Kinetic modeling and exploratory numerical simulation of chloroplastic starch degradation

<p>Abstract</p> <p>Background</p> <p>Higher plants and algae are able to fix atmospheric carbon dioxide through photosynthesis and store this fixed carbon in large quantities as starch, which can be hydrolyzed into sugars serving as feedstock for fermentation to biofuels and precursors. Rational engineering of carbon flow in plant cells requires a greater understanding of how starch breakdown fluxes respond to variations in enzyme concentrations, kinetic parameters, and metabolite concentrations. We have therefore developed and simulated a detailed kinetic ordinary differential equation model of the degradation pathways for starch synthesized in plants and green algae, which to our knowledge is the most complete such model reported to date.</p> <p>Results</p> <p>Simulation with 9 internal metabolites and 8 external metabolites, the concentrations of the latter fixed at reasonable biochemical values, leads to a single reference solution showing β-amylase activity to be the rate-limiting step in carbon flow from starch degradation. Additionally, the response coefficients for stromal glucose to the glucose transporter k_catand K_Mare substantial, whereas those for cytosolic glucose are not, consistent with a kinetic bottleneck due to transport. Response coefficient norms show stromal maltopentaose and cytosolic glucosylated arabinogalactan to be the most and least globally sensitive metabolites, respectively, and β-amylase k_catand K_Mfor starch to be the kinetic parameters with the largest aggregate effect on metabolite concentrations as a whole. The latter kinetic parameters, together with those for glucose transport, have the greatest effect on stromal glucose, which is a precursor for biofuel synthetic pathways. Exploration of the steady-state solution space with respect to concentrations of 6 external metabolites and 8 dynamic metabolite concentrations show that stromal metabolism is strongly coupled to starch levels, and that transport between compartments serves to lower coupling between metabolic subsystems in different compartments.</p> <p>Conclusions</p> <p>We find that in the reference steady state, starch cleavage is the most significant determinant of carbon flux, with turnover of oligosaccharides playing a secondary role. Independence of stationary point with respect to initial dynamic variable values confirms a unique stationary point in the phase space of dynamically varying concentrations of the model network. Stromal maltooligosaccharide metabolism was highly coupled to the available starch concentration. From the most highly converged trajectories, distances between unique fixed points of phase spaces show that cytosolic maltose levels depend on the total concentrations of arabinogalactan and glucose present in the cytosol. In addition, cellular compartmentalization serves to dampen much, but not all, of the effects of one subnetwork on another, such that kinetic modeling of single compartments would likely capture most dynamics that are fast on the timescale of the transport reactions.</p

Examination of Triacylglycerol Biosynthetic Pathways via De Novo Transcriptomic and Proteomic Analyses in an Unsequenced Microalga

Biofuels derived from algal lipids represent an opportunity to dramatically impact the global energy demand for transportation fuels. Systems biology analyses of oleaginous algae could greatly accelerate the commercialization of algal-derived biofuels by elucidating the key components involved in lipid productivity and leading to the initiation of hypothesis-driven strain-improvement strategies. However, higher-level systems biology analyses, such as transcriptomics and proteomics, are highly dependent upon available genomic sequence data, and the lack of these data has hindered the pursuit of such analyses for many oleaginous microalgae. In order to examine the triacylglycerol biosynthetic pathway in the unsequenced oleaginous microalga, Chlorella vulgaris, we have established a strategy with which to bypass the necessity for genomic sequence information by using the transcriptome as a guide. Our results indicate an upregulation of both fatty acid and triacylglycerol biosynthetic machinery under oil-accumulating conditions, and demonstrate the utility of a de novo assembled transcriptome as a search model for proteomic analysis of an unsequenced microalga

Enhancing a Pathway-Genome Database (PGDB) to capture subcellular localization of metabolites and enzymes: the nucleotide-sugar biosynthetic pathways of Populus trichocarpa

Understanding how cellular metabolism works and is regulated requires that the underlying biochemical pathways be adequately represented and integrated with large metabolomic data sets to establish a robust network model. Genetically engineering energy crops to be less recalcitrant to saccharification requires detailed knowledge of plant polysaccharide structures and a thorough understanding of the metabolic pathways involved in forming and regulating cell-wall synthesis. Nucleotide-sugars are building blocks for synthesis of cell wall polysaccharides. The biosynthesis of nucleotide-sugars is catalyzed by a multitude of enzymes that reside in different subcellular organelles, and precise representation of these pathways requires accurate capture of this biological compartmentalization. The lack of simple localization cues in genomic sequence data and annotations however leads to missing compartmentalization information for eukaryotes in automatically generated databases, such as the Pathway-Genome Databases (PGDBs) of the SRI Pathway Tools software that drives much biochemical knowledge representation on the internet. In this report, we provide an informal mechanism using the existing Pathway Tools framework to integrate protein and metabolite sub-cellular localization data with the existing representation of the nucleotide-sugar metabolic pathways in a prototype PGDB for Populus trichocarpa. The enhanced pathway representations have been successfully used to map SNP abundance data to individual nucleotide-sugar biosynthetic genes in the PGDB. The manually curated pathway representations are more conducive to the construction of a computational platform that will allow the simulation of natural and engineered nucleotide-sugar precursor fluxes into specific recalcitrant polysaccharide(s)

