Seminar in bioinformatics
Download
1 / 64

Seminar in bioinformatics - PowerPoint PPT Presentation


  • 51 Views
  • Uploaded on

Seminar in bioinformatics. Computation of elementary modes: a unifying framework and the new binary approach. Julien Gagneur and Steffen Klamt. BMC Bioinformatics 2004, 5:175. Elad Gerson, Spring 2006, Technion. Agenda. Quick overview of last week’s lecture. Extension of the EP concept.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Seminar in bioinformatics' - petra


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Seminar in bioinformatics

Seminar in bioinformatics

Computation of elementary modes: a unifying framework and the new binary approach

Julien Gagneur and Steffen Klamt

BMC Bioinformatics 2004, 5:175

Elad Gerson, Spring 2006, Technion.


Agenda
Agenda

  • Quick overview of last week’s lecture.

  • Extension of the EP concept.

    • Enter EM.

  • General framework for EM computation.

    • Reversible reactions split.

    • Network compression.

    • Post processing.

  • Some implementation tweaks.


Last week on bioinformatics seminar
Last week on bioinformatics seminar!

Given a metabolic network we wish to find all the possible flux distributions which results in a steady state.

Meaning, the overall flux in a pathway is 0.


Last week on bioinformatics seminar1
Last week on bioinformatics seminar!

This is done by describing the pathway as a stoichiometric matrix S, solving the equation –


Last week on bioinformatics seminar2
Last week on bioinformatics seminar!

Notice that we are interested only in solutions where

(sign suggests reaction’s direction).

Solution space is spanned by linearly independent vectors.

We look for a spanning set s.t. every solution can be written as a linear combination of the spanning vector where all coefficients are non-negative (Genetically independent).

Those solutions are called

Extreme pathways (EP).

Can be found using the Null

Space Approach (NSA)

Algorithm.


Problem
Problem

Biology suggests some reaction are reversible.

Consider the following network for instance –

R5 can work in both directions (Not simultaneously!)


Solution
Solution ?

Remove the restriction, signs suggests direction ..

Bad idea ..

  • Not all reactions are reversible.

  • Solutions no longer take the form of a polyhedral cone.


Solution1
Solution !

Split the reversible reactions ..

Find Extreme Pathways using the NSA algorithm.

Post process found EPs, merge split reactions (“opposite direction” should be set with a negative sign).

Post processed EPs are now called - Elementary Modes (EM).

R5a

R5b


Compressing the network
Compressing the network

Removing redundancies

Can be united..


Compressing the network1
Compressing the network

Removing redundancies

R1 is null in any feasible

steady state


Compressing the network2
Compressing the network

Removing redundancies

Contradict each other ..

Can be eliminated.


Compressing the network3
Compressing the network

Removing redundancies

Active in any stead state.


Compressing the network4
Compressing the network

Removing redundancies

  • Some redundancies can be detected as dependent linear rows in the kernel matrix.

  • Iterative approach, remove redundancies until non detected.

    • Produce better results.


General framework
General framework

Preprocessing -

  • Metabolic networks yield deeper insight of organisms metabolism.

  • Failure modes analysis will provide

    • Crucial parts identification.

    • Suitable targets for repressing undesired metabolic functions.

  • Apply NSA algorithm.

  • Post process.


  • One more tweak
    One more tweak

    • The authors offers an efficient implementation to the NSA and CBA (Combined basis – Schuster et. al.) algorithms.

      • Using binary representation for vectors.

        • Fast bit operators.

        • Efficient memory usage (up to 1.6% of original!)


    Seminar in bioinformatics1

    Seminar in bioinformatics

    Minimal cut sets in biochemical reaction

    networks

    Steffen Klamt and Ernst Dieter Gilles

    Bioinformatics Vol. 20 no. 2 2004, pages 226–234

    Elad Gerson, Spring 2006, Technion.


    Abstract
    Abstract

    • Motivation

      • Metabolic networks yield deeper insight of organisms metabolism.

      • Failure modes analysis will provide

        • Crucial parts identification.

        • Suitable targets for repressing undesired metabolic functions.

    • Results

      • The biochemical networks minimal cut sets concept.

      • Algorithm which computes MCS with respect to an objective reaction.

      • Potential applications includes

        • phenotype predictions.

        • Network verifications.

        • Structural robustness and fragility assessment.

        • Metabolic flux analysis.

        • Target identification in drug discovery.


    Introduction
    Introduction

    • Assume we wish to prevent the production of metabolite X.

      • i.e. there is no balanced flux distribution possible which involves obR.

      • Can be done by gene deletion or enzyme inhibition.


    Introduction1
    Introduction

    Definition - We call a set of reactions a cut set(with

    respect to a defined objective reaction) if after the removal

    of these reactions from the network no feasible balanced flux

    distribution involves the objective reaction.


    Introduction2
    Introduction

    • That’s easy .. Consider C0 = {obR}

      • One might wish to cut the reaction at the beginning.

      • What if there are numerous obR’s ?

