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Activation Energy

Activation Energy

A

FIELDS OF STUDY that is higher in energy than the starting materials. An intermediate is a stable chemical structure formed Physical ; Inorganic Chemistry; during a reaction process that can often be captured and isolated by chemical means. Once this structure SUMMARY is formed, the reaction process can either progress to form products or revert back to the original reactants. The of a process is defined, and Activation energy is the energy required for a spe- its importance in chemical processes is elaborated. cific to occur. In a reaction, two Activation energy is a widely variable quantity in dif- reactant contact each other with the en- ferent reactions but is nevertheless characteristic of ergy of their ambient states.(The ambient state of a any specific reaction process. material can be thought of as its “default” state—the state it takes at one atmosphere of pressure and what PRINCIPAL TERMS is commonly considered to be room temperature.) In the case of a spontaneous reaction, the energy of the ƒƒ : a mathematical function collision is sufficient to initiate the formation of the that relates the rate of a reaction to the energy or intermediate. In a nonspontaneous required to initiate the reaction and the absolute reaction, the energy of the molecular collision is not temperature at which it is carried out. sufficient, and the two molecules will not interact. ƒƒ catalyst: a chemical species that initiates or speeds The input of some additional energy is required to up a chemical reaction but is not itself consumed drive the two molecules together so that the transi- in the reaction. tion state or intermediate is formed and the reaction ƒƒ chemical reaction: a process in which the mole- can proceed. The energy released in the transforma- cules of two or more chemical species interact with tion of reactants into products is generally sufficient each other in a way that causes the electrons in the to drive the reactions of other molecules in the reac- bonds between atoms to be rearranged, tion mixture. ƒƒ resulting: in changes to the chemical identities of Another way to look at activation energy is to think the materials. of it as the minimum amount of energy that two inter- ƒƒ : how much of a ­particular reaction or acting molecules must gain in order to weaken bonds reaction step occurs per unit time. between atoms in both molecules so that those bonds ƒƒ transition state: an unstable structure formed can be rearranged. Since chemical reactions are es- during a chemical reaction at the peak of its poten- sentially processes of breaking and making bonds, tial energy that cannot be isolated and ultimately having sufficient energy to overcome the strength of breaks down, either forming the products of the the appropriate bonds is essential if there is to be any reaction or reverting back to the original reactants. reaction between the two molecules.

Activation Energy in Chemical Reactions Activation Energy and Reaction Rates Activation energy can be thought of as a barrier that Reaction rates can be related directly to their ac- the reactants in a chemical reaction must overcome if tivation . This relationship is defined by the reaction is to proceed to the formation of prod- the Arrhenius equation, formulated in 1884 by the ucts. The molecules that are involved must rearrange Swedish scientist Svante Arrhenius (1859–1927), who to form either a transition state or an intermediate received the Nobel Prize in Chemistry in 1903.The

1 Activation energy Principles of

ACTIVATION ENERGY DIAGRAM the rate constant k is determined almost solely by the value of e−E/ RT, which can range over several hundred orders of magnitude, de- pending on the relative values of E and T. Activation The course of a reaction depends Energy (E ) a on the relative difference between the energy of the reactants and that A+B of the products. The greater this dif- ference is, the more impetus there is for the reaction to proceed to the formation of products. This is typi- cally illustrated in a plot of energy C+D versus the reaction coordinate, a symbolic representation of the prog-

