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Basic Concepts Related to Metabolic Pathway Analysis by 4G8D0j

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									    Basic Concepts Related to
    Metabolic Pathway Analysis
• Closed System vs. Open System
  – A closed system is a system that no material
    (and / or energy) flow-in to / -out from the
    system.
     • E.g. test tube (has no material flow, but has energy
       flow), batch reactor, etc.
  – An open system is a system with both
    material and energy flow-in to / -out from the
    system.
     • E.g. CSTR, plug-flow reactor, cell, etc.
      Basic Concepts Related to
      Metabolic Pathway Analysis
• Steady state:
      A state where none of any variable changes vs.
      time.
• Equilibrium:
      A condition where competing influences are
      balanced, e.g. chemical equilibrium – a condition
      that the concentrations of reactants and products
      have no net change over time and in they are in
      equilibrium.
•    You should pay attention to the fact that, in reaction
      engineering, equilibrium is one type of the steady
      state but steady state is not necessarily equilibrium.
      This will be demonstrated in following examples.
           Irreversible Reaction
             in Closed System
• Consider an irreversible reaction that carried out
  in test tube environment.
                       AB
• We put 100 M A and 0 M B into the test tube
  initially.
• Simulate this reaction in Polymath:
                               Irreversible Reaction
                                 in Closed System
• If we have long enough in time, all A will be converted into B, and
  the rate of reaction (rF) will be zero when A is consumed.

                       Irreversible Reaction                                           Irreversible Reaction
                            in Test Tube                                                    in Test Tube

             100                                                            1000
              90                                                             900
              80                                                             800
              70                                                             700




                                                                Conc. (M)
 Conc. (M)




              60                                                             600
                                                        A
              50                                                             500                                     rF
                                                        B
              40                                                             400
              30                                                             300
              20                                                             200
              10                                                             100
               0                                                               0
                   0     0.2    0.4         0.6   0.8       1                      0      0.2   0.4     0.6    0.8        1
                                  t (min)                                                         t (min)
           Reversible Reaction
            in Closed System
• Consider a reversible reaction that carried out in
  test tube environment.
                      A  B
• We put 100 M A and 0 M B into the test tube
  initially.
• Simulate this reaction in Polymath:
Reversible Reaction in a Closed
            System
                                                                 Beq
• Equilibrium constant, Keq, is equal to:              K eq 
                                                                 Aeq

• At equilibrium: forward reaction rate = backward reaction
  rate (they are not zero).                rFeq  rBeq


• At equilibrium:     rFeq  kF   Aeq   rB eq  kB  B eq


                        Beq       kF
• Therefore:     K eq          
                        Aeq       kB


• For this example, Keq = 5, i.e. at equilibrium, [B]eq will be
  5 times of [A]eq.
                                 Reversible Reaction
                                 in a Closed System
•         At equilibrium, [B]eq = 83.3 M and [A]eq = 16.7 M ( [B]eq / [A]eq = Keq = 5.0 ).
•         And rF = rB = 166.67 M / min.
•         This system is in equilibrium and steady state, where [A], [B], rF and rB have no
          further change.
                          Reversible Reaction                                                Reversible Reaction
                             in Test Tube                                                       in Test Tube

                100                                                               1000
                 90                                                                900
                 80                                                                800
                 70                                                                700
    Conc. (M)




                                                                      Conc. (M)
                 60                                                                600
                                                              A                                                              rF
                 50                                                                500
                                                              B                                                              rB
                 40                                                                400
                 30                                                                300
                 20                                                                200
                 10                                                                100
                  0                                                                  0
                      0    0.2    0.4             0.6   0.8       1                      0     0.2   0.4         0.6   0.8        1
                                        t (min)                                                        t (min)
          Reversible Reaction
      in Open System with Feeding
• Consider the same reversible reaction, but it is carried out in cellular
  environment.
                           Ax  (( A  B ))
• Ax is A outside the cell (external). A is transported into the cell by a
  unidirectional transport enzyme.
• Initially, we have 100 M A and 0 M B inside the cell, and we have 10
  M Ax (that Ax always keeps constant).
• Simulate this reaction in Polymath:
                    Reversible Reaction
                in Open System with Feeding
• Note that as the cell keeps uptaking A into the cell , A
  will “accumulate” inside the cell and this system can
  never achieve steady state.
                        Reversible Reaction                                           Reversible Reaction
                        in Cell, with Feeding                                         in Cell, with Feeding

