DOCSLIB.ORG

Math for Biology - an Introduction

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Math for Biology - an Introduction Math for Biology - An Introduction Terri A. Grosso Outline Math for Biology - An Introduction Differential Equations - An Overview The Law of Terri A. Grosso Mass Action Enzyme Kinetics CMACS Workshop 2012 January 6, 2011 Terri A. Grosso Math for Biology - An Introduction Math for Biology - An Introduction Terri A. Grosso Outline 1 Differential Equations - An Overview Differential Equations - An Overview The Law of 2 The Law of Mass Action Mass Action Enzyme Kinetics 3 Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction Differential Equations - Our Goal Math for Biology - An Introduction Terri A. Grosso Outline We will NOT be solving differential equations Differential Equations - An Overview The tools - Rule Bender and BioNetGen - will do that for The Law of us Mass Action This lecture is designed to give some background about Enzyme Kinetics what the programs are doing Terri A. Grosso Math for Biology - An Introduction Differential Equations - An Overview Math for Biology - An Introduction Terri A. Grosso Differential Equations contain the derivatives of (possibly) unknown functions. Outline Differential Represent how a function is changing. Equations - An Overview We work with first-order differential equations - only The Law of Mass Action include first derivatives Enzyme Generally real-world differential equations are not directly Kinetics solvable. Often we use numerical approximations to get an idea of the unknown function's shape. Terri A. Grosso Math for Biology - An Introduction A few solutions. Figure: Some solutions to f 0(x) = 2 Differential Equations - Starting from the solution Math for 0 Biology - An A differential equation: f (x) = C Introduction Terri A. Grosso Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction Differential Equations - Starting from the solution Math for 0 Biology - An A differential equation: f (x) = C Introduction A few solutions. Terri A. Grosso Figure: Some solutions to f 0(x) = 2 Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction A few solutions. Figure: Some solutions to f 0(x) = 2x Differential Equations - Starting from the solution Math for 0 Biology - An A differential equation: f (x) = Cx Introduction Terri A. Grosso Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction Differential Equations - Starting from the solution Math for 0 Biology - An A differential equation: f (x) = Cx Introduction A few solutions. Terri A. Grosso Figure: Some solutions to f 0(x) = 2x Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction 0 Exercise: Given f (x) = 2x and (x0; f (x0)) = (4; 22), what is the solution? f (x) = x2 + 6. Differential Equations - Initial Conditions Math for Biology - An Introduction Terri A. Grosso How do we know which is the correct solution? Outline Differential Need to know the value for a point - the initial conditions. Equations - An Overview Only one necessary for these types of problems. Need an The Law of initial condition for each variable in the equation. Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction f (x) = x2 + 6. Differential Equations - Initial Conditions Math for Biology - An Introduction Terri A. Grosso How do we know which is the correct solution? Outline Differential Need to know the value for a point - the initial conditions. Equations - An Overview Only one necessary for these types of problems. Need an The Law of initial condition for each variable in the equation. Mass Action 0 Enzyme Exercise: Given f (x) = 2x and (x0; f (x0)) = (4; 22), what Kinetics is the solution? Terri A. Grosso Math for Biology - An Introduction Differential Equations - Initial Conditions Math for Biology - An Introduction Terri A. Grosso How do we know which is the correct solution? Outline Differential Need to know the value for a point - the initial conditions. Equations - An Overview Only one necessary for these types of problems. Need an The Law of initial condition for each variable in the equation. Mass Action 0 Enzyme Exercise: Given f (x) = 2x and (x0; f (x0)) = (4; 22), what Kinetics is the solution? f (x) = x2 + 6. Terri A. Grosso Math for Biology - An Introduction Differential Equations - A Slightly More Complex Example Math for Biology - An Introduction Terri A. Grosso The Logistic Curve Outline Models population growth Differential Equations - Differential equation: An Overview d The Law of P(t) = P(t)(1 − P(t)) Mass Action dt Enzyme When does P(t) not change? In other words, when is the Kinetics derivative equal to 0? Under what conditions is the derivative positive? Negative? Terri A. Grosso Math for Biology - An Introduction P(0) = :5 1 P(t) = 1 + e−t Differential Equations - A Slightly More Complex Example Math for