Keynote Lecture-2
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Modelling of Metabolic Processes: Bridging the Gap between Data and Process Understanding Aleš BeliΔ Laboratory for modelling, simulation and control Faculty of Electrical Engineering University of Ljubljana Since we became aware of ourselves, we try to describe our functioning in abstract terms in order to answer the basic questions of our existence ... The Hitchhikers Guide to the Galaxy has this to say on the topic • ... • First, they built a computer named Deep Thought to calculate the answer to the ultimate question of life, universe and everything. • After 7.5 M years of computing Deep Thought announced the answer: forty-two • Next, Deep Thought constructed another computer, to calculate what was actually the question. • The computer was named Earth and the program should run for 10 M years, but the Earth was unfortunately destroyed 5 min before the program ended to make space for the galactic hyperspace by-pass. • ... • Douglas Adams understood modelling better than many of the real-life modellers ο Aleš BeliΔ 4 Understanding how human works • • Motivation – advantages in survival • knowing your limits • healing • making of tools • ... Methods (chronologically) – holistic approaches (psychology, body, effects of chemical substances, ...) – invention of writing enables faster gathering of knowledge and people are no longer able to maintain the overview • development of special areas of science that cover only specific problems – introduction of mathematics and engineering in some areas – universality of mathematical notation could again lead to systemic overview • systems biology • systems medicine Holistic approach!! All processes in an organism are always connected in integral system that enables optimal functioning. When only a part of the system is damaged it causes global adaptation of the system. • Feedback loops prevent simple detection of the disturbance origin – feedback loops are hierarchically nested with aim to maintain the most vital functions at all costs, therefore, the phenomena may be detected far away from the real origin. – dynamic nature of the processes!!! • Without understanding of the integral system we cannot correctly understand the functioning of the sub-systems • Modelling and simulation can be efficiently applied Metabolic networks Monitoring of metabolic processes • Important for healthcare! • Metabolites – chromatography, mass spectrometry, – tedious work – mostly static data – metabolic fluxes • Proteins/Enzymes – adapted methods of chromatography and mass spectrometry – tedious, expensive, poor precision (concentration ≠ activity) – indirect measurement of activity – static data, if any at all ... • Genome/expression – large selection of methods – static and occasionally dynamic data Modelling of metabolic processes • Enzyme reactions – Michaelis-Menten (1916) – still basic equations for describing enzyme reactions dynamics • Gene expression – transcription of mRNA from DNA • Composition of enzymes – proteins with special characteristics – mRNA is translated into amino acids and they are combined into protein • Disturbed balance between concentrations of the key molecules can reduce or elevate: – gene expression – enzyme stability/activity • All the molecules have limited stability so they are subject to constant decay – metabolic processes must have some non-zero steady state flux Michaelis-Menten model kf S + E ES kr kcat P + E π[π] ππ [π] ππ + ππππ‘ = ; πΎπ = ; Vm = k cat E ππ‘ πΎπ + [π] ππ reversible reactions kf1 S + E kr1 ES kf2 kr2 P + E metabolic process S + E kC kCR ES kP kPR P + E 0 M-M model in metabolic conditions ΦπΈππ Φππ S ππΆ ππΆπ E ES ΦπΈππ’π‘ ππ πππ P Φππ’π‘ ππ = Φππ − ππΆ πΈ π + ππΆπ πΈπ ππ‘ π πΈπ = ππΆ πΈ π + πππ πΈ π − ππ πΈπ − ππΆπ πΈπ ππ‘ ππ = ππ πΈπ − Φππ’π‘ − πππ πΈ π ππ‘ ππΈ = ΦπΈππ + ππ πΈπ + ππΆπ πΈπ − ππΆ πΈ π − πππ πΈ π − ΦπΈππ’π‘ ππ‘ Steady-state 0 = Φππ − ππΆ πΈ π + ππΆπ πΈπ 0 = ππΆ πΈ π + πππ πΈ π − ππ πΈπ − ππΆπ πΈπ 0 = ππ πΈπ − Φππ’π‘ − πππ πΈ π 0 = ΦπΈππ + ππ πΈπ + ππΆπ πΈπ − ππΆ πΈ π − πππ πΈ π − ΦπΈππ’π‘ Normalisation introduces relative concentration values 0 = ππΆπ πΈπ ππ + πππ π πΈπ ππ − πππ πΈππ − ππΆπ π πΈππ ππ [π] [πΈ] [π] [πΈπ] = ; πΈπ = ; π = ; πΈππ = [ππ π ] [πΈπ π ] π [ππ π ] [πΈππ π ] ππΆπ = ππΆ πΈππ πππ ; πππ π = πππ πΈππ πππ ; πππ = ππ πΈπππ ; ππΆπ π = ππΆπ πΈπππ Alternative introduction of parameters ΦπΈππ Φππ S ππΆπ ππΆπ π E ES ΦπΈππ’π‘ πππ πππ π πππ π = π1 ππΆπ Φππ’π‘ P ππΆπ π = π2 πππ 0 = ππΆπ πΈπ ππ + ππΆπ π1 πΈπ ππ − πππ πΈππ − πππ π2 πΈππ 0 = ππΆπ πΈπ ππ + π1 ππ − πππ πΈππ 1 + π2 Normalised concentrations are in steady-state = 1 0 = ππΆπ 1 + π1 − πππ 1 + π2 Since high reversibility of reactions makes sense only in special cases we can assume that r1 and r2 are small and equal 0 = ππΆπ 1 + π − πππ 1 + π 0 = ππΆπ − πππ ππΆπ = πππ Basic parameters as functions of new ones ππΆπ = ∅ππ (1 − π) πππ = ∅ππ (1 − π) ππΆπ π = ∅ππ π (1 − π) πππ π = ∅ππ π (1 − π) Substrate to product ratio in steady-state 1 − π2 [ππ ] = + π 2 ππ [πΈπ ] [ππ ] 1 − π2 = + π2 [ππ ] [πΈπ ][ππ ] Description of the basic parameters with reversibility and metabolic flux in steady-state enables studies of enzyme activity on product and substrate concentrations in steady-state without knowing the real metabolic flux through the system!!!! Enzyme concentration affects the substrate to product ratio because of constant flux [ππ ] [ππ ] A. BeliΔ J. AΔimoviΔ, A. Naik, M. GoliΔnik. Analysis of the steady-state relations and control-algorithm characterisation in a mathematical model of cholesterol biosynthesis. Simulation Modelling Practice and Theory 33 (2013) 18–27 = πΎπΆπ π πΎππ π πΎπΆπ πΎππ = π2 Inspecificity of enzymes with respect to substrate • • • Enzymes recognise 3D structures of substrates – distribution and atom types – vibrations of molecular structure of enzyme and substrate Different molecules may have the same key structures (domains) – enzymes may operate on more than one molecule!!! – extremely large interconnected metabolic networks!!! Domains and enzyme effect may be described by a binary code – presence or absence of: • bonds (single, double, triple) • molecular groups or atoms (hydrogen, methyl group, amino group, ...) – a relatively simple algorithm can be constructed for prediction of possible networks based on known enzyme-metabolite interactions! Late part of the cholesterol biosynthesis metabolic network A, BeliΔ, D. Pompon, K. Monostory, D. Kelly, S. Kelly, D. Rozman. An algorithm for rapid computational construction of metabolic networks: A cholesterol biosynthesis example. Computers in Biology and Medicine 43 (2013) 471–480 Liver metabolism modelling • Aim: better understanding of NAFLD (Non-Alcocholic Fatty Liver Disease) • Framework: a network of enzyme reactions for transport and metabolism for control of: – body energy – basic metabolites (cholesterol, glucoze, ...) • Enzyme activity is controlled by – enzyme stability – gene expression • Chemical communication with other organs is important • M-M model of enzyme reactions • Simple piece-wise linear models for expression and stability • Static data Model structure 145 metabolites 259 enzymes 60 proteins Metabolic pathways: • glycolisis/gluconeogenesis • penthose phosphate pathway • synthesis of fatty acids/oxidative pathway • citric acid cycle • cholesterol metabolism • amino acids metabolism • chormonal regulation (insulin, glucagon) • adipokine (adiponectin, leptin) & citokine regulation (TNFa) • expression regulation with transcription factors (PPAR, LXR, FXR, SREBP-1c,-2; FOXO1) • exchange between liver, blood flow, adipocites and periferl tissues (LDL-R, CD36, itd.) Cholesterol biosynthesis • One of the most important pathways in the liver – present in all types of cells – the liver covers most of the body requirements for cholesterol • growth • tissue repair • ... Cholesterol biosynthesis Detailed analysis of cholesterol biosynthesis • Interesting experimental and simulation results: – exogenous substances that influence cholesterol