DOCSLIB.ORG

Estimating the Product Inhibition Constant from Enzyme Kinetic Equations Using the Direct Linear Plot Method in One-Stage Treatment

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Estimating the Product Inhibition Constant from Enzyme Kinetic Equations Using the Direct Linear Plot Method in One-Stage Treatment catalysts Article Estimating the Product Inhibition Constant from Enzyme Kinetic Equations Using the Direct Linear Plot Method in One-Stage Treatment Pedro L. Valencia 1,* , Bastián Sepúlveda 2, Diego Gajardo 2 and Carolina Astudillo-Castro 3 1 Department of Chemical and Environmental Engineering, Universidad Técnica Federico Santa María, P.O. Box 110-V, Valparaíso 2390123, Chile 2 Department of Mathematics, Universidad Técnica Federico Santa María, Valparaíso 2390123, Chile; [email protected] (B.S.); [email protected] (D.G.) 3 School of Food Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2360100, Chile; [email protected] * Correspondence: [email protected] Received: 15 June 2020; Accepted: 8 July 2020; Published: 1 August 2020 Abstract: A direct linear plot was applied to estimate kinetic constants using the product’s competitive inhibition equation. The challenge consisted of estimating three kinetic constants, Vmax, Km, and Kp, using two independent variables, substrates, and product concentrations, in just one stage of mathematical treatment. The method consisted of combining three initial reaction rate data and avoiding the use of the same three product concentrations (otherwise, this would result in a mathematical indetermination). The direct linear plot method was highly superior to the least-squares method in terms of accuracy and robustness, even under the addition of error. The direct linear plot method is a reliable and robust method that can be applied to estimate Kp in inhibition studies in pharmaceutical and biotechnological areas. Keywords: direct linear plot; median method; product inhibition; kinetic constants; non-parametric; distribution-free method 1. Introduction The direct linear plot (DLP) is a graphic method to estimate kinetic constants from enzymatic reactions based on the median as a statistic. The method was developed by Eisenthal and Cornish-Bowden in 1974 [1]. The accuracy and robustness of this method were tested during the estimation of Vmax and Km from the Michaelis–Menten equation [1,2]. As in this article, all of the recent studies regarding the application of DLP are based on the estimation of these two parameters from the Michaelis–Menten equation. The application of DLP to equations with more than two parameters has not been studied until now [3]. This median-based method was applied herein to estimate three kinetic constants from the substrate-uncompetitive inhibition equation. The results indicated that DLP was not only applicable to equations with more than two parameters, but it was reliable and robust when compared to the least-squares (LS) method. In the present article, we explored the application of DLP to the product-competitive inhibition equation, which is a different type of problem, as will be exposed. Some attempts to estimate inhibition constants from enzyme kinetics using DLP have involved estimating apparent kinetic constants and using secondary plots to estimate the values of these inhibition constants. The application of DLP to estimate inhibition constants was first proposed by Eisenthal and Cornish-Bowden [1]. The literature contains outdated examples of this application because the use of DLP to estimate inhibition constants in one-stage has not been assessed [4–8]. In the literature, DLP has been used to estimate the apparent kinetic Catalysts 2020, 10, 853; doi:10.3390/catal10080853 www.mdpi.com/journal/catalysts Catalysts 2020, 10, x FOR PEER REVIEW 2 of 11 Catalysts 2020, 10, 853 2 of 10 assessed [4–8]. In the literature, DLP has been used to estimate the apparent kinetic constants Vmax and Km; however, studies have used secondary plots to estimate the inhibition constant Kp. The constants Vmax and Km; however, studies have used secondary plots to estimate the inhibition constant present article studied the application of DLP to estimate the product inhibition constant in one-stage Kp. The present article studied the application of DLP to estimate the product inhibition constant in one-stagetreatment, treatment, avoiding avoidingthe estimation the estimation of apparent of apparent kinetic constants kinetic constants and secondary and secondary plots. As plots. the proper As the propercharacterization characterization of inhibition of inhibition in pharmaceutical in pharmaceutical and biotechnological and biotechnological applications applications is a major is concern, a major concern,the importance the importance of this proposal of this proposal is that it isopens that itup opens the possibility up the possibility of using ofa reliable using a and reliable robust and method robust to estimate product inhibition constants. The purpose of this study is to