Potential Energy ress of a reaction. In the plot, the energy level of the reactants, on the left, is either higher or lower than Reaction Progress that of the products, on the right. In Arrhenius equation relates the rate constant of a re- between, a curved line rises from the energy level of action to its activation energy and the absolute tem- the reactants to a maximum value before falling to perature and has the form the energy level of the products. The difference be- tween the energy level of the reactants and this peak k = Ae−E/RT energy value represents the activation energy for the reaction, while the difference between the energy where k is the rate constant for the reaction or pro- levels of the reactants and the products represents cess; A is the pre-exponential factor, also known in the energy released in the reaction, also called its some cases as the frequency factor; E (or Ea) is the . activation energy for the reaction or process; R is The specific rate of any individual reaction is de- the gas constant; T is the absolute temperature; termined by its activation energy. However, in mass and the mathematical constant e is the base of the quantities, the energy differences between reactants natural logarithm, so that the natural logarithm and products in the system also play a role. This can (ln) of e is equal to 1.The Arrhenius equation has be understood by considering the Boltzmann frac- been found to apply not only to chemical reactions tion e−E/RT, which describes the fraction of mol- but to physical processes as well. T he relationship ecules in the system having energy greater than E. can be most clearly seen by plotting experimen- As energy is released from several reactions, the frac- tally determined logarithmic values of k against tion of molecules present at any given time with suf- the inverse of the absolute temperature, 1/T. This ficient energy to react increases, and more reactions results in a straight line plot, from which the activa- can occur in any given time period. Each reaction re- tion energy of the reaction or process can be cal- quires the same activation energy, and the amount of culated. The pre-exponential factor A is identified energy that is available in the system to permit reac- as the value that the specific rate constant k would tions to occur may be anything from “barely enough” have if the activation energy E were zero (a sponta- to “excessive.” neous reaction).In that special case, the exponent The activation energy of a reaction can be greatly −E/RT would also be equal to zero, making e−E/RT reduced by the inclusion of a catalyst, a material that equal 1 and thus causing the value of k to be equal takes part in the but is not con- to A. For different specific reactions, the value of sumed in the reaction. Catalysts function by forming A ranges over several orders of magnitude, but an activated complex with the reactants, typically

2 Principles of Biology Activation energy

CATALYZED ACTIVATION ENERGY sufficient to drive many instances of the reaction in the gas mixture, Uncatalyzed Reaction Catalyzed Reaction with each subsequent occurrence releasing an equal amount of en- ergy as the enthalpy of reaction. The second example is the so- a ) (E ) a called thermite reaction, in which (E iron oxide and aluminum metal react to produce aluminum oxide and iron metal. This is a spectacular A+B reaction often demonstrated for Uncatalyzed Activation Energy Z chemistry exhibitions. Because the Catalyzed Activation Energy activation energy of the thermite reaction is very high, the reaction is very difficult to initiate and must typ- C+D ically be ignited by a burning piece of magnesium metal; once it has begun,

Potential Energy however, it is essentially impossible to stop it due to the amount of energy Reaction Progress that is released. Typically, the iron metal falls out of the reaction mix- ture as a white-hot liquid. constraining the reactant molecules in an orientation that they would otherwise have to achieve through Activation Energy in Biological Systems collision with each other. This reduces the energy Activation energy applies to biochemical processes ­necessary to achieve that particular orientation—that as well as to physical processes. The chirping of is, the activation energy—so that the reaction can pro- crickets, for example, is dependent on tempera- ceed. When the reactant molecules are constrained in ture in a manner that is in complete accord with the activated complex with the catalyst, bonds between the Arrhenius equation. In biological systems, the certain atoms are weakened and the orientations of activation energy of processes is made a great deal atomic and molecular orbitals that must interact are lower by the catalytic action of molecules often brought into the proper alignment, or trajectory, called . Enzymes have well-defined three- for the new bonds to form between atoms. dimensional structural shapes that allow them to coordinate with other molecules in specific ways, Activation Energy in Action rather like the way a key works with a lock. The co- The activation energy of a reaction can range from ordination normally alters the three-dimensional exceedingly small to very large. Two examples shape of the or otherwise inter- serve to illustrate this point. For the first, consider acts with it so that specific bonds are weakened and the addition of two parts hydrogen gas (H2) to one the molecular geometry is changed such that reac- part oxygen gas (O2).This is an explosive mixture of tion is highly favored. gases, yet the two mixed gases are quite happy to co- exist quietly in the same container, no matter how Richard M. Renneboog, MSc much is present. The introduction of an initiator such as an electrical , however, results in an al- Further Reading most instantaneous reaction to form water (H2O), Arnaut, Luís, Sebastião Formosinho, and Hugh accompanied by the release of a great deal of en- ­Burrows. : From Molecular ­Structure ergy. The activation energy of the reaction between to Chemical . Oxford: Elsevier, 2007. Print. hydrogen and oxygen is very low, and the amount Bell, Jerry A. Chemistry: A Project of the American of energy released by one reaction is more than ­Chemical Society. New York: Freeman, 2005.Print.

