Bridging the gaps in systems biology.

Systems biology aims at creating mathematical models, i.e., computational reconstructions of biological systems and processes that will result in a new level of understanding-the elucidation of the basic and presumably conserved "design" and "engineering" principles of biomolecular systems. Thus, systems biology will move biology from a phenomenological to a predictive science. Mathematical modeling of biological networks and processes has already greatly improved our understanding of many cellular processes. However, given the massive amount of qualitative and quantitative data currently produced and number of burning questions in health care and biotechnology needed to be solved is still in its early phases. The field requires novel approaches for abstraction, for modeling bioprocesses that follow different biochemical and biophysical rules, and for combining different modules into larger models that still allow realistic simulation with the computational power available today. We have identified and discussed currently most prominent problems in systems biology: (1) how to bridge different scales of modeling abstraction, (2) how to bridge the gap between topological and mechanistic modeling, and (3) how to bridge the wet and dry laboratory gap. The future success of systems biology largely depends on bridging the recognized gaps.

Mechanism of inhibition defines CETP activity: a mathematical model for CETP in vitro.

Because cholesteryl ester transfer protein (CETP) inhibition is a potential HDL-raising therapy, interest has been raised in the mechanisms and consequences of CETP activity. To explore these mechanisms and the dynamics of CETP in vitro, a mechanistic mathematical model was developed based upon the shuttle mechanism for lipid transfer. Model parameters were estimated from eight published experimental datasets, and the resulting model captures observed dynamics of CETP in vitro. Simulations suggest the shuttle mechanism yields behaviors consistent with experimental observations. Three key findings predicted from model simulations are: 1) net CE transfer activity from HDL to VLDL and LDL can be significantly altered by changing the balance of homoexchange versus heteroexchange of neutral lipids via CETP; 2) lipemia-induced increases in CETP activity are more likely caused by increases in lipoprotein particle size than particle number; and 3) the inhibition mechanisms of the CETP inhibitors torcetrapib and JTT-705 are significantly more potent than a classic competitive inhibition mechanism with the irreversible binding mechanism having the most robust response. In summary, the model provides a plausible representation of CETP activity in vitro, corroborates strong evidence for the shuttle hypothesis, and provides new insights into the consequences of CETP activity and inhibition on lipoproteins.

Kinetic modeling of ace operon genetic regulation in Escherichia coli.

A family of kinetic models has been developed that takes into account available experimental information on the regulation of ace operon expression in Escherichia coli. This has allowed us to study and analyze possible versions of regulation of the ace operon and to test their possibilities. Based on literature analysis, we found that there is an ambiguity of properties of IclR (main repressor of ace operon). The main aspect of this ambiguity are two different forms of IclR purified from E. coli K strain and different coeffector sets for IclR purified from E. coli K and B strains. It has been shown that the full-length form of IclR is physiologically relevant and that IclR truncation is a result of purification of the protein from E. coli K strains. We also found that the IclR protein purified from E. coli B strain carries two coeffector binding sites. Using model-developed levels of steady state aceBAK expression against physiological ranges of coeffectors, concentration has been predicted.

The impact of the regulatory design on the response of epidermal growth factor receptor-mediated signal transduction towards oncogenic mutations.

Epidermal growth factor receptor (EGFR)-mediated signal transduction is often hyperactivated in tumour cells and therefore considered a promising target for cancer therapy. A number of computational models have been developed which describe the pathway in great detail. These models are similar in their description of the activation events. The deactivation of the EGFR signalling seems to be cell type-specific and is less understood. Deactivation via receptor internalization, feedback inhibition of son of sevenless (SOS) by double phosphorylated, extracellular signal-regulated kinase (ERKPP) or transiently activated Ras-GTPase activating protein (Ras-GAP) proteins is discussed to play a role. In this study we address the question of to what extent the effect of oncogenic perturbations on EGFR signalling depend on the specific regulation structure. This is investigated using a detailed pathway model under two regulatory modes: the negative feedback via ERKPP to SOS and feed-forward deactivation via transiently activated Ras-GAP proteins. We show that the effect of receptor overexpression differs qualitatively under both regulations. In the system with transiently activated Ras-GAP it may result in an attenuation of the ERK activation. Such a nonintuitive effect was also observed experimentally. In general we find the model with transiently activated Ras-GAP to have a higher robustness towards receptor overexpression and Ras mutations. In particular, we demonstrate that this model can compensate for these oncogenic perturbations if the regulation is strong. The negative feedback can not protect the system against Ras mutations. A general sensitivity analysis, however, shows a higher robustness of the model under negative feedback, indicating the limited significance of such analyses for the prediction of specific oncogenic perturbations.