Biology - An Introduction The Logistic Curve - Solution Terri A. What more do we need before we find a solution? Grosso Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction 1 P(t) = 1 + e−t Differential Equations - A Slightly More Complex Example Math for Biology - An Introduction The Logistic Curve - Solution Terri A. What more do we need before we find a solution? Grosso P(0) = :5 Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction Differential Equations - A Slightly More Complex Example Math for Biology - An Introduction The Logistic Curve - Solution Terri A. What more do we need before we find a solution? Grosso P(0) = :5 Outline 1 Differential P(t) = Equations - −t An Overview 1 + e The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction Differential Equations - How about this one? Math for Biology - An Introduction Terri A. Grosso Outline Differential Equations - An Overview The Law of Mass Action Enzyme Kinetics Terri A. Grosso Math for Biology - An Introduction Biochemical Reactions - An Application of Differential Equations Math for Biology - An Introduction Terri A. Grosso Outline How can we represent the concentrations of molecules in Differential solution? Equations - An Overview We can represent how much the concentrations change The Law of Mass Action over time as differential equations. Enzyme A set of differential equations that closely describe how a Kinetics system develops is a model of the system. Terri A. Grosso Math for Biology - An Introduction Biochemical Reactions - Terminology Review Math for Biology - An Introduction Terri A. Grosso Chemical Reaction A process that changes a set of Outline chemical species into another Differential Reactants The initial set of chemical species Equations - An Overview Products The new set of chemical species The Law of Mass Action A basic synthesis reaction A + B ! C Enzyme Kinetics An equilibrium reaction A + B )−*− C Conservation of Mass The mass of the products has to equal that of the reactants (in a closed system) Terri A. Grosso Math for Biology - An Introduction Biochemical Reactions - Some Basic Questions Math for Biology - An Introduction Terri A. Grosso Outline How quickly does a biochemical reaction take place? Differential Equations - An Overview How will different concentrations of the reactants affect The Law of the reaction rate? Mass Action What will be the concentrations of the reactants and Enzyme Kinetics products at equilibrium? Terri A. Grosso Math for Biology - An Introduction The Law of Mass Action Math for Biology - An Introduction Terri A. Describes the rate at which chemicals collide and form Grosso new compounds Outline It's a model that describes molecular interactions Differential Equations - Example: A + B ! C An Overview The Law of Concentration is represented as [A], [B] and [C]. Mass Action The rate can be expressed as the change in the amount of Enzyme d[C] Kinetics compound C: dt This rate is determined by the number of collisions between A and B and the probability that a collision will lead to the combination of the molecules. Terri A. Grosso Math for Biology - An Introduction The Law of Mass Action Math for Biology - An Introduction Terri A. Grosso d[C] Outline = k[A][B] Differential dt Equations - An Overview Called the Law of Mass Action The Law of k is the rate constant. Takes into account shapes, Mass Action Enzyme attraction and temperature. Kinetics k is different for every reaction. Terri A. Grosso Math for Biology - An Introduction Equilibrium Constant Math for Biology - An Introduction k+ Terri A. −* Grosso A + B )− C k− Outline A is consumed by forward reaction and produced by the Differential reverse reaction, so Equations - An Overview d[A] The Law of = k−[C] − k+[A][B] Mass Action dt At equilibrium, the reactions cancel each other out and Enzyme Kinetics k− [A]eq[B]eq ≡ Keq = k+ [C]eq Exercise: Show that this equation follows from the previous one Terri A. Grosso Math for Biology - An Introduction Equilibrium Constant - Exercise Math for Biology - An Introduction Terri A. Grosso k− [A]eq[B]eq Outline ≡ Keq = Differential k+ [C]eq Equations - An Overview What is the relationship between the equilibrium The Law of concentrations of A, B and C if Keq is greater than 1? Mass Action Less than 1? Enzyme Kinetics Almost equal to 1? Terri A. Grosso Math for Biology - An Introduction Enzyme Basics Math for Biology - An Introduction Terri A. Grosso Enzymes help to convert substrates into products Outline Differential Catalysts - affect the rate of the reaction but are not Equations - An Overview changed by it The Law of Speed up biological reactions by up to 10 million times Mass Action Enzyme Very specific - usually one enzyme catalyzes one reaction Kinetics Regulated by feedback loops - like those found in signalling pathways Terri A.
