

Apoptosis is a form of a programmed cell death for multicellular organisms to remove unwanted or damaged cells. This critical choice of cellular fate is an all-or-none process, but its dynamics remains unraveled. The switch-like apoptotic decision has to be reliable, and once a pro-apoptotic fate is determined it requires fast and irreversible execution. One of the key regulators in apoptosis is caspase-3. Interestingly, activated caspase-3 quickly executes apoptosis, but it takes considerable time to activate it. Here, we have analyzed this "slow induction plus fast switching" mechanism of caspase-3 through mathematical modeling and computational simulation. First, we have shown that two positive feedbacks, composed of caspase-8 and XIAP, are essential for the "slow induction plus fast switching" behavior of caspase-3. Second, we have found that XIAP in the feedback loops primarily regulates induction time of caspase-3. In many cancer cells activation of caspase-3 is suppressed. Our results suggest that reinforcement of the positive feedback by XIAP, which relieves XIAP-mediated caspase-3 inhibition, might favor a pro-apoptotic cellular fate.     

Molecular titration and ultrasensitivity in regulatory networks

Protein sequestration occurs when an active protein is sequestered by a repressor into an inactive complex. Using mathematical and computational modeling, we show how this regulatory mechanism (called “molecular titration”) can generate ultrasensitive or “all-or-none” responses that are equivalent to highly cooperative processes. The ultrasensitive nature of the input-output response is mainly determined by two parameters: the dimer dissociation constant and the repressor concentration. Because in vivo concentrations are tunable through a variety of mechanisms, molecular titration represents a flexible mechanism for generating ultrasensitivity. Using physiological parameters, we report how details of in vivo protein degradation affect the strength of the ultrasensitivity at steady state. Given that developmental systems often transduce signals into cell-fate decisions on timescales incompatible with steady state, we further examine whether molecular titration can produce ultrasensitive responses within physiologically relevant time intervals. Using Drosophila somatic sex determination as a developmental paradigm, we demonstrate that molecular titration can generate ultrasensitivity on timescales compatible with most cell-fate decisions. Gene duplication followed by loss-of-function mutations can create dominant negatives that titrate and compete with the original protein. Dominant negatives are abundant in gene regulatory circuits, and our results suggest that molecular titration might be generating an ultrasensitive response in these networks.     

Space in systems biology of signaling pathways--towards intracellular molecular crowding in silico

How cells utilize intracellular spatial features to optimize their signaling characteristics is still not clearly understood. The physical distance between the cell-surface receptor and the gene expression machinery, fast reactions, and slow protein diffusion coefficients are some of the properties that contribute to their intricacy. This article reviews computational frameworks that can help biologists to elucidate the implications of space in signaling pathways. We argue that intracellular macromolecular crowding is an important modeling issue, and describe how recent simulation methods can reproduce this phenomenon in either implicit, semi-explicit or fully explicit representation.     

E-photosynthesis: web-based platform for modeling of complex photosynthetic processes

E-photosynthesis framework is a web-based platform for modeling and analysis of photosynthetic processes. Compared to its earlier version, the present platform employs advanced software methods and technologies to support an effective implementation of vastly diverse kinetic models of photosynthesis. We report on the first phase implementation of the tool new version and demonstrate the functionalities of model visualization, presentation of model components, rate constants, initial conditions and of model annotation. The demonstration also includes export of a model to the Systems Biology Markup Language format and remote numerical simulation of the model.     

The influence of the signal dynamics of activated form of IKK on NF-kappaB and anti-apoptotic gene expressions: a systems biology approach

NF-kappaB activation plays a crucial role in anti-apoptotic responses in response to the apoptotic signaling during tumor necrosis factor (TNF)-alpha stimulation. TNF-alpha induces apoptosis sensitive to the hepatitis B virus (HBV) infected cells, despite sustained NF-kappaB activation. Our results indicate that the HBV infection induces sustained NF-kappaB activation, in a manner similar to the TNF-alpha stimulation. However, these effects are not merely combined. Computational simulations show that the level of form of the IKK complex activated by phosphorylation (IKK-p) affects the dynamic pattern of NF-kappaB activation during TNF-alpha stimulation in the following ways: (i) the initial level of IKK-p determines the incremental change in IKK-p at the same level of TNF-alpha stimulation, (ii) the incremental change in IKK-p determines the amplitudes of active NF-kappaB oscillation, and (iii) the steady state level of IKK-p after the incremental change determines the period of active NF-kappaB oscillation. Based on experiments, we observed that the initial level of IKK-p was upregulated and the active NF-kappaB oscillation showed smaller amplitudes for a shorter period in HepG2.2.15 cells (HBV-producing cells) during TNF-alpha stimulation, as was indicated by the computational simulations. Furthermore, we found that during TNF-alpha stimulation, NF-kappaB-regulated anti-apoptotic genes were upregulated in HepG2 cells but were downregulated in HepG2.2.15 cells. Based on the previously mentioned results, we can conclude that the IKK-p-level changes induced by HBV infection modulate the dynamic pattern of active NF-kappaB and thereby could affect NF-kappaB-regulated anti-apoptotic gene expressions. Finally, we postulate that the sensitive apoptotic response of HBV-infected cells to TNF-alpha stimulation is governed by the dynamic patterns of active NF-kappaB based on IKK-p level changes.     