A retrospective study detects a novel variant of porcine epidemic diarrhea virus in England in archived material from the year 2000.

Outbreaks of porcine epidemic diarrhea (PED) were first recorded in England in the 1970s and continued to be confirmed until 2002. Retrospective analysis of archived material from one of the last confirmed cases in England in the year 2000 demonstrates the previous existence of a very diverse PED virus strain. Following the outbreaks of PED in North America in 2013, there has been renewed interest in phylogenetic analysis of sequences from PEDV strains worldwide. There is a gap in the available sequence data between the mid 1980s and the mid 2000s. This work is an example of how this gap can be at least partially filled by the examination of archived material.

Response to continuous and pulsatile PTH dosing: a mathematical model for parathyroid hormone receptor kinetics.

In this paper, we propose a mathematical model for parathyroid hormone receptor (PTH1R) kinetics, focusing on the receptor's response to PTH dosing to discern bone formation responses from bone resorption. The PTH1R is a major target for new osteoporosis treatments, as pulsatile PTH dosing has been shown to induce net bone formation in both animals and humans, and PTH(1-34) was recently FDA approved for the treatment of post-menopausal osteoporosis. PTH has also been shown to cause net bone loss when given continuously, so that the net action of PTH on bone is dependent on the dosing pattern. We have developed a simplified two-state receptor kinetics model for the PTH1R, based on the concepts of Segel et al., to distinguish the activity of active and inactive receptor and receptor-ligand complexes. The goal is to develop a plausible model of the minimal essential biological relationships necessary for understanding the responses to PTH dosing. A two-state model is able to effectively discriminate between continuous and pulsatile PTH dosing using the active species as surrogates for the downstream anabolic response. For continuous PTH dosing, the model predicts a desensitized system dominated by the inactive receptor and complex, consistent with downstream net bone loss that has been demonstrated experimentally. Using pulsatile PTH dosing, the model system predicts a highly sensitized state dominated by the active receptor and complex, corresponding to net bone formation. These results are consistent with the hypothesis that the kinetics of the receptor plays a critical role in the downstream effects of PTH dosing. Moreover, these results indicate that within a range of biologically relevant PTH doses, the two-state model is able to capture the differential behavior of the system for both continuous and pulsatile PTH dosing. The development of such a model provides a rational basis for developing more biologically extensive models that may support the design of optimal dosing strategies for PTH-based anti-osteoporosis treatments. Moreover, this model provides a unique starting point from which to design experiments investigating PTH receptor biology.

Correlation of protein and gene expression profiles of inflammatory proteins after endotoxin challenge in human subjects.

Administration of endotoxin (LPS) in humans results in profound physiological responses, including activation of peripheral blood mononuclear cells and the release of inflammatory factors. The time course of the response of selected inflammatory proteins was examined in healthy subjects (n = 6) administered a single intravenous dose of the purified derivative of endotoxin (3.0 ng/kg). Microarray analysis demonstrated changes in the expression of a number of genes, which were confirmed in separate in vitro endotoxin stimulation experiments. Subsequent TaqMan analysis of genes of interest indicated time-dependent changes in the expression of many of these genes. This included pre-B cell enhancing factor, which was identified on microarray analysis as being markedly upregulated following endotoxin stimulation. Protein expression of the genes examined by TaqMan analysis was measured and demonstrated the appearance of tumor necrosis factor (TNF)-alpha and sTNF-R proteins in the plasma beginning within 1 h after dosing, followed by other cytokines/ inflammatory markers (e.g., IL-1ra, G-CSF, IL-6, IL-8, and IL-10) and suppressors of cytokine signaling (SOCS-1 and SOCS-3). In general, cytokine protein expression correlated well with gene expression; however, the temporal profile of expression of some genes did not correlate well with the protein data. For many of these proteins, the lack of correlation was attributable to alternate tissue sources, which were demonstrated on TaqMan analysis. Principal component analysis indicated that cytokines could be grouped according to their temporal pattern of response, with most transcript levels returning to baseline 24 h following endotoxin administration. The combination of cDNA microarray and TaqMan analysis to identify and quantify changes in gene expression, along with the analysis of protein expression, can be useful in investigating inflammatory and other diseases.

Fitting the elementary rate constants of the P-gp transporter network in the hMDR1-MDCK confluent cell monolayer using a particle swarm algorithm.