synthesis can either reduce cholesterol concentration to zero or have no effect on the concentration while gene expression is altered in both cases • Modelling purpose: – to understand basic regulation structure of cholesterol biosynthesis through SREBF2 transcription factor Model of cholesterol biosynthesis path DNA SREBF2 The character of SREBF2 regulator Simplifications DNA SREBF2 The flux through the pathway is regulated by all the enzymes simultaneously, therefore the simplification is sensible!! Standard control scheme R E - regulator U process Y Description of the bio-controller DNA U mRNA E nonact. act. E cholesterol SREBF2 E controller U From the scheme to the equations πΈ = ππ π − π U π = ππ + ππ Ge P E act. nonact. E cholesterol ππ = π ππ ≈ const. πππ = ππππ‘ πΈ + ππ πΊπ − ππ ππ ππ‘ πππ = −ππππ‘ πΈ ππ‘ ππΊπ = πππ₯ ππ − ππΊ πΊπ ππ‘ ππ = ππππ‘ πΈ + ππ πΊπ − ππ π ππ‘ ππΊπ = πππ₯ π − ππΊ πΊπ ππ‘ Evolving the equations ππ = ππππ‘ πΈ + ππ πΊπ − ππ π ππ‘ U Ge P E act. nonact. E cholesterol π πΊπ + ππΊ πΊπ = πππ₯ π πΊπ (π + ππΊ ) = πππ₯ π πΊπ = πππ₯ π π + ππΊ ππΊπ = πππ₯ π − ππΊ πΊπ ππ‘ π π = ππππ‘ πΈ + ππ πΊπ − ππ π π πΊπ = πππ₯ π − ππΊ πΊπ πππ₯ π π π = ππππ‘ πΈ + ππ − ππ π π + ππΊ β (π + ππΊ ) π π(π + ππΊ ) = ππππ‘ πΈ(π + ππΊ ) + ππ πππ₯ π − ππ π(π + ππΊ ) π π 2 + π (ππΊ + ππ + ππ ππΊ − ππ πππ₯ ) = ππππ‘ πΈ(π + ππΊ ) ππππ‘ (π + ππΊ ) π= 2 πΈ π + π (ππΊ + ππ ) + ππ ππΊ − ππ πππ₯ Re-arranging the equations ππππ‘ (π + ππΊ ) π= 2 πΈ π + π (ππΊ + ππ ) + ππ ππΊ − ππ πππ₯ ππ = ππππ‘ πΈ + ππ πΊπ − ππ π ππ‘ ππΊπ = πππ₯ π − ππΊ πΊπ ππ‘ π= ππππ‘ (π + ππΊ ) πΈ π 2 + π (ππΊ + ππ ) We can always find some steady-state! 0= ππ πΊπ − ππ π 0= πππ₯ π − ππΊ πΊπ ππ ππΊ − ππ πππ₯ = 0 ππππ‘ (π + ππΊ ) π= πΈ π (π + (ππΊ +ππ )) Consequences of the control algorithm π= PI controller π = πΎπ πΈ + πΎπΌ • No error in the steady-state!!!! πΈππ‘ 1 π = πΎπ πΈ + πΎπΌ πΈ π ππ ππ 1 π = πΎπ πΈ + πΎπΈ π + ππ π πΌ π + ππ π= ππππ‘ (π + ππΊ ) πΈ π (π + (ππΊ +ππ )) ππ (πΎπ π + πΎπΌ ) πΈ π (π + ππ ) – until relatively large pool of SREBF2 is depleted • Slower response because of additional structures • Changed mRNA levels at normal levels of cholesterol Understanding of statin activity DNA statin influence SREBF2 To explain statin effect we need additional control loop, that allows cholesterol levels reduction at non-complete HMGCR blockade! The consequences of the findings for the whole-body functioning • Precise and robust system for cholesterol control in the cell – for long-term disturbance of normal levels very intense intervention on major metabolic pathways is required! – reduction of cholesterol levels in the cell causes uptake of cholesterol from blood stream (measurements on living organisms) – Intervention on the level of cell reference (SREBF2) does not result in reduction of cholesterol levels in blood (experimentally proven) – spontaneous elevation of cholesterol blood cannot result from biosynthesis deregulation in the liver (genetic disorder) • too many things would have to be affected simultaneously which is in contrast with the disease prevalence • the cause for elevated cholesterol levels lies in the periferal tissues (false cholesterol demand signals or tissue cannot reach the cholesterol in blood, interaction with other metabolic processes.) Conclusion • Regarding our experience most effective models are the most simple ones, since only the simplest models contain only vital informations – biological systems are not too complex for modelling, however they require a lot of innovation and improvisation • Expert knowledge inclusion is important even if some details must be omitted • Modelling procedure often provides more information than the final model • Control loops are essential part of biological models – many times they are discovered on the bases of discrepancy between model simulations and real data • Never forget holistic approach!!! – sub-systems must be adequately placed within the context of the integral system!!!! If the reality does not fit the model ... ... it‘s reality‘s fault!
