GPU-based Linear Algebra for Calculating Steady-State Probability and Dynamics of Molecular Networks

In this thesis we present a GPU-based implementation for the linear algebra kernels necessary to perform steady-state and dynamics study of biochemical reaction networks. The underlying goal is to provide a practical implementation for the Chemical Master Equation framework, a stochastic and discrete-state continuos-time formulation that provides a fundamental framework for biochemical reaction networks in the cell. In general, the study of CME may provide some deeper understanding of the issues involved through concrete biological network. The CME framework provides an exact representation of the microscopical state by considering the detailed chemical amount of each and every molecular species. This leads to an exponentially growing microstate space and, hence, to a computational challenge. From these premises it follows that we need a more efficient implementation for the linear algebra methods used by the theoretical framework to calculate steady-state and dynamics. A viable solution to accelerate linear algebra kernels is the use of Graphic Processing Units (GPUs), an emerging highly parallel computer architecture available on a single chip. This technology is well suited for dense linear algebra due to its high floating point instruction throughput and due to its large memory bandwidth. Therefore, we design a GPU-based implementation of a steady-state probability landscape solver (based on Jacobi iteration) and a dynamics simulation (based on Arnoldi) According to experimental results, it is now possible to efficiently deal with more realistic biochemical networks, up to 56 million microscopic states and 99x faster for steady-state analysis and up to 18 million states and 28x faster for dynamics analysis, allowing a close comparison between theoretical predictions and laboratory experiments

Sparse Convex Optimization on GPUs

Convex optimization is a fundamental mathematical framework used for general problem solving. The computational time taken to optimize problems formulated as Linear Programming, Integer Linear Programming or Quadratic Programming has an immediate impact on countless application fields, and it is critical to determining which problems we will be able to solve in the future. Since the very beginning, the research community has always been investigating on new algorithmic and numerical techniques to speed up convex optimization. Recently, the focus has included parallel computer architectures and their ability to perform high-throughput computation. This dissertation continues on the same research direction developing novel computational techniques tailored for modern GPUs. We focus on problems with sparse structure which are, arguably, the most challenging to solve on throughput-oriented many-core architectures naturally well-suited for dense computations As original contribution, we combine the leading ideas in SpMV optimization on GPUs into an advanced sparse format known as AdELL+. We also speed up the class of optimization algorithms known as Interior Points Methods with GPU-based adaptive strategies to select between Cholesky factorization and Conjugate Gradient. Last, we design an incremental matrix data structure that provides the foundation for implementing “branch-and-cut” ILP solvers

Cytoplasmic vesicle localisation.

<p>Fluorescence microscopy images confirming intra-cellular vesicle localisation. (A) Hcc-1, (B) HepG2, (C) Hep3B, and (D) SNU475 cells. Sunitinib autofluorescence (green), CD29 staining (red) and Hoechst 33342 nuclear staining (blue). Original magnification 40x.</p

Immunophenotyping.

<p>The table shows the mean percentage of cells positive for each marker.</p><p>Immunophenotyping.</p

Hypothesised mechanism of the enhanced efficacy of drug pre-treatment before verapamil administration and PGP blockade.

<p>A) HCC cells expressing active PGP can expel a drug (e.g. sunitinib) from the cytoplasm or store it in lysosomes. B) Blocking PGP with verapamil before the co-administration sunitinib and verapamil allows the drugs to enter the cell and diffuse into cytoplasm/nucleus. C) If sunitinib is used for pre-treatment, it is stored in giant lysosomes and, after the co-administration of sunitinib and verapamil and subsequent PGP blockade, the drugs can enter the cytoplasm/nucleus from both extra-cellular space and the lysosomes.</p

Flow cytometry evaluation of MDRPs.

<p>LRP and MRP1 were not detected by means of flow cytometry in any cell line. ABCG2 was expressed on only 9% of the Hcc-1 cells, and was almost absent on the surface of the other cell lines. ABCB1 (PGP) was highly expressed on the plasma membrane of HepG2 (58%), Hcc-1 (18%) and HuH7 cells (13%), but expressed on only about 3% of PLC/PRF/5 cells. Left column negative controls; middle column ABCG2 expression; right column PGP expression.</p

Immunofluorescence staining of MDRPs.

<p>Representative pictures of MDRP staining in HCC cell lines. The expression and localisation of MDRPs was different in the various HCC cell lines: ABCG2, LRP and MRP1 were localised on the membrane of the few groups of cells on which they were expressed, whereas PGP was mainly found in the cell cytoplasm, particularly on the membrane of intra-cellular vesicles. Nuclei stained with DAPI (blue). Original magnification 20x.</p

Time-lapse experiments.

<p>Over a period of seven hours it is possible to see that some lysosomes released their content outside the cells (top row, white circles), whereas others started to accumulate new sunitinib in their lumens (bottom row, white arrowheads).</p

Sunitinib accumulation in cytoplasmic vesicles of HCC cell lines.

<p>Representative pictures of cell lines cultured without (left) or with (right) sunitinib 12 µM. Cytoplasmic vesicles are visible in the Hep3B and SNU475 cells only after sunitinib incubation. Original magnification 20x.</p

Chemoresistance assays.

<p>A) When treated with sorafenib, the cell lines with giant PGP-positive lysosomes (Hcc-1, HepG2, PLC/PRF/5 and HuH7) showed higher IC₅₀ values than those with normal lysosomes (Hep3B and SNU475) (p<0.01). B) The HCC cell lines were incubated with different concentrations of sorafenib in order to verify their chemosensitivity (green lines). The cells with larger cytoplasmic vesicles were characterised by a curve with a sort of plateau of viability at sorafenib concentrations of between 5 and 20 µmol. One hour of verapamil pre-treatment used to inhibit ABC proteins before co-incubation with sorafenib and sunitinib increased the chemosensitivity of all of the cell lines (black curves). *p<0.01 green vs. black curves. One hour of sorafenib pre-treatment (red lines) before co-incubation with sorafenib and sunitinib enhanced treatment efficacy in comparison with verapamil pre-treatment in the cell lines carrying giant lysosomes. ^§p<0.05 red vs. black curves.</p