Transmission of Single HIV-1 Genomes and Dynamics of Early Immune Escape Revealed by Ultra-Deep Sequencing

We used ultra-deep sequencing to obtain tens of thousands of HIV-1 sequences from regions targeted by CD8+ T lymphocytes from longitudinal samples from three acutely infected subjects, and modeled viral evolution during the critical first weeks of infection. Previous studies suggested that a single virus established productive infection, but these conclusions were tempered because of limited sampling; now, we have greatly increased our confidence in this observation through modeling the observed earliest sample diversity based on vastly more extensive sampling. Conventional sequencing of HIV-1 from acute/early infection has shown different patterns of escape at different epitopes; we investigated the earliest escapes in exquisite detail. Over 3–6 weeks, ultradeep sequencing revealed that the virus explored an extraordinary array of potential escape routes in the process of evading the earliest CD8 T-lymphocyte responses – using 454 sequencing, we identified over 50 variant forms of each targeted epitope during early immune escape, while only 2–7 variants were detected in the same samples via conventional sequencing. In contrast to the diversity seen within epitopes, non-epitope regions, including the Envelope V3 region, which was sequenced as a control in each subject, displayed very low levels of variation. In early infection, in the regions sequenced, the consensus forms did not have a fitness advantage large enough to trigger reversion to consensus amino acids in the absence of immune pressure. In one subject, a genetic bottleneck was observed, with extensive diversity at the second time point narrowing to two dominant escape forms by the third time point, all within two months of infection. Traces of immune escape were observed in the earliest samples, suggesting that immune pressure is present and effective earlier than previously reported; quantifying the loss rate of the founder virus suggests a direct role for CD8 T-lymphocyte responses in viral containment after peak viremia. Dramatic shifts in the frequencies of epitope variants during the first weeks of infection revealed a complex interplay between viral fitness and immune escape

Machine Learning-Based Classification of Lignocellulosic Biomass from Pyrolysis-Molecular Beam Mass Spectrometry Data

High-throughput analysis of biomass is necessary to ensure consistent and uniform feedstocks for agricultural and bioenergy applications and is needed to inform genomics and systems biology models. Pyrolysis followed by mass spectrometry such as molecular beam mass spectrometry (py-MBMS) analyses are becoming increasingly popular for the rapid analysis of biomass cell wall composition and typically require the use of different data analysis tools depending on the need and application. Here, the authors report the py-MBMS analysis of several types of lignocellulosic biomass to gain an understanding of spectral patterns and variation with associated biomass composition and use machine learning approaches to classify, differentiate, and predict biomass types on the basis of py-MBMS spectra. Py-MBMS spectra were also corrected for instrumental variance using generalized linear modeling (GLM) based on the use of select ions relative abundances as spike-in controls. Machine learning classification algorithms e.g., random forest, k-nearest neighbor, decision tree, Gaussian Naïve Bayes, gradient boosting, and multilayer perceptron classifiers were used. The k-nearest neighbors (k-NN) classifier generally performed the best for classifications using raw spectral data, and the decision tree classifier performed the worst. After normalization of spectra to account for instrumental variance, all the classifiers had comparable and generally acceptable performance for predicting the biomass types, although the k-NN and decision tree classifiers were not as accurate for prediction of specific sample types. Gaussian Naïve Bayes (GNB) and extreme gradient boosting (XGB) classifiers performed better than the k-NN and the decision tree classifiers for the prediction of biomass mixtures. The data analysis workflow reported here could be applied and extended for comparison of biomass samples of varying types, species, phenotypes, and/or genotypes or subjected to different treatments, environments, etc. to further elucidate the sources of spectral variance, patterns, and to infer compositional information based on spectral analysis, particularly for analysis of data without a priori knowledge of the feedstock composition or identity

Modeling and Simulation of Aggregation of Membrane Protein LAT with Molecular Variability in the Number of Binding Sites for Cytosolic Grb2-SOS1-Grb2