        • Simultaneous failure might be achieved more efficiently.


    Introduction3
    Introduction

    • Take two – Remove all reactions except for oBR.

      • Not efficient.

      • Notintelligent.


    Introduction4
    Introduction

    • Consider C1 = {R5, R8}

      • Sufficient.

      • Neither the removal of R5 nor R8 is sufficient.

    • No subset of C1 is a valid cut set → C1 is minimal.


    Introduction5
    Introduction

    Definition - A cut set C (related to a defined objective reaction)

    is a minimal cut set (MCS) if no proper subset of C is a

    cut set.

    Can you spot all the MCS in the network ?


    Introduction6
    Introduction

    Is C2 = {R2, R4, R6} minimal ?


    Introduction7
    Introduction

    Is C3 = {R2, R5, R7} ?


    Introduction8
    Introduction

    How about C1 = {R1} ?


    Introduction9
    Introduction

    • OK, what about Graph disconnectivity algorithms ?

      • No good, They don’t take the hypergraph nature of metabolic pathways into account.


    The algorithm
    The algorithm

    Initialization

    • Calculate the EMs in the given network

    • Define the objective reaction obR

      (3) Choose all EMs where reaction obR is non-zero and

      store it in the binary array em_obR (em_obR[i][j]==1

      means that reaction j is involved in EM i)

      (4) Initialize arrays mcs and precutsets as follows (each

      array contains sets of reaction indices): append {j } to mcs if reaction j is

      essential (em_obR[i][j]=1 for each EM i), otherwise to precutsets


    The algorithm1
    The algorithm

    (5) FOR i=2 TO MAX_CUTSETSIZE

    (5.1) new_precutsets=[ ];

    (5.2) FOR j = 1 TO q (q: number of reactions)

    (5.2.1) Remove all sets from precutsets where reaction j participates

    (5.2.2) Find all sets of reactions in precutsets that do not cover at least one EM in em_obR where reaction j participates; combine each of these sets

    with reaction j and store the new preliminary cut sets in temp_precutsets

    (5.2.3) Drop all temp_precutsets which are a superset of any of the already determined minimal cut sets stored in mcs

    (5.2.4) Find all retained temp_precutsets which do nowcover all EMs and

    append them to mcs; append all others to new_precutsets

    ENDFOR

    (5.3) If isempty(new_precutsets)

    (5.3.1) Break

    ELSE

    (5.3.2) precutsets=new_precutsets

    ENDIF

    ENDFOR

    (6) result: mcs contains the MCSs


    Running example
    Running example

    Initialization – Calculate EM

    We are only interested

    in EM containing obR


    Running example1
    Running example

    Initialization

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}


    Running example2
    Running example

    I = 2, j = 1

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {}


    Running example3
    Running example

    I = 2, j = 1

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {{1 2}}


    Running example4
    Running example

    I = 2, j = 1

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {{1 2}, {1 3}, {1 4}, {1 5} {1 6}}


    Running example5
    Running example

    I = 2, j = 1

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {{1 2}, {1 3}, {1 4}, {1 5} {1 6} {1 7} {1 8}}


    Running example6
    Running example

    I = 2, j = 1

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {{1 2}, {1 3}, {1 4}, {1 5}, {1 6}, {1 7}, {1 8}}


    Running example7
    Running example

    I = 2, j = 2

    mcs = {{1}}, precutsets = {{2},{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {}


    Running example8
    Running example

    I = 2, j = 2

    mcs = {{1}}, precutsets = {{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {}


    Running example9
    Running example

    I = 2, j = 2

    mcs = {{1}}, precutsets = {{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {{2 4}}


    Running example10
    Running example

    I = 2, j = 2

    mcs = {{1}}, precutsets = {{3},{4},{5},{6},{7},{8}}

    new_precutsets = {}

    temp_precutsets = {{2 4},{2 6},{2 7},{2 8}}


    Running example11
    Running example

    I = 2, j = 2

    mcs = {{1}}, precutsets = {{3},{4},{5},{6},{7},{8}}

    new_precutsets = {{2 4}}

    temp_precutsets = {{2 6},{2 7},{2 8}}


    Running example12
    Running example

    I = 2, j = 2

    mcs = {{1}}, precutsets = {{3},{4},{5},{6},{7},{8}}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}}

    temp_precutsets = {}


    Running example13
    Running example

    I = 2, j = 5

    mcs = {{1}}, precutsets = {{5},{6},{7},{8}}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}, ..}

    temp_precutsets = {}


    Running example14
    Running example

    I = 2, j = 5

    mcs = {{1}}, precutsets = {{6},{7},{8}}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}, ..}

    temp_precutsets = {{5 6},{5 7},{5 8}}


    Running example15
    Running example

    I = 2, j = 5

    mcs = {{1}}, precutsets = {{6},{7},{8}}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}, ..}

    temp_precutsets = {{5 6},{5 7},{5 8}}


    Running example16
    Running example

    I = 2, j = 5

    mcs = {{1}, {5 6}}, precutsets = {{6},{7},{8}}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}, ..}