estimate Vmax, Km, and Kp from method to estimate product inhibition constants. The purpose of this study is to estimate Vmax, Km, the competitive inhibition equation in just one stage of calculations, avoiding the apparent constants and Kp from the competitive inhibition equation in just one stage of calculations, avoiding the apparent constantsand secondary and secondaryplots. This plots.means Thisthe values means of the the values product of inhibition the product constants inhibition must constants be obtained must from be obtainedthe DLP method, from the which DLP method, has never which been has tried never before. been The tried problem before. Theis outlined problem as is follows. outlined as follows. The equation for competitive product inhibition involves three parameters—Vmax, Km, and Kp— The equation for competitive product inhibition involves three parameters—Vmax, Km, and Kp—and threeand variables—substratethree variables—substrate concentration, concentration, product concentration,product concentration, and initial reaction and initial rate (Equation reaction (1)).rate (Equation (1)). VmaxS v = (1) = K K + S + m P m Kp (1) + + This is a different type of problem compared to previous articles where the substrate-uncompetitive This is a different type of problem compared to previous articles where the substrate- inhibition equation involved three parameters—Vmax, Km, and KS—but only two variables—substrate uncompetitive inhibition equation involved three parameters—Vmax, Km, and KS—but only two concentration and initial reaction rate (Equation (2)) [3]. variables—substrate concentration and initial reaction rate (Equation (2)) [3]. V S v = max (2) = S2 Km + S + (2) + K+s TheThe experimental dataset dataset required required is istraditionally traditionally used used in the in initial the initial reaction reaction rate method, rate method, which whichdenotes denotes a series a seriesof initial of initial rates ratesvs. substrate vs. substrate conc concentrationsentrations at constant at constant product product concentrations, concentrations, as asindicated indicated in inthe the scheme scheme of ofFigure Figure 1.1 . P = P1 P = P2 P = Pm S v S v S v S1 v11 S1 v21 S1 vm1 … … … … … … Sn v1n Sn v2n Sn vmn FigureFigure 1.1. SchemeScheme ofof thethe traditionaltraditional experimentalexperimental designdesign based on thethe initialinitial reactionreaction raterate methodmethod toto estimateestimate inhibitioninhibition constantsconstants inin enzymeenzyme kinetics.kinetics. EquationEquation (1)(1) cancan bebe rearrangedrearranged toto EquationEquation (3)(3) inin thethe followingfollowing form:form: v P Km − + ij i = − (3) vijKm SjVmax + = vijSj (3) − Kp − The definition of vij is the rate of product concentration Pi and substrate concentration Sj. As the The definition of v is the rate of product concentration P and substrate concentration S . As the estimation of three parametersij is required, three data pairs andi three equations are neededj to solve estimation of three parameters is required, three data pairs and three equations are needed to solve the the matrix system in Equation (4). matrix system in Equation (4). 0 − 10 1 0 − 1 v S v P Km v S B ii0 −i0 ii0iCB ⎛ ⎞C =B −ii0 i0 C (4) B − CB C B − C B v S v P CB Vmax C = B v S C (4) B jj0 −j0 jj0jCB C B −jj0 j0 C B − CB K C B − C @ v S v P A@B ⎝ m ⎠AC @ v S A kk0 − k0 kk0 k Kp − kk0 k0 Likewise, the definition of vii’ = v(Pi, Si’), i.e., i values are between 1 and m (the number of product concentrations), and i’ values are between 1 and n (the number of substrate concentrations). Alternatively, the solution for Equation (4) is presented in Equation (5) in algebraic form. ( − + − + (− + )) = (5) − + ( −) + − Catalysts 2020, 10, 853 3 of 10 Likewise, the definition of vii’ = v(Pi, Si’), i.e., i values are between 1 and m (the number of product concentrations), and i’ values are between 1 and n (the number of substrate concentrations). Alternatively, the solution for Equation (4) is presented in Equation (5) in algebraic form. vii vjj vkk (Pk(Si Sj )+Pi(Sj Sk )+Pj( Si +Sk )) Vmax = 0 0 0 0 − 0 0 − 0 − 0 0 (Pj Pi)S v v +(Pi P )S v v +(Pj Pi)S v v − k0 ii0 jj0 − k j0 ii0 kk0 − i0 jj0 kk0 PiSj Sk vii (vkk vjj )+PkSi Sj vkk (vjj vii )+PjSi Sk vjj (vii vkk ) Km = 0 0 0 0 − 0 0 0 0 0 − 0 0 0 0 0 − 0 (5) (Pi Pj) S v v +v ( PiS v +P S v +PjS v P S v ) − k0 ii0 jj0 kk0 − j0 ii0 k j0 ii0 i0 jj0 − k i0 jj0 S S v (v v )+S S v (v v )+S S v (v v ) Km j0 k0 ii0 jj0 − kk0 i0 j0 kk0 ii0 − jj0 i0 k0 jj0 kk0 − ii0 K = p (Pi Pj)S v v +v ( PiS v +P S v +PjS v P S v ) − k0 ii0 jj0 kk0 − j0 ii0 k j0 ii0 i0 jj0 − k i0 jj0 The rank of the matrix in Equation (4) must be 3 for the system to have a solution. For the case when three product concentrations are taken from the same set, Pi = Pj = Pk, the system has no solution because the rank of the resulting matrix is 2. This problem can be easily checked by observing the denominators of Equation (5) when replacing Pi, Pj, and Pk with the same value of product concentration.
