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UNDERSTANDING BIOCHEMICAL SYSTEM FOR PATHWAYS RECONSTRUCTION Hiren Karathia (Ph.D- System Biology and Bioinformatics) Supervisor: Dr. Rui Alves Ref from: Prof. Michael A. Savageu and Dr. Claudio cobelli, David Foster and Gianna Toffolo 14 th January 2010

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System System is a set of interacting or interdependent entities forming an integrated whole. The concept of an 'integrated whole' can also be stated in terms of a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the set and elements not a part of the relational regime. System dynamics is an approach to understanding the behavior of system over time.

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Most systems share common characteristics, including: Structure: defined by parts and their composition; Behavior: which involves inputs, processing and outputs of material, energy or information; Interconnectivity: the various parts of a system have functional as well as structural relationships between each other.

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Biological System In Biology, a Biological system is a group of biological entities that work together to perform certain task. ENERGY COMPLEXITY LEVEL OF CLASSIFICATION

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System complexity at the scale of size & time Atom coordinate at 0.1 - 1.0 nm Atoms are interact at 0.1 - 10 ns Molecules coordinate at 0.1 - 1.0 nm Molecules interact at 10ns - 10 ms Cellular Scale Concentration of molecules 10 - 100 nm Diffusion rate 10ms – 1000 s

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System complexity at the scale of size & time Tissue Scale Metabolic input can be provided 0.01m - 1.0 m Metabolic output can be obtained 1 s – 1 hr Tracer Kinetics Organism scale Behaviors of animal could be studied for 0.01m – 4.0 m Habitats could be studied for 1 hr – 100 yrs

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ENERGY CONCEPT IN BIOLOGICAL SYSTEM Organisms must deal with many form of energy to do functions but the basic unit of energy is by mean of exchange CHEMICAL ENERGY. All other types of energies, i.e., mechanical energy, are inter-convertible with the chemical forms by means of specialized energy transduction process.

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What are the chemicals in cellular systems Common chemical basis in all form of life in a cell are -Proteins -Nucleic Acids -Minerals -Vitamins -Metabolites Major functional unit of cells, which gives dynamicity to cell is Proteins: Proteins are functionally classified as -Enzymes -Regulators -Interactors -Transcription factors -Receptors -Ligands Major functional unit of cells, which gives dynamicity to cell is Proteins: Proteins are functionally classified as -Enzymes -Regulators -Interactors -Transcription factors -Receptors -Ligands

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Understanding of How protein made as a functional molecule in a cell: Amino Acid: Atomic change Secondary structure of Poly peptide: Molecular change Primary sequence of Poly peptide: Molecular change Tertiary structure: Molecular change Quaternary structure: Molecular change

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Understanding multi component systems interaction at cellular level Free molecules Binary interactions Multiple and complex interactions: Pathway Multiple and complex pathways interactions Multiple pathways interaction between two Cells: Inter Pathways interactions

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What types of chemical changes characterize functions in cells 1.Numbers and types of atoms or functional groups undergoing change. 2.Alteration in geometry or steric configuration of reacting molecules. 3.Number of nature and bonds that are made and broken. UNDERSTANDING PROPERTIES OF ENERGY WITH EACH CHEMICAL SPECIES, DETERMINE CHARACTERISTICS OF FUNCTIONS AT MOLECULAR LEVEL.

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Analysis of chemicals at ENERGY level to characterize Systems functions Qualitative and Quantitative analysis gives information about 1.What extent a function normally take place. STUDY OF MOLECULAR THERMODYNAMICS 2.How fast a function proceeds. STUDY OF MOLECULAR KINETICS

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THERMODYNAMICS A collection of laws and principles describing the flow and interchange of heat, energy and matter in a system of interest. Thermodynamics allows us to determine whether a chemical process or reaction will occur spontaneously in specific direction (either forward or reverse). But it doesn’t tell about the speed at which the reaction take place.

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Two laws of Thermodynamics First Law: The total amount of energy in an isolated system is conserved, though the form of the energy may change. Second Law: In all natural processes, the entropy of the universe increases.