<div><p>The linker for activation of T cells (LAT), the linker for activation of B cells (LAB), and the linker for activation of X cells (LAX) form a family of transmembrane adaptor proteins widely expressed in lymphocytes. These scaffolding proteins have multiple binding motifs that, when phosphorylated, bind the SH2 domain of the cytosolic adaptor Grb2. Thus, the valence of LAT, LAB and LAX for Grb2 is variable, depending on the strength of receptor activation that initiates phosphorylation. During signaling, the LAT population will exhibit a time-varying distribution of Grb2 valences from zero to three. In the cytosol, Grb2 forms 1∶1 and 2∶1 complexes with the guanine nucleotide exchange factor SOS1. The 2∶1 complex can bridge two LAT molecules when each Grb2, through their SH2 domains, binds to a phosphorylated site on a separate LAT. In T cells and mast cells, after receptor engagement, receptor phosphoyrlation is rapidly followed by LAT phosphorylation and aggregation. In mast cells, aggregates containing more than one hundred LAT molecules have been detected. Previously we considered a homogeneous population of trivalent LAT molecules and showed that for a range of Grb2, SOS1 and LAT concentrations, an equilibrium theory for LAT aggregation predicts the formation of a gel-like phase comprising a very large aggregate (superaggregate). We now extend this theory to investigate the effects of a distribution of Grb2 valence in the LAT population on the formation of LAT aggregates and superaggregate and use stochastic simulations to calculate the fraction of the total LAT population in the superaggregate.</p> </div

Two phase regions in space spanned by bivalent and trivalent LAT concentrations.

<p>(<b>A</b>) Two phase(sol-gel) regions for Grb2 and SOS1 cellular populations of and molecules per cell respectively. The population of monovalent LAT is fixed at three different values, molecules per cell (solid line), molecules per cell (dashed line) and molecules per cell (dotted line). The solid horizontal and vertical lines correspond to the cellular populations of bivalent LAT () and trivalent LAT () being fixed at 10 and 1.5 molecules per cell respectively. (<b>B</b>) Plot of , the fraction of the cellular inhomogeneous LAT population present in the gel phase, as a function of the cellular trivalent LAT population , as predicted from stochastic simulations. The cellular bivalent LAT population () is fixed at 10 molecules per cell. In sync with (A), the solid, dashed and dotted lines correspond to fixed cellular monovalent LAT populations () of , and molecules per cell respectively, and cellular Grb2 and SOS1 populations are fixed at the same values as in (A). The vertical lines correspond to the theoretically predicted boundaries between the one phase (sol) and two-phase (sol-gel) regions obtained by varying along the horizontal line in (a) corresponding to a fixed value of 10 molecules per cell. (<b>C</b>) Plot of simulated values as a function of keeping fixed at 1.5 molecules per cell, and Grb2 and SOS1 fixed at the same values as in (A), for each of the three fixed monovalent LAT populations () in (A). The vertical lines correspond to the theoretically predicted boundaries between the one phase (sol) and two-phase (sol-gel) regions obtained by varying along the vertical line in (A) corresponding to a fixed value of 1.5 molecules per cell.</p

Parameters used in the simulations and the equilibrium model calculations.

<p>This table furnishes values of parameters used in the simulations and the equilibrium model calculations. is a negative cooperativity factor for the binding of a second Grb2 to a Grb2-SOS1 complex (see Eq. (1)) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Houtman1" target="_blank">[6]</a>. The equilibrium constants for the binding of Grb2 to one of the three terminal phosphotyrosines on LAT range from M<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Houtman1" target="_blank">[6]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Houtman2" target="_blank">[33]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Houtman3" target="_blank">[45]</a>. In our model the affinities for these three binding sites are identical. We take M. The values for and are from biacore studies of the binding of the SH2 domain in a Grb2-SOS1 complex to an eleven peptide sequence from the cytoplasmic domain of EGFR that includes the Grb2 binding site pY1068 <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Chook1" target="_blank">[48]</a>. The values of these rate constants have no effect on any of the equilibrium results. The value of the equilibrium crosslinking constant is estimated from the value as in Nag et al. (2009). The rate constant is calculated using the values of and which we assume equals . The value of is taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Sastry1" target="_blank">[49]</a>. The dissociation constants for the binding of the Grb2 SH3 domain to the N-terminal and C-terminal proline-rich regions of SOS1 are 260 and 510 respectively <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Houtman1" target="_blank">[6]</a>. In our model we do not distinguish between the two SH3 binding sites on SOS1 and take , the geometric mean of the two values. The value of is calculated using the value of and the geometric mean of the values. The value of is estimated using Eq. (3) and taking . The diameter of the Jurkat cell, , has been measured by Rosenbluth et al. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0028758#pone.0028758-Rosenbluth1" target="_blank">[50]</a> to be 11.5 with the cytosol taking up about of the total cell volume. is the cytosolic volume. The surface area of the Jurkat cell is taken to be approximately twice the area of a sphere of diameter 11.5 . In the stochastic simulations, only unimolecular rate constants can be used directly so the solution bimolecular rate constants are scaled by the cytosolic volume and the surface bimolecular rate constants are scaled by . The exact values of the parameters we used are given in the table to allow our results to be reproduced. The accuracy of the parameters that have been determined by experiment is at best two significant figures.</p