Load more

Recommended publications
  • 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]
  • 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]
  • 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]
  • Enzyme Kinetics in This Exercise We Will Look at the Catalytic Behavior of Enzymes
    1 Enzyme Kinetics In this exercise we will look at the catalytic behavior of enzymes. You will use Excel to answer the questions in the exercise section. At the end of this session, you must hand in answers to all the questions, along with print outs of any plots you created. Background Enzymes are the catalysts of biological systems and are extremely efficient and specific as catalysts. In fact, typically, an enzyme accelerates the rate of a reaction by factors of at least a million compared to the rate of the same reaction in the absence of the enzyme. Most biological reactions do not occur at perceptible rates in the absence of enzymes. One of the simplest biological reactions catalyzed by an enzyme is the hydration of CO2. The catalyst in this reaction is carbonic anhydrase. This reaction is part of the respiration cycle which expels CO2 from the body. Carbonic anhydrase is a highly efficient enzyme – each enzyme molecule 5 can catalyze the hydration of 10 CO2 molecules per second. Enzymes are highly specific. Typically a particular enzyme catalyzes only a single chemical reaction or a set of closely related chemical reactions. As is true of any catalyst, enzymes do not alter the equilibrium point of the reaction. This means that the enzyme accelerates the forward and reverse reaction by precisely the same factor. For example, consider the interconversion of A and B. A ↔ B (1) -4 -1 Suppose that in the absence of the enzyme the forward rate constant (kf) is 10 s and the -6 -1 reverse rate constant (kr) is 10 s .
    [Show full text]
  • Enzyme Catalysis: Structural Basis and Energetics of Catalysis
    PHRM 836 September 8, 2015 Enzyme Catalysis: structural basis and energetics of catalysis Devlin, section 10.3 to 10.5 1. Enzyme binding of substrates and other ligands (binding sites, structural mobility) 2. Energe(cs along reac(on coordinate 3. Cofactors 4. Effect of pH on enzyme catalysis Enzyme catalysis: Review Devlin sections 10.6 and 10.7 • Defini(ons of catalysis, transi(on state, ac(vaon energy • Michaelis-Menten equaon – Kine(c parameters in enzyme kine(cs (kcat, kcat/KM, Vmax, etc) – Lineweaver-Burk plot • Transi(on-state stabilizaon • Meaning of proximity, orientaon, strain, and electrostac stabilizaon in enzyme catalysis • General acid/base catalysis • Covalent catalysis 2015, September 8 PHRM 836 - Devlin Ch 10 2 Structure determines enzymatic catalysis as illustrated by this mechanism for ____ 2015, September 8 PHRM 836 - Devlin Ch 10 www.studyblue.com 3 Substrate binding by enzymes • Highly complementary interac(ons between substrate and enzyme – Hydrophobic to hydrophobic – Hydrogen bonding – Favorable Coulombic interac(ons • Substrate binding typically involves some degree of conformaonal change in the enzyme – Enzymes need to be flexible for substrate binding and catalysis. – Provides op(mal recogni(on of substrates – Brings cataly(cally important residues to the right posi(on. 2015, September 8 PHRM 836 - Devlin Ch 10 4 Substrate binding by enzymes • Highly complementary interac(ons between substrate and enzyme – Hydrophobic to hydrophobic – Hydrogen bonding – Favorable Coulombic interac(ons • Substrate binding typically involves some degree of conformaonal change in the enzyme – Enzymes need to be flexible for substrate binding and catalysis. – Provides op(mal recogni(on of substrates – Brings cataly(cally important residues to the right posi(on.