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SYSTEM AND ENVIRONMENT IN UNIVERSE Thermodynamic Concepts: The SYSTEM is the portion of the universe we are concerned with; everything else is the surroundings (ENVIRONMENT). The system + surroundings = UNIVERSE CLOSED SYSTEM ENVIRONMENT UNIVERSE NO EXCHANGE OF ENERGY OR MATTER CLOSED SYSTEM ISOLATED SYSTEM ENVIRONMENT EXCHANGE OF ONLY ENERGY OCCURS ISOLATED SYSTEM OPEN SYSTEM ENVIRONMENT EXCHANGE OF ENERGY AND MATTERS OCCUR OPEN SYSTEM

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What Functions could be study at system level A V [A] B U U = De novo production of molecule U’ = Disposal of a molecule [A] or C = Concentration of A (mass/volume) either increase or decrease T = Transformation of molecule (A -> B) T’ = Reverse Transformation of molecules (B -> A) U’ TT’

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QUANTIFICATION OF FUNCTION WITH RESPECT TO ENERGY ΔG = Δ H - TΔ S ΔG : Gibbs free energy: The amount of energy capable of doing work during a reaction at constant temperature and pressure. ΔH : Enthalpy : The heat content of a system (H). When a chemical reaction releases heat, it is exothermic and has a negative Δ H. ΔS: Entropy : Randomness or disorder of a system (S). When the products of a reaction are less complex and more disordered than the reactants, the reaction proceeds with a gain in entropy (positive ΔS).

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X1X2 E1 H1S1 E2 H2S2 S1 – S2 = ΔS is positive i.e., Randomness increases in X1 and function is forward (Spontaneous) H1 – H2 = ΔH is negative Heat is released and function is forward (Spontaneous) F F’

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What happen in simple Enzymatic reaction In simple reaction, where molecule X1 (Substrate) is activating molecule X2 (Product) is expressed as two states in an energy level diagram. If the level of energy is grater in Substrate (X1) than product (X2) then the reaction is favorable and it proceed towards lower energy state of by releasing amount of energy to make possible function F (here reaction between X1 and X2). But the reaction is proceed in both the direction (imbalance of energy level after passing one state) at the same time (resolution of time here is limited factor to separate the two events). In this situation only small number of molecules out of total molecules, obtain enough thermal energy to overcome the energy barrier.

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What happen to energy, when the population of molecule is high Since there are more than one molecules in a system and each molecules in system will have different levels of energy at different time, that define their states of functions. The E per molecule is proportional to Boltzmann factor [exp(-e/kT)], where, T is absolute temperature k is Boltzmann constant (related to Gas constant R and Avogadro’s number A o [R = k A o ]). In standard level to analyze in chemistry groups of molecules are characterized as general, this standard is called mole (M). At mole level molecules energy E is expressed as exp(-E/RT) Where E = A 0 e (Energy per mole of molecules, each with energy ‘e’). Thus number of molecules having E is given by where a is proportionality constant Proportionality constant ‘a’ is determined by integrating all possible energies that are associated with total number of molecules N t.

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Equilibrium Equilibrium is when the rates of forward and reverse reactions are equal and no further change in the system occurs. Equilibrium constant is when the rate of forward and reverse reaction is taken as ratio (K eq ) When a system is not at equilibrium, the tendency to move toward equilibrium represents a driving force, the magnitude of which is ΔE (E R ). ΔE O is called Standard free energy, when free energy change under standard conditions: 298K; reactants and products present at 1M. Biochemical reactions occur at pH = 7 so we define ΔEo. Relationship between ΔEo and K eq : ΔEo = -2.303RT log K eq T= temperature in K; R = gas constant (8.314 J/mol x K)

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Who can perform function? As previously described, out of total number of molecules, the number of molecule which have energies greater than some critical energy (E c ), can perform respective function. This expression is used to estimate the number of product molecule, in total number of molecules, which has sufficient thermal energy to overcome the energy barrier (E 1 – E 2 = – E R ) and perform specific function.

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The product formed from this function again perform reverse reaction to make substrate If, K eq = 1.0 (reaction at equilibrium) then ΔE (E R ) is = 0 K eq > 0 (function is spontaneous) then ΔE (E R ) is negative K eq < 0 (Function in reverse direction) then ΔE (E R ) is positive

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STUDY OF MOLECULAR KINETICS Kinetics (Dynamics) are roughly synonymous terms referring to the study of functions of chemical systems (interaction, concentration, self production etc.) that change with time. dF/dt

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Transition state EE X1 X3 X4 X1 E X2 TRANSITION STATE (Unstable state) E A = ACTIVATION ENERGY

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Rate of function Rate of function for chemical (proteins) is proportional to the number of substrate (X1) molecules possessing sufficient thermal energy to overcome the activation energy barrier. So, the rate is proportional to exp(-E A /RT).

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Understanding of Kinetic study at molecule or interaction of molecule level Monomolecular function: Intra molecular rearrangement – probability that certain molecules in population is having sufficient activation energy at constant temperature (T) and gas constant (R), then that number of molecules undergoing conversion from one state to other state per unit time is: The conversion rate in terms of concentration is obtained by dividing volume V in both side of the equation. - dX/dt = kX Where X is concentration of substrate X and k is called rate constant.