Load more

Recommended publications
  • Chapter 4. Enzyme Kinetics
    Chapter 4. Enzyme Kinetics Enzyme Engineering 4.1 Why is enzyme kinetics important? 1. It provides valuable information for enzyme mechanism 2. It gives an insight into the role of an enzyme under physiological conditions 3. It can help show how the enzyme activity is controlled and regulated 1 4.2 How to obtain enzyme kinetics? Measure the formation of product or disappearance of substrate Mg2+ D-Glucose + ATP D-Glucose-6-phosphate + ADP 1. Discontinuous method Add the enzyme, then stop the reaction at different time by adding acid to the sample Measure the concentration of substrate or product using HPLC or other chromatography 4.2 How to obtain enzyme kinetics? 2. Continuous method Mg2+ D-Glucose + ATP D-Glucose-6-phosphate + ADP NADP+ NADPH D-Glucono-δ-lactone 6-phosphate + ADP NADPH absorb at 340nm, while NADP+ does not If a coupled reaction is used, the second reaction should not be rate-limiting (sufficient amount of the enzyme must be provided) Continuous method is not always available 2 4.2 How to obtain enzyme kinetics? Radioactive or fluorescent-labeling is useful Precautions The substrate, buffers, etc. must be extremely pure Enzyme should be pure Enzyme should be stable as the assay is proceeded * Temp, pH must be maintained carefully Once steady state is achieved, reaction rate must be constant and proportional to the enzyme added Initial rate of reaction should be measured to avoid possible complexity 4.3 How to analyze kinetic data? 4.3.1 One substrate reactions k 1 k2 E + S ES E + P k-1 Equilibrium assumption (1913) Second reaction is slower than first reverse reaction (k-1 >> k2) Vmax[S] V0 = Michaelis-Menten eqn K s +[S] [E][S] Vmax = k2[E]0 K = s [ES] 3 4.3 How to analyze kinetic data? Steady state assumption (1925) [ES] is constant Vmax[S] V0 = Km +[S] Vmax = k2[E]0 k2 + k−1 Km = k1 4.3.1 One substrate reactions Lineweaver-Burk equation 1 K 1 1 = m + v [S] Vmax Vmax Eddie-Hofstee equation v V v = max − [S] Km Km 4 4.3.1 One substrate reactions Significance of the result 1.
    [Show full text]
  • The Practice of Chemistry Education (Paper)
    CHEMISTRY EDUCATION: THE PRACTICE OF CHEMISTRY EDUCATION RESEARCH AND PRACTICE (PAPER) 2004, Vol. 5, No. 1, pp. 69-87 Concept teaching and learning/ History and philosophy of science (HPS) Juan QUÍLEZ IES José Ballester, Departamento de Física y Química, Valencia (Spain) A HISTORICAL APPROACH TO THE DEVELOPMENT OF CHEMICAL EQUILIBRIUM THROUGH THE EVOLUTION OF THE AFFINITY CONCEPT: SOME EDUCATIONAL SUGGESTIONS Received 20 September 2003; revised 11 February 2004; in final form/accepted 20 February 2004 ABSTRACT: Three basic ideas should be considered when teaching and learning chemical equilibrium: incomplete reaction, reversibility and dynamics. In this study, we concentrate on how these three ideas have eventually defined the chemical equilibrium concept. To this end, we analyse the contexts of scientific inquiry that have allowed the growth of chemical equilibrium from the first ideas of chemical affinity. At the beginning of the 18th century, chemists began the construction of different affinity tables, based on the concept of elective affinities. Berthollet reworked this idea, considering that the amount of the substances involved in a reaction was a key factor accounting for the chemical forces. Guldberg and Waage attempted to measure those forces, formulating the first affinity mathematical equations. Finally, the first ideas providing a molecular interpretation of the macroscopic properties of equilibrium reactions were presented. The historical approach of the first key ideas may serve as a basis for an appropriate sequencing of
    [Show full text]
  • Enzyme Activity and Assays Introductory Article
    Enzyme Activity and Assays Introductory article Robert K Scopes, La Trobe University, Bundoora, Victoria, Australia Article Contents . Factors that Affect Enzymatic Analysis Enzyme activity refers to the general catalytic properties of an enzyme, and enzyme assays . Initial Rates and Steady State Turnover are standardized procedures for measuring the amounts of specific enzymes in a sample. Measurement of Enzyme Activity . Measurement of Protein Concentration Factors that Affect Enzymatic Analysis . Methods for Purifying Enzymes . Summary Enzyme activity is measured in vitro under conditions that often do not closely resemble those in vivo. The objective of measuring enzyme activity is normally