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catalysis.html
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<!DOCTYPE html>
<html>
<head>
<title>Catalysis</title>
<style type="text/css">
body {
background-color: #FFFFFF;
font-family: Verdana, sans-serif;
font-size: 12 px
}
</style>
<script type="text/x-mathjax-config">
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</script>
<script type="text/x-mathjax-config">
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src="https://c328740.ssl.cf1.rackcdn.com/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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<script type="text/javascript" src="functions.js"></script>
</head>
<body>
<div style="display:none">
$
\newcommand{\avg}[1]{\langle #1 \rangle}
\newcommand{\conc}[1]{[\mathrm{#1}]}
\newcommand{\conceq}[1]{[\mathrm{#1}]^{\mathrm{eq}}}
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$
</div>
<h2>
Essentials of Catalysis (Enzyme Action)
</h2>
<h3>
Key points
</h3>
<ul>
<li> <b>Catalysis</b> is the acceleration of a molecular process, such as a chemical reaction (i.e., covalent change), isomerization (i.e., conformational change), or a binding process. The catalyst remains unchanged after the process. </li>
<li> <b>It goes both ways:</b> All molecular processes are reversible, and a given catalyst (e.g., an enzyme) necessarily catalyzes both directions of the reaction equally well, as explained below. This key point is sometimes overlooked. </li>
<li> <b>In the cell:</b> Very few chemical reactions necessary for cellular activity (e.g., <a href="javascript:changeTo('catalysis','phosphor')">phosophorylation</a>, <a href="javascript:changeTo('catalysis','synthesis')">chemical synthesis</a>) occur spontaneously during the lifetime of a cell.
This necessitates catalysis, but more importantly, <i>provides a means for the cell to regulate its processes.</i>
In essence, reactions only happen when the necessary enzyme is present and active, and the presence/activity of enzymes is tightly regulated through control of protein expression, degradation, and post-translational modifications such as phosphorylation. </li>
</ul>
<h3>
Basic Catalysis: Isomerization or Unimolecular Chemical Change
</h3>
<ul>
<p style="text-align:center">
<img src="images/catalysis-landscape.gif" height = "250" />
</p>
<li> Isomerization is a conformational change in a small molecule or a macromolecule like protein, RNA, or DNA. </li>
<li> A unimolecular reaction is one affecting only a single molecule, perhaps by forming or breaking a single covalent bond within the molecule. </li>
<li> Either situation can be schematized using a simple energy landscape, in which high energy barriers are rarely overcome (i.e., characterized by low rates). </li>
</ul>
In catalysis, rates increase. Denoting catalyzed rates with primes, we have
\begin{equation}
\label{kcat}
k'_+ > k_+
\hspace{0.5cm} \mbox{and} \hspace{0.5cm}
k'_- > k_- .
\end{equation}
However, catalysis cannot change the <a href="javascript:changeTo('catalysis','equil')">equilibrium</a> ratio of the state populations $\conc{A} / \conc{A*}$.
Mathematically,
<p style="text-align:center">
<img src="images/catalysis-equil-eqns.gif" height = "150" />
</p>
In words, the catalyzed rates <i>increase together</i> so as to maintain the proper equilibrium - which is unaffected by the presence of a catalyst.
<p>
There is a nice way to convince yourself that catalysis cannot change the equilibrium point - it is a worthwhile <b>exercise</b>.
Consider a <a href="javascript:changeTo('catalysis','cycles')">cycle</a> in which the two states of interest are connected by both a catalyzed and uncatalyzed process.
You can show that, if the ratio of forward and reverse rates does not agree for the two cases, the cycle will spontaneously circulate - violating the second law of thermodynamics and enabling the construction of (imaginary) energy-creating processes.
</p>
</body>
</html>