6: Biochemical Reactions
- Page ID
- 93487
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Biochemistry is the study of the chemistry of life. It can be considered a branch of molecular biology, perhaps more focused on specific molecules and their reactions, or a branch of chemistry focused on the complex chemical reactions occurring in living organisms. One can guess that the first application of biochemistry happened about 5000 years ago when bread was made using yeast.
Modern biochemistry, however, had a relatively slow start among the sciences, as did modern biology. Isaac Newton’s publication of Principia Mathematica in 1687 preceded Darwin’s Origin of Species in 1859 by almost 200 years. I find this amazing because the ideas of Darwin are in many ways simpler and easier to understand than the mathematical theory of Newton. Most of the delay must be attributed to a fundamental conflict between science and religion. The physical sciences experienced this conflict early-witness the famous prosecution of Galileo by the Catholic Church in 1633, during which Galileo was forced to recant his heliocentric viewbut the conflict of religion with evolutionary biology continues even to this day. Advances in biochemistry were initially delayed because it was long believed that life was not subject to the laws of science the way non-life was, and that only living things could produce the molecules of life. Certainly, this was more a religious conviction than a scientific one. Then Friedrich Wöhler in 1828 published his landmark paper on the synthesis of urea (a waste product neutralizing toxic ammonia before excretion in the urine), demonstrating for the first time that organic compounds can be created artificially.
Here, we present mathematical models for some important biochemical reactions. We begin by introducing a useful model for a chemical reaction: the law of mass action. We then model what may be the most important biochemical reactions, namely those catalyzed by enzymes. Using the mathematical model of enzyme kinetics, we consider three fundamental enzymatic properties: competitive inhibition, allosteric inhibition, and cooperativity.
- 6.3: Competitive Inhibition
- Competitive inhibition occurs when inhibitor molecules compete with substrate molecules for binding to the same enzyme’s active site. When an inhibitor is bound to the enzyme, no product is produced so competitive inhibition will reduce the velocity of the reaction.
- 6.4: Allosteric Inhibition
- The term allostery comes from the Greek word allos, meaning different, and stereos, meaning solid, and refers to an enzyme with a regulatory binding site separate from its active binding site. In our model of allosteric inhibition, an inhibitor molecule is assumed to bind to its own regulatory site on the enzyme, resulting in either a lowered binding affinity of the substrate to the enzyme, or a lowered conversion rate of substrate to product.