to determine the exactly what the concentration is (some preparations of amount of enzyme present under defined conditions, so unusual substrates may be impure, or the exact amount that activity can be compared between one sample and present may not be known). This is because the rate another, and between one laboratory and another. The measured varies with substrate concentration more rapidly conditions chosen are usually at the optimum pH, as the substrate concentration decreases, as can be seen in ‘saturating’ substrate concentrations, and at a temperature Figure 1. In most cases an enzyme assay has already been that is convenient to control. In many cases the activity is established, and the substrate concentration, buffers and measured in the opposite direction to that of the enzyme’s other parameters used previously should be used again. natural function. Nevertheless, with a complete study of There are many enzymes which do not obey the simple the parameters that affect enzyme activity it should be Michaelis–Menten formula.
    [Show full text]
  • Opportunities for Catalysis in the 21St Century
    Opportunities for Catalysis in The 21st Century A Report from the Basic Energy Sciences Advisory Committee BASIC ENERGY SCIENCES ADVISORY COMMITTEE SUBPANEL WORKSHOP REPORT Opportunities for Catalysis in the 21st Century May 14-16, 2002 Workshop Chair Professor J. M. White University of Texas Writing Group Chair Professor John Bercaw California Institute of Technology This page is intentionally left blank. Contents Executive Summary........................................................................................... v A Grand Challenge....................................................................................................... v The Present Opportunity .............................................................................................. v The Importance of Catalysis Science to DOE.............................................................. vi A Recommendation for Increased Federal Investment in Catalysis Research............. vi I. Introduction................................................................................................ 1 A. Background, Structure, and Organization of the Workshop .................................. 1 B. Recent Advances in Experimental and Theoretical Methods ................................ 1 C. The Grand Challenge ............................................................................................. 2 D. Enabling Approaches for Progress in Catalysis ..................................................... 3 E. Consensus Observations and Recommendations..................................................
    [Show full text]
  • Catalase Kinetics
    Experiment #4: Catalase Kinetics MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Chemistry 5.310 Laboratory Chemistry 1 EXPERIMENT #4 A Study of the Kinetics of the Enzyme Catalase and its Reaction 2 3 With H2O2. A Further Study on Protein Assay Quantitation of Catalase I. OVERVIEW OF THE EXPERIMENT In this experiment, the student will investigate the enzyme activity of catalase by studying the decomposition of H2O2 to form water and oxygen. Using an oxygen based pressure sensor the student measures the amount of oxygen produced and then calculates the rate of the enzyme catalyzed reaction under various conditions. The student also completes a Protein Assay on an unknown sample of catalase using the Coomassie® Plus Protein Assay from Pierce to determine the protein concentration of the sample. The correlation between the actual and calculated concentration gives an indication of the experimental skills used in carrying out the experiment. II. OBJECTIVES This is an integrated experiment that includes topics from physical chemistry and biochemistry. It is designed to introduce students to the basics of: • Studying the effects of reaction environment, including temperature, and varying substrate concentration on the rate of an enzyme-catalyzed reaction. • Combining physical chemistry and biochemistry, principles and theory, with the goal of determining various biochemical and biophysical constants for the enzyme catalase. • How to acquire experimental kinetic data for an enzyme catalyzed reaction. • Learning how to perform data manipulation in order to extract out information such as rate constants from experimental kinetic data. • Correct handling of UV-VIS Spectroscopy 1 This experiment was synthesized by John J.
