Computational Modeling of Cell Signaling Dynamics: Hypothesis Management and Parameter Estimation Methods Applied to the Akt Pathway

Ph.DDOCTOR OF PHILOSOPH

SPEDRE: a web server for estimating rate parameters for cell signaling dynamics in data-rich environments

Cell signaling pathways and metabolic networks are often modeled using ordinary differential equations (ODEs) to represent the production/consumption of molecular species over time. Regardless whether a model is built de novo or adapted from previous models, there is a need to estimate kinetic rate constants based on time-series experimental measurements of molecular abundance. For data-rich cases such as proteomic measurements of all species, spline-based parameter estimation algorithms have been developed to avoid solving all the ODEs explicitly. We report the development of a web server for a spline-based method. Systematic Parameter Estimation for Data-Rich Environments (SPEDRE) estimates reaction rates for biochemical networks. As input, it takes the connectivity of the network and the concentrations of the molecular species at discrete time points. SPEDRE is intended for large sparse networks, such as signaling cascades with many proteins but few reactions per protein. If data are available for all species in the network, it provides global coverage of the parameter space, at low resolution and with approximate accuracy. The output is an optimized value for each reaction rate parameter, accompanied by a range and bin plot. SPEDRE uses tools from COPASI for pre-processing and post-processing. SPEDRE is a free service at http://LTKLab.org/SPEDRE.Singapore-MIT Alliance (IUP R-154-001-348-646

CBESW: Sequence Alignment on the Playstation 3

<p>Abstract</p> <p>Background</p> <p>The exponential growth of available biological data has caused bioinformatics to be rapidly moving towards a data-intensive, computational science. As a result, the computational power needed by bioinformatics applications is growing exponentially as well. The recent emergence of accelerator technologies has made it possible to achieve an excellent improvement in execution time for many bioinformatics applications, compared to current general-purpose platforms. In this paper, we demonstrate how the PlayStation^®3, powered by the Cell Broadband Engine, can be used as a computational platform to accelerate the Smith-Waterman algorithm.</p> <p>Results</p> <p>For large datasets, our implementation on the PlayStation^®3 provides a significant improvement in running time compared to other implementations such as SSEARCH, Striped Smith-Waterman and CUDA. Our implementation achieves a peak performance of up to 3,646 MCUPS.</p> <p>Conclusion</p> <p>The results from our experiments demonstrate that the PlayStation^®3 console can be used as an efficient low cost computational platform for high performance sequence alignment applications.</p

Initial concentrations of the species in the H0 model.

<p>Note that the PIP3 time-course is interpolated from experimental observations and not governed by the equations of the model. Aktp³⁰⁸ is defined to be the sum of Aktp³⁰⁸m and Aktp³⁰⁸c. Initial concentrations of PIP3:PDK1m and Aktp³⁰⁸c were chosen such that the total (membrane plus cytosolic) amount of PDK1 (PDK_total) and Akt (Akt_total) would be 10.</p

Akt is retained at the cell membrane after a decrease in PIP3.

<p>MEF PTEN-/- cells were treated with 25μM LY29 or 6μM DPI for 2hrs before the cytosol and membrane fractions were separated. Abundance of total Akt or total PDK1 were assessed in each fraction by Western blot. The fractionation of membrane-bound from cytosolic is demonstrated by the presence of Cadherin and absence of SOD1 (superoxide dismutase-1). Treatment with DPI (diphenylene iodonium) can be viewed as providing an additional control for the effect of LY29 toward the membrane-bound pool of Akt, because we had previously shown DPI treatment affects phosphorylation of the cytosolic fraction of Akt but not the membrane-bound fraction [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004505#pcbi.1004505.ref048" target="_blank">48</a>]. DMSO: dimethylsulfoxide.</p

Five alternative hypotheses, each with one non-canonical effect (in red).