3 Active transport Principles of Biology

Lafferty, Peter, and Julian Rowe, eds. The Hutchinson Raymond, Kenneth W. General, Organic, and Biological Dictionary of Science. 2nd ed. Oxford: Helicon, Chemistry: An Integrated Approach. 4th ed. Hoboken: 1998.Print. Wiley, 2014.Print. Masterton, William L., Cecile N. Hurley, and Edward Zumdahl, Steven S., and Susan Zumdahl. Chemistry. Neth. Chemistry: Principles and Reactions. 7th ed. 9th ed. Belmont: Brooks Coles, 2013. Print. Belmont: Brooks, 2012. Print.

ACTIVATION ENERGY SAMPLE PROBLEM

Use the Arrhenius equation to determine the activation en- ln k = ln A + ln(e−ER/ T ) ergy at 0°C for a reaction having a specific rate­constant (k) E of 0.023 moles per liter per second and a pre-exponential ln kA= ln − factor (A) of 2,303 moles per liter per second. Use the gas RT E constant. = ln Ak− ln RT J R = 8.314 EA=−RT (lnln)k mol K J Answer: Substitute in the values of R (8.314 ), T mol K Convert the temperature from degrees Celsius to kelvins, (temperature), A (pre-exponential factor), and k (rate con- given that K = °C + 273.15: stant). Calculate, paying attention to the units throughout: ER=−Tk(lln A n ) K = 0 + 273.15 = 273.15 J E =×(8.314 273.15 K)(ln 2303 − ln 0.023) The Arrhenius equation is mol K J k = Ae−E/RT E =×(8.314 273.15 K)[7.742 −−( 3.772)] mol K Rearrange the equation using natural logarithmic (ln) J relationships: E = 26147.938 mol

Active transport

FIELDS OF STUDY PRINCIPAL TERMS

Biochemistry; Molecular Biology; Genetics ƒƒ (ATP): a molecule con- sisting of adenine, ribose, and a triphosphate SUMMARY chain that is used to transfer the energy needed to carry out numerous cellular processes. The process of active transport is defined, and its ƒƒ cell membrane: a biological membrane that forms importance in biochemical processes is elaborated. a semipermeable barrier separating the interior of Active transport is an essential feature of the bio- a cell from the exterior. chemistry of living systems and helps maintain the ƒƒ concentration gradient: the gradual change in the necessary concentrations of various biochemical concentration of solutes in a solution across a spe- components and electrolytes for the proper func- cific distance. tioning of cellular metabolism.

4 Principles of Biology Active transport

ACTIVE TRANSPORT

Outside of Cell

ATP

+P ADP

Inside of Cell

ƒƒ diffusion: the process by which different particles, of passive transport. Instead, those entities must be such as atoms and molecules, gradually become physically transported across membranes by various intermingled due to random motion caused by mechanisms collectively termed pumps. A pump is a thermal energy. type of mediated transport system that functions to ƒƒ passive transport: the passage of materials through conduct ions, amino acids, , and other polar a membrane with no input of energy required. compounds through the nonionic lipid bilayer, the highly nonpolar material that makes up the cell wall. The Mechanics of Active Transport Pumps always work against the concentration gradient In living cells, biochemical processes transport mate- to move materials out of regions of low concentration rials necessary for a properly functioning metabolism and into regions of higher concentration, using energy through cell membranes. Passive transport does not derived from biochemical reactions. The transported require an input of energy to move materials across material is subsequently used in other biochemical re- cell walls because it operates in the same direction actions that return the energy used during transport. as the concentration gradient, moving the materials from an area of high pressure to one of low pressure. Cell Walls and Lipid Bilayers Active transport can be thought of as a “shuttle ser- Long-chain fatty acids are organic molecules vice” for ions and other polar materials that cannot whose molecular structure consists of a single hy- pass through a cell membrane by diffusion, a kind drocarbon chain terminated by a carboxylic acid