Immune signal transduction in leishmaniasis from natural to artificial systems: Role of feedback loop insertion

Background

Modulated immune signal (CD14–TLR and TNF) in leishmaniasis can be linked to EGFR pathway involved in wound healing, through crosstalk points. This signaling network can be further linked to a synthetic gene circuit acting as a positive feedback loop to elicit a synchronized intercellular communication among the immune cells which may contribute to a better understanding of signaling dynamics in leishmaniasis.

Methods

Network reconstruction with positive feedback loop, simulation (ODE 15s solver) and sensitivity analysis of CD14–TLR, TNF and EGFR was done in SimBiology (MATLAB 7.11.1). Cytoscape and adjacency matrix were used to calculate network topology. PCA was extracted by using sensitivity coefficient in MATLAB. Model reduction was done using time, flux and sensitivity score.

Results

Network has five crosstalk points: NIK, IκB–NFκB and MKK (4/7, 3/6, 1/2) which show high flux and sensitivity. PI3K in EGFR pathway shows high flux and sensitivity. PCA score was high for cytoplasmic ERK1/2, PI3K, Atk, STAT1/3 and nuclear JNK. Of the 125 parameters, 20% are crucial as deduced by model reduction.

Conclusions

EGFR can be linked to CD14–TLR and TNF through the MAPK crosstalk points. These pathways may be controlled through Ras and Raf that lie upstream of signaling components ERK ½ (c) and JNK (n) that have a high PCA score via a synthetic gene circuit for activating cell–cell communication to elicit an inflammatory response. Also a disease resolving effect may be achieved through PI3K in the EGFR pathway.

General significance

The reconstructed signaling network can be linked to a gene circuit with a positive feedback loop, for cell–cell communication resulting in synchronized response in the immune cell population, for disease resolving effect in leishmaniasis.     

An Integrated Model of Eicosanoid Metabolism and Signaling Based on Lipidomics Flux Analysis

There is increasing evidence for a major and critical involvement of lipids in signal transduction and cellular trafficking, and this has motivated large-scale studies on lipid pathways. The Lipid Metabolites and Pathways Strategy consortium is actively investigating lipid metabolism in mammalian cells and has made available time-course data on various lipids in response to treatment with KDO₂-lipid A (a lipopolysaccharide analog) of macrophage RAW 264.7 cells. The lipids known as eicosanoids play an important role in inflammation. We have reconstructed an integrated network of eicosanoid metabolism and signaling based on the KEGG pathway database and the literature and have developed a kinetic model. A matrix-based approach was used to estimate the rate constants from experimental data and these were further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data well for all species, and simulated enzyme activities were similar to their literature values. The quantitative model for eicosanoid metabolism that we have developed can be used to design experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways.     

Mapping photoautotrophic metabolism with isotopically nonstationary (13)C flux analysis

Understanding in vivo regulation of photoautotrophic metabolism is important for identifying strategies to improve photosynthetic efficiency or re-route carbon fluxes to desirable end products. We have developed an approach to reconstruct comprehensive flux maps of photoautotrophic metabolism by computational analysis of dynamic isotope labeling measurements and have applied it to determine metabolic pathway fluxes in the cyanobacterium Synechocystis sp. PCC6803. Comparison to a theoretically predicted flux map revealed inefficiencies in photosynthesis due to oxidative pentose phosphate pathway and malic enzyme activity, despite negligible photorespiration. This approach has potential to fill important gaps in our understanding of how carbon and energy flows are systemically regulated in cyanobacteria, plants, and algae.     

Photoelectrochemical control of the balance between cyclic- and linear electron transport in photosystem I. Algorithm for P700 induction kinetics

Redox transients of chlorophyll P700, monitored as absorbance changes ΔA₈₁₀, were measured during and after exclusive PSI excitation with far-red (FR) light in pea (Pisum sativum, cv. Premium) leaves under various pre-excitation conditions. Prolonged adaptation in the dark terminated by a short PSII + PSI− exciting light pulse guarantees pre-conditions in which the initial photochemical events in PSI RCs are carried out by cyclic electron transfer (CET). Pre-excitation with one or more 10 s FR pulses creates conditions for induction of linear electron transport (LET). These converse conditions give rise to totally different, but reproducible responses of P700⁻ oxidation. System analyses of these responses were made based on quantitative solutions of the rate equations dictated by the associated reaction scheme for each of the relevant conditions. These provide the mathematical elements of the P700 induction algorithm (PIA) with which the distinguishable components of the P700⁺ response can be resolved and interpreted. It enables amongst others the interpretation and understanding of the characteristic kinetic profile of the P700⁺ response in intact leaves upon 10 s illumination with far-red light under the promotive condition for CET. The system analysis provides evidence that this unique kinetic pattern with a non-responsive delay followed by a steep S-shaped signal increase is caused by a photoelectrochemically controlled suppression of the electron transport from Fd to the PQ-reducing Q_r site of the cytb₆f complex in the cyclic pathway. The photoelectrochemical control is exerted by the PSI-powered proton pump associated with CET. It shows strong similarities with the photoelectrochemical control of LET at the acceptor side of PSII which is reflected by release of photoelectrochemical quenching of chlorophyll a fluorescence.