P-glycoprotein, a human multidrug resistance transporter, has been extensively studied due to its importance to human health and disease. In order to understand transport kinetics via P-gp, confluent cell monolayers overexpressing P-gp are widely used. The purpose of this study is to obtain the mass action elementary rate constants for P-gp's transport and to functionally characterize members of P-gp's network, i.e., other transporters that transport P-gp substrates in hMDR1-MDCKII confluent cell monolayers and are essential to the net substrate flux. Transport of a range of concentrations of amprenavir, loperamide, quinidine and digoxin across the confluent monolayer of cells was measured in both directions, apical to basolateral and basolateral to apical. We developed a global optimization algorithm using the Particle Swarm method that can simultaneously fit all datasets to yield accurate and exhaustive fits of these elementary rate constants. The statistical sensitivity of the fitted values was determined by using 24 identical replicate fits, yielding simple averages and standard deviations for all of the kinetic parameters, including the efflux active P-gp surface density. Digoxin required additional basolateral and apical transporters, while loperamide required just a basolateral tranporter. The data were better fit by assuming bidirectional transporters, rather than active importers, suggesting that they are not MRP or active OATP transporters. The P-gp efflux rate constants for quinidine and digoxin were about 3-fold smaller than reported ATP hydrolysis rate constants from P-gp proteoliposomes. This suggests a roughly 3∶1 stoichiometry between ATP hydrolysis and P-gp transport for these two drugs. The fitted values of the elementary rate constants for these P-gp substrates support the hypotheses that the selective pressures on P-gp are to maintain a broad substrate range and to keep xenobiotics out of the cytosol, but not out of the apical membrane.

Perspectives on mathematical modeling for receptor-mediated processes.

Mathematical modeling is a potent in silico tool that can help investigate, interpret, and predict the behavior of biological systems. The first step is to develop a working hypothesis of the biology. Then by "translating" the biological phenomena into equations, models can harness the power of mathematical analysis techniques to explore the dynamics and interactions of the biological components. Models can be used together with traditional experimental models to help design new experiments, test hypotheses, identify mechanisms, and predict outcomes. This article reviews the process of building, calibrating, and using mathematical models in the context of the kinetics of receptor and signal transduction biology. An example model related to the androgen receptor-mediated regulation of the prostate is presented to illustrate the steps in the modeling process and to highlight the potential for mathematical modeling in this area.

The kinetic model of the shikimate pathway as a tool to optimize enzyme assays for high-throughput screening.

Four-enzyme section of the shikimate pathway (Aro B, D, E, and K) of Streptococcus pneumoniae has been studied. Kinetic properties of the individual enzymes and three- and four-enzyme linked reactions have been characterized in vitro. On the basis of the data measured in spectrophotometric and LC-MS experiments, kinetic mechanisms of the enzymes have been suggested and all kinetic parameters have been identified. Kinetic models for these three- and four-enzyme sections of the shikimate pathway have been constructed and validated. The model of the four-enzyme section of shikimate pathway has been employed to design an inhibition-sensitive reconstituted pathway for a high-throughput screening effort on the shikimate pathway. It was demonstrated that using the model it was possible to optimize this reconstituted pathway in such a way to provide equal sensitivity of the enzymes to inhibition.

Modeling the interactions between osteoblast and osteoclast activities in bone remodeling.

We propose a mathematical model explaining the interactions between osteoblasts and osteoclasts, two cell types specialized in the maintenance of the bone integrity. Bone is a dynamic, living tissue whose structure and shape continuously evolves during life. It has the ability to change architecture by removal of old bone and replacement with newly formed bone in a localized process called remodeling. The model described here is based on the idea that the relative proportions of immature and mature osteoblasts control the degree of osteoclastic activity. In addition, osteoclasts control osteoblasts differentially depending on their stage of differentiation. Despite the tremendous complexity of the bone regulatory system and its fragmentary understanding, we obtain surprisingly good correlations between the model simulations and the experimental observations extracted from the literature. The model results corroborate all behaviors of the bone remodeling system that we have simulated, including the tight coupling between osteoblasts and osteoclasts, the catabolic effect induced by continuous administration of PTH, the catabolic action of RANKL, as well as its reversal by soluble antagonist OPG. The model is also able to simulate metabolic bone diseases such as estrogen deficiency, vitamin D deficiency, senescence and glucocorticoid excess. Conversely, possible routes for therapeutic interventions are tested and evaluated. Our model confirms that anti-resorptive therapies are unable to partially restore bone loss, whereas bone formation therapies yield better results. The model enables us to determine and evaluate potential therapies based on their efficacy. In particular, the model predicts that combinations of anti-resorptive and anabolic therapies provide significant benefits compared with monotherapy, especially for certain type of skeletal disease. Finally, the model clearly indicates that increasing the size of the pool of preosteoblasts is an essential ingredient for the therapeutic manipulation of bone formation. This model was conceived as the first step in a bone turnover modeling platform. These initial modeling results are extremely encouraging and lead us to proceed with additional explorations into bone turnover and skeletal remodeling.