Mathematical Modeling and Analysis of Nonlinear Enzyme Catalyzed Reaction Processes

<table>Profile of dimensionless free enzyme product concentration<svg height="7.9499998" id="M120" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 23.5625 7.9499998" width="23.5625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,7.675)"><path d="M689 332q0 -81 -40 -161.5t-103.5 -131.5t-127.5 -51q-32 0 -58.5 16t-40.5 46q-70 -62 -139 -62q-45 0 -77.5 30t-32.5 86q0 8 7 52q11 77 45 187q6 19 6 34q0 6 -7 6q-24 0 -78 -64l-20 23q32 48 73 77t78 29q32 0 32 -43q0 -30 -12 -73q-27 -95 -38 -152
q-8 -44 -8 -58q0 -77 68 -77q31 0 60 33.5t39 77.5l62 260l75 16l5 -6l-63 -246q-8 -29 -8 -58q0 -77 68 -77q66 0 116 75.5t50 194.5q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D464"></path></g>
</svg>is calculated using (<a href="https://static.hindawi.com/articles/jtc/volume-2013/931091/figures/#EEq49">35</a>) for various values of dimensionless parameters<svg height="7.9499998" id="M121" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 12.7625 7.9499998" width="12.7625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,7.675)"><path d="M387 375q0 -16 -17 -31t-29 -15q-9 0 -12 13q-13 74 -80 74q-36 0 -61 -24.5t-25 -56.5t24 -51.5t68 -19.5q33 0 47 2l2 -7l-32 -42q-20 2 -54 2q-45 0 -74 -21.5t-29 -60.5q0 -41 28 -65.5t73 -24.5q78 0 145 67l17 -23q-33 -47 -84.5 -75t-111.5 -28q-70 0 -114.5 35.5
t-44.5 92.5q0 46 38 78t95 45v2q-35 10 -54.5 33t-19.5 52q0 55 53 88.5t122 33.5q67 0 98.5 -23.5t31.5 -49.5z" id="x1D700"></path></g>
</svg>,<svg height="16.3125" id="M122" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 21.512501 16.3125" width="21.512501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,12.162)"><path d="M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5
q27 -249 51 -392q7 -46 23 -46q24 0 70 60z" id="x1D706"></path></g>
<g transform="matrix(.012,-0,0,-.012,15.113,16.25)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>,<svg height="16.3125" id="M123" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 27.174999 16.3125" width="27.174999" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,12.162)"><path d="M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5
q27 -249 51 -392q7 -46 23 -46q24 0 70 60z" id="x1D706"></path></g>
<g transform="matrix(.012,-0,0,-.012,15.113,16.25)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>and<svg height="16.450001" id="M124" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 21.512501 16.450001" width="21.512501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,5.725,12.162)"><path d="M529 97q-70 -109 -136 -109q-41 0 -56 94q-23 144 -37 284q-38 -88 -99 -202.5t-93 -156.5q-26 -8 -76 -19l-9 21q71 78 145.5 193t124.5 232q-5 84 -15 128q-12 55 -29.5 75.5t-42.5 20.5q-21 0 -45 -13l-8 24q16 17 46 30t55 13q43 0 70 -46.5t40 -169.5
q27 -249 51 -392q7 -46 23 -46q24 0 70 60z" id="x1D706"></path></g>
<g transform="matrix(.012,-0,0,-.012,15.113,16.25)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg>. Solid line: (<a href="https://static.hindawi.com/articles/jtc/volume-2013/931091/figures/#EEq49">35</a>); dotted line: numerical simulation.</table>

Journal of Theoretical Chemistry

fig5

Figure 5

Figure 5: Mathematical Modeling and Analysis of Nonlinear Enzyme Catalyzed Reaction Processes 