    [Show full text]
  • PDF (Chapter 5
    ~---=---5 __ Heterogeneous Catalysis 5.1 I Introduction Catalysis is a term coined by Baron J. J. Berzelius in 1835 to describe the property of substances that facilitate chemical reactions without being consumed in them. A broad definition of catalysis also allows for materials that slow the rate of a reac­ tion. Whereas catalysts can greatly affect the rate of a reaction, the equilibrium com­ position of reactants and products is still determined solely by thermodynamics. Heterogeneous catalysts are distinguished from homogeneous catalysts by the dif­ ferent phases present during reaction. Homogeneous catalysts are present in the same phase as reactants and products, usually liquid, while heterogeneous catalysts are present in a different phase, usually solid. The main advantage of using a hetero­ geneous catalyst is the relative ease of catalyst separation from the product stream that aids in the creation of continuous chemical processes. Additionally, heteroge­ neous catalysts are typically more tolerant ofextreme operating conditions than their homogeneous analogues. A heterogeneous catalytic reaction involves adsorption of reactants from a fluid phase onto a solid surface, surface reaction of adsorbed species, and desorption of products into the fluid phase. Clearly, the presence of a catalyst provides an alter­ native sequence of elementary steps to accomplish the desired chemical reaction from that in its absence. If the energy barriers of the catalytic path are much lower than the barrier(s) of the noncatalytic path, significant enhancements in the reaction rate can be realized by use of a catalyst. This concept has already been introduced in the previous chapter with regard to the CI catalyzed decomposition of ozone (Figure 4.1.2) and enzyme-catalyzed conversion of substrate (Figure 4.2.4).
    [Show full text]
  • Lactate in the Brain: from Metabolic End-Product to Signalling Molecule
    REVIEWS Lactate in the brain: from metabolic end-product to signalling molecule Pierre J. Magistretti1,2,3* and Igor Allaman2 Abstract | Lactate in the brain has long been associated with ischaemia; however, more recent evidence shows that it can be found there under physiological conditions. In the brain, lactate is formed predominantly in astrocytes from glucose or glycogen in response to neuronal activity signals. Thus, neurons and astrocytes show tight metabolic coupling. Lactate is transferred from astrocytes to neurons to match the neuronal energetic needs, and to provide signals that modulate neuronal functions, including excitability, plasticity and memory consolidation. In addition, lactate affects several homeostatic functions. Overall, lactate ensures adequate energy supply, modulates neuronal excitability levels and regulates adaptive functions in order to set the ‘homeostatic tone’ of the nervous system. Pyruvate dehydrogenase When studied at the organ level, brain energy meta­ Notably, under physiological conditions, the (PDH). The first component bolism can be considered as being almost fully oxida­ lactate:pyruvate concentration ratio is at least 10:1 enzyme of the pyruvate tive: elegant studies pioneered in the 1940s and 1950s (REF. 11). Thus, when considering the intercellular trans­ dehydrogenase complex; by Schmitt and Kety1 and later by Sokoloff 2 showed fer of a glycolytic substrate, lactate is the predominant it converts pyruvate into acetyl-CoA, which enters the that glucose is the obligatory physiological energy substrate in the brain. This ratio can also massively tricarboxylic acid (TCA) cycle substrate of the brain and is metabolized to CO2 and increase under hypoxia, as decreases in the partial for cellular respiration.