    temp_precutsets = {{5 7},{5 8}}


    Running example17
    Running example

    I = 2, j = 5

    mcs = {{1}, {5 6}, {5 7}}, precutsets = {{6},{7},{8}}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}, ..}

    temp_precutsets = {{5 8}}


    Running example18
    Running example

    I = 2, j = 8

    mcs = {{1}, {5 6}, {5 7}, {5 8}}, precutsets = {}

    new_precutsets = {{2 4},{2 6},{2 7},{2 8}, ..}

    temp_precutsets = {}


    Running example19
    Running example

    I = 3, j = 2

    mcs = {{1}, {5 6}, {5 7}, {5 8}}, precutsets = {{2 4},{2 6},{2 7},{2 8},…{4 6},…}

    new_precutsets = {}

    temp_precutsets = {}


    Running example20
    Running example

    I = 3, j = 2

    mcs = {{1}, {5 6}, {5 7}, {5 8}}, precutsets = {…{4 6},…}

    new_precutsets = {}

    temp_precutsets = {…}


    Running example21
    Running example

    I = 3, j = 2

    mcs = {{1}, {5 6}, {5 7}, {5 8}}, precutsets = {…{4 6},…}

    new_precutsets = {…}

    temp_precutsets = {{2 4 6},…}


    Running example22
    Running example

    I = 3, j = 2

    mcs = {{1}, {5 6}, {5 7}, {5 8}, {2 4 6}}, precutsets = {…{4 6},…}

    new_precutsets = {…}

    temp_precutsets = {…}


    Running example23
    Running example

    I = 3, j = 8

    mcs = {{1}, {5 6}, {5 7}, {5 8}, {2 4 6},…}, precutsets = {}

    new_precutsets = {…}

    temp_precutsets = {…}


    Complexity
    Complexity

    • Let q be the number of reactions.

    • Assuming |EM| << q.

    • In initialization q singletons are generated and tested.

    • In the i-th iteration

      • Overall number of temp_precutsets generated

      • O(p) comparisons are made.

    • Hence, (All subsets of q items)

      • Yes .. exponential..

    • Maximal MCS size << q bounds polynomial approximation.


    Mcs in central metabolism of e coli
    MCS in central metabolism of E. coli

    • MCS calculated with ‘biomass synthesis’as objective reaction (growth).

      • Network comprises 110 reactions and 89 metabolites.

      • Catabolic (material breakdown) part modeled in details.

        • Enables excretion of 5 metabolites.

        • Uptake of glucose, acetate, glyceroland succinate.

        • Growth on each substrate was tested separately.



    Possible applications
    Possible applications

    Structural fragility and robustness

    • MCS can be used for “risk assessment” in metabolic pathways.

      • More EMs suggested a more robust and less fragile pathway.

        • EMs number and MCSs size are strongly correlated. (More elements must fail).

        • We seek a better criteria.

    Glucose is known to be the least fragile growth substrate

    having most EMs and apparently longest MCSs

    ‘Dangerous’ MCSs


    Possible applications1
    Possible applications

    Structural fragility and robustness

    Definition – Reaction fragility factor Fi is the reciprocal of the

    average size of all the MCSs the reaction i participates.


    Possible applications2
    Possible applications

    Structural fragility and robustness

    Definition – Reaction fragility factor Fi is the reciprocal of the

    average size of all the MCSs the reaction i participates.

    May suggest reaction’s

    importance.


    Possible applications3
    Possible applications

    Structural fragility and robustness

    Definition – Reaction fragility factor Fi is the reciprocal of the

    average size of all the MCSs the reaction i participates.

    Is there a correlation between Fi

    and the number of EMs the

    reaction participates?


    Possible applications4
    Possible applications

    Structural fragility and robustness


    Possible applications5
    Possible applications

    Structural fragility and robustness

    Definition – Network fragility F is defined as

    where q is then number of reactions.


    Possible applications6
    Possible applications

    Network verification and mutant phenotype predictions.

    • Cutting an MCS is predicted to leave a metabolic pathway dysfunctional.

    • Apply the algorithm with ‘growth’ as obR.

      • If a set of gene deletions (or mutants) contains an MCS a non-viable phenotype is expected.

        • Viable phenotype would be a false negative.

          • Proof for incorrect or incomplete network.

      • Otherwise growth is possible.

        • Non-viable phenotype would be a false positive.

          • May suggest a false assumption in the network structure.

            • One of the reactions in the MCS might be of regulatory nature.


    Possible applications7
    Possible applications

    Target identification and repressing cellular functions.

    MCS offers a theoretical tool for target identification in drug discovery.

    • An irreducible set of interventions needed for pathway dysfunction.

    • Usually we will look for minimal size of MCS.

    • Other pathways should be weakly affected.

      • Can be checked easily – set of untouched EM’s.

      • MCS 0, 2, 3, 4 will not affect EM1


    ad