    [Show full text]
  • Estimation of the Overall Kinetic Parameters of Enzyme Inactivation Using an Isoconversional Method D
    Estimation of the overall kinetic parameters of enzyme inactivation using an isoconversional method D. Oancea, Alexandrina Stuparu, Madalina Nita, Mihaela Puiu, Adina Raducan To cite this version: D. Oancea, Alexandrina Stuparu, Madalina Nita, Mihaela Puiu, Adina Raducan. Estimation of the overall kinetic parameters of enzyme inactivation using an isoconversional method. Biophysical Chemistry, Elsevier, 2008, 138 (1-2), pp.50. 10.1016/j.bpc.2008.09.003. hal-00501718 HAL Id: hal-00501718 https://hal.archives-ouvertes.fr/hal-00501718 Submitted on 12 Jul 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ÔØ ÅÒÙ×Ö ÔØ Estimation of the overall kinetic parameters of enzyme inactivation using an isoconversional method D. Oancea, Alexandrina Stuparu, Madalina Nita, Mihaela Puiu, Adina Raducan PII: S0301-4622(08)00176-2 DOI: doi: 10.1016/j.bpc.2008.09.003 Reference: BIOCHE 5155 To appear in: Biophysical Chemistry Received date: 17 August 2008 Revised date: 2 September 2008 Accepted date: 3 September 2008 Please cite this article as: D. Oancea, Alexandrina Stuparu, Madalina Nita, Mi- haela Puiu, Adina Raducan, Estimation of the overall kinetic parameters of en- zyme inactivation using an isoconversional method, Biophysical Chemistry (2008), doi: 10.1016/j.bpc.2008.09.003 This is a PDF file of an unedited manuscript that has been accepted for publication.
    [Show full text]
  • Determination of Enzyme Kinetics in the Eppendorf Biospectrometer® Kinetic Using a Hexokinase and Glucose-6- Phosphate-Dehydrogenase from Saccharomyces Cerevisiae
    USERGUIDE No. 39 I Detection I September 2014 Determination of enzyme kinetics in the Eppendorf BioSpectrometer® kinetic using a hexokinase and glucose-6- phosphate-dehydrogenase from Saccharomyces cerevisiae Martin Armbrecht, Eppendorf AG, Hamburg, Germany Abstract This Userguide will demonstrate measurement of enzyme activity using the Eppendorf BioSpectrometer. In order to optimize the measurement process, preliminary measurements were performed using the method “single continuous”. The actual activity measurements were then performed based on these results. Enzyme activities were determined via linear regression. For the measurements, a coupled reaction of a hexokinase and a glucose-6-phosphate-dehydrogenase from the baker’s yeast ‚ was used. Since the Eppendorf BioSpectrometer kinetic is equipped with a temperature controlled cuvette chamber, temperature dependence of this reaction could also be demonstrated. The highest activity was detected at 37 °C. Introduction Metabolic significance of the hexokinase reaction Activation of glucose via the hexokinase reaction Glycolysis Glucose degradation thus sustains respiration of all living beings. One central area within the metabolism of nearly all living beings is Prior to degradation, glucose needs to be rendered susceptible for the enzymatic degradation of glucose in the cytosol, or cytoplasma, degradation, i.e., activated. This process involves phosphorylation by respectively, in their cells. This process is called glycolysis. Glucose a hexokinase; with the expenditure of ATP, glucose-6-phosphate is is converted to 2 molecules of pyruvate in a stepwise fashion. One produced. Thus, the latter is the actual initial substrate of glycolysis molecule of glucose yields 2 ATP and 2 redox equivalents in the form (fig.1). In addition, glucose-6-phosphate is the initial substrate of a further of NADPH2.