5 Active transport Principles of Biology functional group (−COOH). The carboxyl group in the metabolic functions that occur within cells. is highly polar and hydrophilic, while the hydro- This is a very important function, and the nature carbon moiety, or portion, of the molecule is very of active transport allows cells to retain a relatively nonpolar and hydrophobic. Carboxylic acids are high concentration of such materials even when converted to esters by -mediated reactions their concentrations outside of the cell are quite with alcohols. In an ester, the carboxyl functional low. A second important function of active-trans- group retains the highly polar character that it had port systems is to regulate and maintain the organ- in its free carboxylic acid form, giving the long- ism’s metabolic steady state, a balanced state in chain esters, called lipids, a polar-nonpolar struc- which the material and energy that the organism ture similar to that of the free carboxylic acids. removes from its environment through living When carboxylic acids are esterified with glyc- functions is equal to the energy and materials that erol, which has three hydroxyl (−OH) functional it returns to the environment through those same groups, the resulting triesters are called triglyc- functions. The biochemical processes of metabo- erides. Lipids and triglycerides are the principal lism use energy and materials taken from the en- forms in which long-chain fatty acids are found in vironment. Anabolic processes remove materials biological systems. from the environment and use energy from reac- The hydrocarbon chains and the carboxyl- tions involving those materials to build and sup- based portions of fatty acids and their esters do port the life of the organism. Catabolic processes not interact with each other due to their different remove used materials from the organism and re- ­hydrophilicities—that is, the degrees to which they turn them to the environment, releasing the en- attract and interact with water and other polar ergy stored in those materials. ­molecules—but they are quite capable of inter- Active transport maintains a constant optimal acting with the corresponding portions of other amount of various inorganic elements within the molecules. The hydrocarbon chains associate pref- living cells of an organism. Potassium ions, for ex- erentially with each other, as do the carboxyl por- ample, are essential to the proper functioning of tions. The basic structure of the lipid bilayer results many intracellular processes. An active-transport from the hydrocarbon portions of the acids of two system produces potassium-ion channels in cell layers of such molecules intermingling and essen- walls of nerves and muscles, including the cardiac tially dissolving each other. The carboxyl functions muscles. Potassium ions are delivered into the cy- on the other ends of the one on either side of the toplasm of the cell via these channels to replace very hydrophobic interior layer. The resulting struc- ejected sodium ions, thus maintaining a constant ture is a lipid bilayer. ionic concentration within the cell. The system The walls of all animal cells are formed of lipid maintains a relatively high concentration of potas- bilayers, allowing them to interact with water-based sium ions in most aerobic cells, between 100 and fluids while isolating the sensitive materials and 150 millimolars (mM), whether they are plant, processes that take place within each cell. The fluid animal, or microbial in nature and regardless of inside of each cell is also water based, which neces- the concentration outside of the cells. (A 1 mM sitates some means of transporting vital polar mate- solution has a concentration of 0.001 moles per rials from the exterior of the cell to the interior and liter.) The potassium ions that are pumped into moving extraneous materials and metabolites in the the cell also serve to maintain the electric poten- opposite direction for elimination. This movement is tial across the cell membrane, a factor that affects accomplished by active transport. the free-energy change in reactions involved in active-transport systems. Functions of Active-Transport Systems Active-transport systems serve a variety of func- Active Transport in Action tions in the biochemistry of living systems. Their The transfer of ions across a membrane or against principal function is to allow the organism to ex- a concentration gradient by active transport is ac- tract “” and other essential materials for use companied by a free-energy change (ΔG) that can