                                                                            500
              120                                                           450
                                                                                                                      rF
              100                                                           400
                                                                                                                      rB
                                                                            350
                                                                                                                      rIN


                                                                Conc. (M)
  Conc. (M)




               80                                                           300
                                                        A
                                                                            250
               60                                       B
                                                                            200
               40                                                           150
                                                                            100
               20
                                                                             50
                0                                                             0
                    0      1      2             3   4       5                     0     1       2             3   4         5
                                      t (min)                                                       t (min)
          Reversible Reaction
    in Open System with Withdrawal
•   Consider the same reversible reaction, but it is carried out in cellular
    environment.
                                (( A  B ))  Bx
•   Bx is B outside the cell (external). B is transported out from the cell by a
    unidirectional transport enzyme.
•   Initially, we have 100 M A and 0 M B inside the cell, and we have 10 M Bx
    (that Bx always keeps constant).
•   Simulate this reaction in Polymath (note that Bx will not affect this system):
          Reversible Reaction
    in Open System with Withdrawal
• Note that as the cell keeps losing B, this system can be at steady
  state when all A converted into B and all B transported out from the
  cell. (I.e., [A] = [B] = 0 M.)
                         Reversible Reaction                                           Reversible Reaction
                        in Cell, with Withdraw                                        in Cell, with Withdraw

              100                                                           300
               90
                                                                            250
               80
               70
                                                                            200
  Conc. (M)




                                                                Conc. (M)
               60                                                                                                     rF
                                                        A
               50                                                           150                                       rB
                                                        B
               40                                                                                                     rOUT
                                                                            100
               30
               20
                                                                             50
               10
                0                                                             0
                    0      1      2             3   4       5                     0      1      2             3   4        5
                                      t (min)                                                       t (min)
                Reversible Reaction
                 in Open System
           with Feeding and Withdrawal
•   Consider the same reversible reaction, but it is carried out in cellular
    environment.
                              Ax  (( A  B ))  Bx
•   A is transported into the cell and B is transported out from the cell by
    unidirectional transport enzymes.
•   Initially, we have 100 M A and 0 M B inside the cell, and we have 10 M Ax, 10
    M Bx (that Ax and Bx always keeps constant).
•   Simulate this reaction in
    Polymath (note that Bx
    will not affect this
    system):
                               Reversible Reaction
                                 in Open System
                           with Feeding and Withdraw
•   Note that the system finally achieves steady state, where rIN = rOUT = (rF - rB).
•   [A]final = 3.0 M, [B]final = 10.0 M, [B]final / [A]final = 3.33 ≠ Keq (where is 5 in this example).
•   Therefore, steady state is not always equivalent to equilibrium, but equilibrium is
    always equivalent to steady state.
                           Reversible Reaction                                            Reversible Reaction
                           in Cell, with Feeding                                          in Cell, with Feeding
                               and Withdraw                                                   and Withdraw

                 100                                                            200
                  90                                                            180                                       rF
                  80                                                            160                                       rB
                  70                                                            140                                       rIN
     Conc. (M)




                                                                    Conc. (M)
                  60                                       A                    120
                                                                                                                          rOUT
                  50                                       B                    100
                  40                                                             80
                  30                                                             60
                  20                                                             40
                  10                                                             20
                   0                                                              0
                       0     2       4             6   8       10                     0     2       4             6   8         10
                                         t (min)                                                        t (min)
     Steady State vs. Equilibrium
        in Reaction Pathway
• In a reaction pathway that consists many
  reactions in series, and we have a reversible
  reaction (A  B) in this pathway.
• At steady state, rF = rB and we have net
  reaction rate = 0.
• In order to have net forward reaction rate (at
  steady state), [A]ss > [A]eq, and/or [B]ss < [B]eq.
• Therefore, [B]ss / [A]ss must be less than Keq.

								
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