    [Show full text]
  • Recitation Section 4 Answer Key Biochemistry—Energy and Glycolysis
    MIT Department of Biology 7.014 Introductory Biology, Spring 2005 Recitation Section 4 Answer Key February 14-15, 2005 Biochemistry—Energy and Glycolysis A. Why do we care In lecture we discussed the three properties of a living organism: metabolism, regulated growth, and replication. Today we will focus on metabolism and biosynthesis. 1. It was said in lecture that chemical reactions are the basis of life. Why do we say that? Being alive implies being able to change your state in response to a change in internal or environmental conditions. We discussed previously that any change in the observable characteristics of a cell begins as and is propagated by molecular interactions. Molecular interactions propagate the signal by changing the state of molecules, i.e. by reactions. 2. Why is metabolism required for life? A cell is subject to all laws of chemistry and physics, including the first and second law of thermodynamics. Changing the state of molecules dissipates energy along the way, so getting or making new energy is essential to life. The energy is then used for many purposes, including making the building blocks and precursors and then using them to build macromolecules that make up cells—biosynthesis. 3. Can an entity that performs no chemical reactions be considered “alive?” In general, no. But there are special cases of the cells that do not perform reactions right at the moment, but have the potential to perform reactions if they encounter particular conditions. Some examples of such cells are spores in nature or frozen permanents in laboratory. If they experience certain conditions, such as availability of food for spores, or defrosting and food source for frozen permanents, these cells will again perform metabolism.
    [Show full text]
  • Detection of Errors of Interpretation in Experiments in Enzyme Kinetics
    METHODS 24, 181±190 (2001) doi:10.1006/meth.2001.1179, available online at http://www.idealibrary.com on Detection of Errors of Interpretation in Experiments in Enzyme Kinetics Athel Cornish-Bowden1 Institut FeÂdeÂratif ªBiologie Structurale et Microbiologie,º BioeÂnergeÂtique et IngeÂnierie des ProteÂines, Centre National de la Recherche Scientifique, 31 chemin Joseph-Aiguier, B.P. 71, 13402 Marseille Cedex 20, France points necessary for modern users are to be aware (at Although modern statistical computing will often be the method least qualitatively) of the assumptions that underlie of choice for analyzing kinetic data, graphic methods provide an important supplement that ought not to be neglected. Residual the statistical analysis and to be aware also that they plots, or plots of differences between observed and calculated are not always true (2). By contrast we shall be con- values against variables not expected to be correlated with these cerned with methods that require no detailed mathe- differences, permit a rapid judgment of whether data have been matics and can readily be applied to published graphs correctly interpreted and analyzed. The rapid increase in the fre- (or even to graphs displayed on a screen during a lec- quency with which artificially modified or mutated enzymes are ture) without access to the numerical coordinates of studied is making it less and less safe to assume that enzymes the observations. More generally, this article argues for are stable under assay conditions, and there is thus an increased more reliance on common sense and graphic analysis need for methods to check for enzyme stability, and a method and less on automatic analysis performed by computer: for doing this is briefly described.
    [Show full text]
  • 2.4 the Breakdown Chemical Reactions Bonds Break and Form During Chemical Reactions
    DO NOT EDIT--Changes must be made through “File info” CorrectionKey=B 2.4 Chemical Reactions KEY CONCEPT VOCABULARY Life depends on chemical reactions. chemical reaction MAIN IDEAS reactant Bonds break and form during chemical reactions. product Chemical reactions release or absorb energy. bond energy equilibrium activation energy Connect to Your World exothermic When you hear the term chemical reaction, what comes to mind? Maybe you think endothermic of liquids bubbling in beakers. You probably do not think of the air in your breath, but most of the carbon dioxide and water vapor that you breathe out are made by chemical reactions in your cells. MAIN IDEA Bonds break and form during chemical reactions. Plant cells make cellulose by linking simple sugars together. Plant and animal cells break down sugars to get usable energy. And all cells build protein mol- ecules by bonding amino acids together. These are just a few of the chemical reactions in living things. Chemical reactions change substances into different substances by breaking and forming chemical bonds. Although the matter changes form, both matter and energy are conserved in a chemical reaction. Reactants, Products, and Bond Energy Your cells need the oxygen molecules that you breathe in. Oxygen (O2) plays a part in a series of chemical reactions that provides usable energy for your cells. These reactions, which are described in detail in the chapter Cells and Energy, break down the simple sugar glucose (C6H12O6). The process uses oxygen and glucose and results in carbon dioxide (CO2), water (H2O), and usable energy. Oxygen and glucose are the reactants.