    [Show full text]
  • Synthetic Biology Applications Inventory
    INVENTORY OF SYNTHETIC BIOLOGY PRODUCTS – EXISTING AND POSSIBLE (Draft – July 27, 2012) Why This Inventory? For good or ill, new technologies are often defined by a few iconic examples that capture the public imagination. Early on, nanotechnology was defined by its application to stain-resistant clothing and sunscreens, convenient improvements but hardly transformational. Of course, the real revolution was occurring in the background, which involved a newfound ability to see, simulate, and manipulate matter at an atomic scale. Slowly, it became apparent that nanoscale science and engineering were having pervasive impacts across multiple economic sectors and products, as well as up and down value chains, and creating significant potential for improvements in costs and efficiency. So far, synthetic biology has been associated with a few limited applications, but this initial inventory provides a glimpse of its impact on multiple sectors ranging from energy to pharmaceuticals, chemicals, and food. The real power of synthetic biology may be creating a field of knowledge critical to the design of new technologies and manufacturing processes in general. This exploratory inventory is an attempt to look over the horizon of this emerging science. As such, it is a “work in progress” and we hope others will help us as we update and expand the inventory. Research on specific applications or near-commercial activities does not guarantee eventual market entry and economic impact, but the breadth of commercial and upstream activity is important to track as the science advances. Methodology This inventory of the applications of synthetic biology was compiled from a) a Lexis-Nexis search of US newspapers and newswires on the terms “’synthetic biology’ and applications” for the years 2008-2011; b) a Web of Science search on the term “synthetic biology” for 2008-2011; c) a visual search of project descriptions and websites entered into the 2010 and 2011 iGEM competition, as provided on the iGEM website1; and d) a web search for specific companies and synthetic biology via Google.
    [Show full text]
  • Heterogeneous Catalyst Deactivation and Regeneration: a Review
    Catalysts 2015, 5, 145-269; doi:10.3390/catal5010145 OPEN ACCESS catalysts ISSN 2073-4344 www.mdpi.com/journal/catalysts Review Heterogeneous Catalyst Deactivation and Regeneration: A Review Morris D. Argyle and Calvin H. Bartholomew * Chemical Engineering Department, Brigham Young University, Provo, UT 84602, USA; E-Mail: [email protected] * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel: +1-801-422-4162, Fax: +1-801-422-0151. Academic Editor: Keith Hohn Received: 30 December 2013 / Accepted: 12 September 2014 / Published: 26 February 2015 Abstract: Deactivation of heterogeneous catalysts is a ubiquitous problem that causes loss of catalytic rate with time. This review on deactivation and regeneration of heterogeneous catalysts classifies deactivation by type (chemical, thermal, and mechanical) and by mechanism (poisoning, fouling, thermal degradation, vapor formation, vapor-solid and solid-solid reactions, and attrition/crushing). The key features and considerations for each of these deactivation types is reviewed in detail with reference to the latest literature reports in these areas. Two case studies on the deactivation mechanisms of catalysts used for cobalt Fischer-Tropsch and selective catalytic reduction are considered to provide additional depth in the topics of sintering, coking, poisoning, and fouling. Regeneration considerations and options are also briefly discussed for each deactivation mechanism. Keywords: heterogeneous catalysis; deactivation; regeneration 1. Introduction Catalyst deactivation, the loss over time of catalytic activity and/or selectivity, is a problem of great and continuing concern in the practice of industrial catalytic processes. Costs to industry for catalyst replacement and process shutdown total billions of dollars per year. Time scales for catalyst deactivation vary considerably; for example, in the case of cracking catalysts, catalyst mortality may be on the order of seconds, while in ammonia synthesis the iron catalyst may last for 5–10 years.
    [Show full text]
  • Introduction to Catalysis
    1 1 Introduction to Catalysis Ask the average person in the street what a catalyst is, and he or she will probably tell you that a catalyst is what one has under the car to clean up the exhaust. Indeed, the automotive exhaust converter represents a very successful application of cataly- sis; it does a great job in removing most of the pollutants from the exhaust leaving the engines of cars. However, catalysis has a much wider scope of application than abating pollution. Catalysis in Industry Catalysts are the workhorses of chemical transformations in the industry. Approximately 85–90 % of the products of chemical industry are made in cata- lytic processes. Catalysts are indispensable in . Production of transportation fuels in one of the approximately 440 oil refi- neries all over the world. Production of bulk and fine chemicals in all branches of chemical industry. Prevention of pollution by avoiding formation of waste (unwanted byproducts). Abatement of pollution in end-of-pipe solutions (automotive and industrial exhaust). A catalyst offers an alternative, energetically favorable mechanism to the non- catalytic reaction, thus enabling processes to be carried out under industrially feasible conditions of pressure and temperature. For example, living matter relies on enzymes, which are the most specific cata- lysts one can think of. Also, the chemical industry cannot exist without catalysis, which is an indispensable tool in the production of bulk chemicals, fine chemicals and fuels. For scientists and engineers catalysis is a tremendously challenging, highly multi- disciplinary field. Let us first see what catalysis is, and then why it is so important for mankind.
    [Show 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.
    [Show full text]