<p>Enumerating the steps of the canonical pathway, downstream of PIP3 and upstream of Aktp³⁰⁸, yielded five alternatives: (<b>A</b>) the PIP3-dependent recruitment model M1, (<b>B</b>) the PIP3-independent recruitment model M2, (<b>C</b>) the retention model M3, (<b>D</b>) the dephosphorylation model M4, and (<b>E</b>) the phosphorylation model M5. For each alternative model, a pseudo-reaction (shown in red) perturbs the canonical pathway, and the strength of the deviation over time is determined by a time-dependent spline curve (not shown). In the retention model (M3), the membrane-bound phosphorylated Akt (Aktp³⁰⁸m) is divided into two hypothetical subpopulations: membrane-free (Aktp³⁰⁸mf, which can dissociate from the membrane) and membrane-trapped (Aktp³⁰⁸mt, which cannot dissociate from the membrane). In the dephosphorylation model (M4), cytosolic phosphatases (including PP2A and other factors capable of dephosphorylating Aktp³⁰⁸) are represented by two subpopulations: normal phosphatases (Phosphatase), and inaccessible/inactive phosphatases (InaccPhosphatase). <b>(F)</b> Flowchart for optimizing each alternative model, with its non-canonical effect, to fit the experimental data. The model consists of a canonical network with rate parameters, and a non-canonical deviation. The non-canonical deviation was encoded as a pseudo-species with an unknown spline curve for its time series profile. Unknown parameters of the model (including the knots of the spline curve and some of the biochemical reaction rates) were optimized, with many cycles of iteration, until the simulated model was able to fit the data.</p

The fits of alternative models to the experimental data.

<p>Comparisons show experimental time-series (dotted lines) and simulated time courses (solid lines) for (<b>A-B</b>) the PIP3-independent recruitment model, (<b>C-D</b>) the PIP3-dependent recruitment model, (<b>E-F</b>) the retention model, (<b>G-H</b>) the dephosphorylation model and (<b>I-J</b>) the phosphorylation model, each with Aktp³⁰⁸ in the total cell lysate (blue curve), membrane PDK1 (red curve), TotMemAkt (purple curve), and membrane Aktp³⁰⁸ (green curve). All plots of concentration (abundance) use arbitrary units. The criteria for match are whether the model can reproduce the peak time, peak duration and peak amplitude of the observed trend. The purple curves in (H) and (J) were considered implausible by human inspection and their scores showed high violations (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004505#pcbi.1004505.s005" target="_blank">S1 Tables</a>) due to the mismatch shown by the purple arrows. The green curves in (<b>F</b>), (<b>H</b>) and (<b>J</b>) were considered problematic but not necessarily in violation of the data. (<b>K-O</b>) The peak time of each model (red diamond) was compared with the observed peak (blue triangle), and gray bars indicate the difference. Σ(err) shows the sum of the error in peak time, across the four species of comparison.</p

Model predictions and experimental measurements of total membrane-bound Akt after LY29 treatment.

<p>(<b>A</b>) Time course simulation of: (<b>i</b>) Aktp³⁰⁸, (<b>ii</b>) membrane PDK1, (<b>iii</b>) total membrane-bound Akt, and (<b>iv</b>) membrane phosphorylated Akt. Simulations used three alternative models: PIP3-dependent recruitment, PIP3-independent recruitment, and retention. The simulations of the “control” experiments (solid lines, called 10%FBS) are repeated from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004505#pcbi.1004505.g006" target="_blank">Fig 6</a> and they used the experimentally observed PIP3 levels as upstream input. The simulations of PIP3 inhibition (dashed lines) used the same models and same parameters, but the PIP3 input curve was set to be constant, at the observed level of PIP3 in unstimulated cells. Model predictions suggested that total membrane-bound Akt (black arrow) has non-trivial dynamics under the PIP3-independent recruitment hypothesis. (<b>B</b>) Immunoblot of membrane fraction Akt in serum-stimulated MEFs after pre-treatment with LY29 (representative of n = 3 repeats, other repeats not shown). (<b>C)</b> Quantified measurements of TotMemAkt after LY29 treatment (dashed black line) were plotted for comparison with simulations of the three alternative models (solid color lines). Black dashed line: observed time-series for TotMemAkt (n = 3 replicates). Solid color lines: simulated time course of membrane total Akt from each model.</p

The canonical model of Akt activation.

<p>(<b>A</b>) Network diagram for the canonical pathway, which is the null hypothesis (H0). The phosphatases capable of dephosphorylating Aktp³⁰⁸ are represented by a single entity in the model, named “Phosphatase.” (<b>B</b>) Time course simulations of 100 best-fit models for H0 (black solid lines) compared with measured Aktp³⁰⁸ time-series (red dashed line) show major, qualitative discrepancies. All simulated time courses were normalized to have the same concentration at t = 120min. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004505#sec017" target="_blank">materials and methods</a> for the construction and simulation of the models.</p