    [Show full text]
  • Chromatographic Resolution and Kinetic Characterization Of
    Proc. NatL Acad. Sci. USA Vol. 80, pp. 8589, January 1983 Biochemistry Chromatographic resolution and kinetic characterization of glucokinase from islets of Langerhans (hexoldnase/islet glucose metabolism /N-acetylglucosamine kdnase/Cibacron blue) MARTIN D. MEGLASSON, PAMELA TRUEHEART BURCH, DONNA K. BERNER, HABIBA NAJAFI, ALAN P. VOGIN, AND FRANZ M. MATSCHINSKY* Diabetes Research Center and Department of Biochemistry and Biophysics, School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania 19104 Communicated by Robert E. Forster, October 4, 1982' ABSTRACT Glucokinase (ATP:D-glucose 6-phosphotransfer- ofislets equals serum glucose and islet glucose 6-phosphate in- ase, EC 2.7.1.2) from rat islets of Langerhans was partially pu- creases in proportion to extracellular glucose (1, 13). Ninety rified by chromatography on DEAE-Cibacron blue F3GA agar- percent ofislet glucose utilization occurs with an apparent glu- ose. The enzyme eluted in two separate peaks. Sigmoidal rate cose affinity constant 11.1 mM (6). Also, mannoheptulose, an dependence was found with respect to glucose (Hill coefficient inhibitor of glucokinase (8), profoundly inhibits islet glucose = 1.5) for both enzyme fractions. K. values for glucose were 5.7 metabolism. (14). mM for the major fraction and 4.5 mM for the minor fraction. The chromatographic separation of glucokinase from other Neither fraction phosphorylated GlcNAc. A' GlcNAc kinase is the most direct (ATP. 2-acetamido-2-deoxy-D-glucose' 6-phosphotransferase; EC glucose phosphorylating enzymes approach 2.7.1.59)-enriched fraction; prepared by affinity chromatography to establish its presence in pancreatic islets. It is the purpose on Sepharose-N46-aminohexanoyl)-GlcNAc, had a K.
    [Show full text]
  • Kinetics the Michaelis-Menten Model for Enzyme Kinetics Presumes A
    Michaelis-Menten (steady-state) Kinetics The Michaelis-Menten model for enzyme kinetics presumes a simple 2-step reaction: Step 1 : Binding – the substrate binds to the enzyme k1 k2 Step 2 : Catalysis – the substrate is converted to product and released E + S ES E + P (Note that enzymes not matching this reaction scheme may still show similar kinetics.) k-1 k-2 The Michaelis-Menten equation shows how the initial rate of Binding Catalysis ͐(3 ʞSʟ this reaction, Vo, depends on the substrate concentration, [S]: ͐* = ͅ( + ʞSʟ Several simplifying assumptions allow for the derivation of the Michaelis-Menten equation: (1) The binding step ( E + S ES ) is fast, allowing the reaction to quickly reach equilibrium ratios of [E], [S], and [ES]. The catalytic step ( ES E + P ) is slower, and thus rate-limiting. (2) At early time points, where initial velocity ( Vo) is measured, [P] ≈ 0. (3) ES immediately comes to steady state, so [ES] is constant (throughout the measured portion of the reaction). (4) [S] >> [E T], so the fraction of S that binds to E (to form ES) is negligible, and [S] is constant at early time points. (5) The enzyme exists in only two forms: free (E), and substrate-bound (ES). Thus, the total enzyme concentration (E T) is the sum of the free and substrate-bound concentrations: [E T] = [E] + [ES] A derivation of the Michaelis-Menten equation shows how to use the above assumptions to describe the rate of the enzyme-catalyzed reaction in terms of measurable quantities: From (1), we know the overall rate of the reaction is determined by the rate of the catalytic step: ͐* = ͦ͟ʞES ʟ − ͯͦ͟ʞEʟʞPʟ From (2), the second term equals zero, so we are left with: ͐* = ͦ͟ʞES ʟ We want to describe Vo in measurable quantities, but [ES] is not easy to Rate of formation of ES = Rate of breakdown of ES measure.
    [Show full text]