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Understanding of Kinetic study at molecule or interaction of molecule level Bimolecular function: X1 + X2 X3 F1: Probability of individual molecules have enough energy to be stable F2: Probability of two molecules collide and perform specific function. (Joint probability of two molecules at the same place, same time with appropriate orientation.) The probability of finding given X1 molecule at given time in a given position within a volume V is pX1(r, t) α σX1/V, where r = three dimentional position vector t = time σX1 = effective volume of cross section for considering orientation optimization. V = volume of whole reaction. Therefore the net probability of X1-X2 pair form X3 is proportional to Px1x2(r, t) α exp(-E A /RT)[(σX1/V x σX2/V)] or Px1x2(r, t) = k/V 2 In unit volume X3 is formed depending on how number of X1-X2 (N1xN2) pair forms, Thus, (1/V)d(N3/dt) = k/V 2 N1N2, In term of concentration, dX3/dt = kX1X2 = -dX1/dt = -dX2/dt

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Kinetic Order in chemical functions In system there are not single copy of chemical, rather there are multiple copies of identical chemicals. for example in tri molecular reaction: X1 + X1 + X2 X4, So, dX4/dt = kX1 2 X2 (superscript 2 is kinetic order of molecule X1) = -dX2/dt = -1/2(dX1/dt) (1/2 is stoichiometric factor) (X1 disappears twice at the rate compare to X2)

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A reaction defining as a function of a particular time Kinetic equation, together with stoichiometric constraints and set of initial concentration values, determines a reaction as a function of time. dX/dt = X(0)exp(-kt)

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Understanding Non linearity of Biological system A V [A] B U U’ TT’ If U = U’ -> de novo synthesized A enter into a system at time t1 is disposal at time t2. if, Rate of concentration at entry dU1/dt = Rate of concentration at disposal dU2/dt, then A is not utilized in system and results can be reproduced several time. If T = T’ -> Rate of transforming from A to B (dA/dt) = rate of transformation of B to A (dA/dt) then both A and B remain constant at the system level. But fortunately (unfortunately for us to make research easy), neither of these cases happen in biological systems. If it could happen, then thermodynamically, biological system could not have been existed in universe.

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Why Biological system is Non linear Biological system has thousands of molecules. Each molecule has its own law of function Complexity get worsen when two molecules interacts with their own laws. There is feedback control mechanisms, which controls, biological reactions between two molecules More than one identical molecules interacting with other to perform reaction (Kinetic order problem). Same molecules are distributed in various compartments of a cell (Cell as a system). Various reactions are influenced by various physiological parameters (PH, Osmolarity, Temperature etc.)

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Biochemical system as Non linear X0X1X2X3 X0 X1 X2 X3 t0t1 - t3 X4 X5 + t4

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Power law Approximation In general the flux from X i to X j is a non-linear function of all the X's, that is Vij = vij(X1, X 2..... Xn) The form of this non-linearity for a broad class of enzymatic mechanisms is a ratio of polynomials in the reactant and modifier concentrations. The degree of the numerator is always less than or equal to the degree of the denominator, and all the coefficients are positive real.

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Power Law If we hold all the variables constant (X1, X2, X3….) except one, we can write the rate law as a simple rational function and factor the numerator and denominator polynomials to identify the poles and zeros. vij = co(X1+c1)(X2+C2)….(Xl+Cm) Such a rate law can be analyzed in a log-log plot of velocity vs. concentration (X1 + d1)(X2 + d2).... (Xl + dl) log v = log k + p log X or v = kX p Here, p = apparent kinetic order of the reaction with respect to the variable concentration The values for the parameters "p" and "k" are to be minimize the mean squared error in velocity over the experimentally determined concentration range

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Power Law Experimentally determined concentration range are thus functions of the operating point Xo in general. Xo may be considered the mid-range value of X, or the steady-state value when we are concerned with small variations about this state.

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General Term of Power Law Consider v ij as a function of n variables. The approximation of v U by a sum of linear terms in the n-dimensional log space is equivalent to an approximation that is a product of power- laws in the corresponding Cartesian space. Thus, v ij = kij X l pij (where pij may be any real number) l = 1 n

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General Formula for Power law dX i /dt = αi X k gik – βi X j hik i = 1, 2, 3,…….n variables k = 1 n j= 1 n

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X0X1X2X3 Constant dX 1 /dt = α1 X 0 g10 X 3 g13 β1 X 1 h11 dX 2 /dt = β1 X 1 h11 β2 X 2 h22 dX 3 /dt = β2 X 2 h22 β3 X 3 h33 X 4 h34

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END OF CHAPTER-1 Following is subsequent chapter’s goal to discuss

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