6 Principles of Biology Active transport be calculated by one of two equations. The first from the structure by the enzymatic cleavage of the equation represents the free-energy change for third phosphate segment from the triphosphate the transfer of neutral materials against a concen- moiety, transforming the molecule into adensosine tration gradient. This is described by the following diphosphate (ADP), and it is restored by concate- equations: nating, or joining, a third phosphate ion to ADP to c re-form ATP. G = RT ln 2 c The function of muscle cells depends on the ac- 1 tive transport of calcium ions and sodium ions, a 2+ J process termed the calcium ion pump or Ca pump. 8.314 mol K The calcium ion pump works in an organelle of muscle cells called the sarcoplasmic reticulum and where R is the gas constant and T is the absolute tem- is powered by ATP hydrolysis reactions mediated by perature in kelvins, ln is the natural logarithm func- the enzyme calcium adenosine triphosphatase. This tion, and c1 and c2 are concentrations on either side process is critical to the contraction and relaxation of the membrane in molars, or moles per liter (M), of muscle fibers, especially heart muscles. The sar- with c2 being greater than c1. coplasmic reticulum is a cell structure that stores The second equation, which represents the and releases calcium ions to aid in this contraction free-energy change for the transfer of electrically and relaxation. In muscle cells, the rapid release of charged materials, needs to account for the charge calcium ions from the sarcoplasmic reticulum into on the material being transported and the differ- the cytosol, the cellular fluid outside of the organ- ence in electric potential across the membrane. The elles, triggers contraction of the muscle, while rapid latter is determined by the neutral nature of the removal of calcium ions from the cytosol and back lipid bilayer, which causes it to act as a capacitor, or into the sarcoplasmic reticulum triggers relaxation energy-storage device, and the presence of charge of the muscle. as maintained by the potassium ions in the cytosol. The normal concentration of free calcium ions in The free-energy expression for the transport of the cytosol is between 0.1 and 0.2 micromolar (µM, charged species across a cell membrane is given by or 10−6 moles per liter), increasing when the muscle the following equation: contracts and returning to the normal value when it relaxes. c G = RT ln 2 +ZF c 1 Richard M. Renneboog, MSc where Z is the charge on the ion, F is the Faraday constant (96,485.3365 coulombs per mole, the elec- Further Reading tric charge on one mole of electrons), and is the Lafferty, Peter, and Julian Rowe, eds. The Hutchinson difference in electric potential across the membrane Dictionary of Science. 2nd ed. Oxford: Helicon, in volts. 1998. Print. Lehninger, Albert L. Biochemistry: The Molecular ATP and Active Transport Basis of Cell Structure and Function. 2nd ed. New The energy used in active-transport systems is York: Worth, 1975. Print. ­obtained through enzyme-mediated reactions of ad- Lodish, Harvey, et al. Molecular Cell Biology. 7th ed. enosine triphosphate (ATP). ATP molecules ­consist New York: Freeman, 2013. Print. of a molecule of the nucleobase adenine that is Pelczar, Michael J., Jr., E. C. S. Chan, and Noel R. bonded to a molecule of ribose sugar, which in turn Krieg. Microbiology: Concepts and Applications. New is bonded to a triphosphate ion. A magnesium ion York: McGraw, 1993. Print. coordinates and stabilizes the second and third seg- Reece, Jane B., et al. Campbell Biology. 10th ed. San ments of the triphosphate moiety. Energy is derived Francisco: Cummings, 2013. Print.

7 Aging Principles of Biology

ACTIVE TRANSPORT SAMPLE PROBLEM

Use the free-energy equation for active transport against a Convert the concentration values from micromolars to concentration gradient to determine the free energy associ- molars: ated with transporting neutral amino-acid molecules across a membrane from a concentration of 20 μM to one of 43 −6 c1 = 20 μM = 20 × 10 M = 0.00002 M μM. Assume normal body temperature of 37°C. Use. −6 J c2 = 43 μM = 43 × 10 M = 0.000043 M R = 8.314 mol K Substitute in the values of R, T, c1, and c2 and calculate, paying attention to the units throughout: c Answer: G = RT ln 2 The materials being transported are electrically c1 neutral. Therefore, use the equation J 0.000043 G = (8.314 )(310.15 K)ln c mol K 0.00002 G = RT ln 2 J c1 G = 1973.8 mol Convert the temperature from °C to K: The free energy of active transport of neutral amino ­acids across a concentration gradient from 20 μM to 43 μM is K = °C + 273.15 1973.8 joules per mole, or 1.9738 kilojoules per mole. K = 37 + 273.15 = 310.15

Aging

FIELDS OF STUDY Basic Principles Progressive and irreversible change has been called Anatomy, cell biology, developmental biology, ge- the single common property of all aging systems. netics, neurobiology, pathology, physiology When change is reversible or self-maintaining, such as one would see in a forest, for example, the effects SUMMARY of aging are often not observable. Growth of the forest is evident, but with the right conditions, trees Aging is the process of progressive and irreversible within the forest may grow for hundreds of years in change common to all living organisms. There are the absence of disease. Certain conditions of the striking similarities in the physical process of aging forest system help to regenerate, renew, and reverse among all animal species. changes that happen within that system. However, in animals some change is not revers- PRINCIPAL TERMS ible. The changes in the cells of the body accumulate over time and result in a steady downward trend. The ƒƒ aging: a process common to all living organisms, end point of this trend is the death of the organism. eventually resulting in death or conclusion of the Aging is a normal part of the life cycle. This is known life cycle to be true because aging changes within populations ƒƒ cognition: ability to perceive or understand death: are rather predictable. The changes associated with the cessation of all body and brain functions aging that are seen in all animal species may occur ƒƒ function: ability, capacity, performance for similar reasons. These may include chemical ƒƒ life span: length of life from birth to death aging, extracellular aging, intracellular aging, and ƒƒ longevity: length of life aging of cells.

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