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</settings> <regions> <region region-id="237" left="6" top="2.25" width="428.25" height="24" align-x="6" align-y="12" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Problem 9.2 of Shuler & Kargi.<sp count="2"/>Batch fermentor operated in two stages.<sp count="2"/>Given..Odesolve Instructor: Nam Sun Wang </text> </region> <region region-id="238" left="6" top="30" width="436.5" height="9.75" align-x="6" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="435" display-height="8.25"/> </picture> <rendering item-idref="3"/> </region> <region region-id="240" left="6" top="44.25" width="102.75" height="12" align-x="6" align-y="54" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text 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push-down="false" lock-width="true"> g/liter </text> </region> <region region-id="288" left="270" top="63" width="34.5" height="16.5" align-x="285.75" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="x">Y</ml:id> <ml:real>0.4</ml:real> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="266" left="312" top="62.25" width="75" height="12" align-x="312" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> g cell/g substrate </text> </region> <region region-id="280" left="18" top="82.5" width="263.25" height="35.25" align-x="68.25" align-y="102" show-border="false" show-highlight="false" is-protected="true" z-order="0" 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<ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve" subscript="y">μ</ml:id> <ml:boundVars> <ml:id xml:space="preserve">s</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:lessThan/> <ml:real>0</ml:real> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve" subscript="m1">μ</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="s">K</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="283" left="6" top="116.25" width="131.25" height="12" align-x="6" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Product formation parameters: </text> </region> <region region-id="289" left="18" top="129" width="36" height="16.5" align-x="35.25" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="p">Y</ml:id> <ml:real>0.6</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="290" left="66" top="128.25" width="92.25" height="12" align-x="66" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> g product/g substrate </text> </region> <region region-id="291" left="168" top="129" width="140.25" height="16.5" align-x="219" align-y="138" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" 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use-page-width="false" push-down="false" lock-width="true"> g product/(g cell<f family="Symbol" charset="2"></f>h) </text> </region> <region region-id="298" left="6" top="146.25" width="64.5" height="12" align-x="6" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Initial condition </text> </region> <region region-id="302" left="84" top="147" width="33" height="16.5" align-x="98.25" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0">x</ml:id> <ml:real>0.1</ml:real> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="301" left="132" top="147" width="27" height="16.5" align-x="147" align-y="156" 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subscript="f2">t</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>9.3360444498424755</ml:real> <ml:real>39.9999153490966</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="371" left="210" top="543" width="90" height="16.5" align-x="267" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">prod</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="f1">t</ml:id> <ml:id xml:space="preserve" subscript="f2">t</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.021531727076413449</ml:real> </result> </ml:eval> </math> <rendering item-idref="33"/> </region> <region region-id="380" left="192" top="560.25" width="244.5" height="12" align-x="192" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> The productivity in 2 CSTRs in series was 0.027 g/(L<f family="Symbol" charset="2"></f>h) </text> </region> <region region-id="373" left="6" top="578.25" width="25.5" height="12" align-x="6" align-y="588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> profile </text> </region> <region region-id="701" left="42" top="568.5" width="79.5" height="45.75" align-x="67.5" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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region-id="392" left="6" top="750" width="436.5" height="9.75" align-x="6" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="37" display-width="435" display-height="8.25"/> </picture> <rendering item-idref="38"/> </region> <region region-id="393" left="6" top="764.25" width="432" height="24" align-x="6" align-y="774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> The product is encoded in a plasmid. 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Optimal profile </text> </region> <region region-id="763" left="78" top="1268.25" width="84.75" height="62.25" align-x="103.5" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:matrix> <ml:apply> <ml:id xml:space="preserve">xysp</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="f1">t</ml:id> <ml:id xml:space="preserve" subscript="f2">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="780" left="6" top="1332" width="177" height="146.25" align-x="6" 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Fermentation time for 5-h induction was longer than that for 10-h induction (~32h versus ~20h). Product concentration for 5-h induction was lower than that for 10-h induction (0.236 g/L versus 0.353 g/L).<sp count="2"/>5-h induction led to a fermentor full of nonproductive plasmid-free cells, the fraction of nonproductive plasmid-free cells being 0.777 for 5-h induction versus 0.022 for 10-h induction. </text> </region> <region region-id="799" left="6" top="1712.25" width="80.25" height="12" align-x="6" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sub optimal profile </text> </region> <region region-id="800" left="102" top="1713" width="33" height="16.5" align-x="118.5" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" 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xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:matrix> <ml:apply> <ml:id xml:space="preserve">xysp</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="f1">t</ml:id> <ml:id xml:space="preserve" subscript="f2">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="808" left="6" top="1734" width="177" height="146.25" align-x="6" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="75"/> <rendering item-idref="76"/> </region> <region region-id="814" left="192" top="1754.25" width="167.25" height="12" align-x="192" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> product concentration at end of the run </text> </region> <region region-id="815" 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tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Cell growth parameters: </text> </region> <region region-id="309" left="18" top="63" width="42" height="16.5" align-x="41.25" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="m1">μ</ml:id> <ml:real>0.3</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="310" left="66" top="59.25" width="15" height="15" align-x="66" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> h-1 <sp/> </text> </region> <region region-id="311" left="108" top="63" width="35.25" height="16.5" align-x="131.25" align-y="72" show-border="false" 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subscript="f2">t</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="2" cols="1"> <ml:real>9.3360444498424755</ml:real> <ml:real>39.9999153490966</ml:real> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="32"/> </region> <region region-id="371" left="210" top="543" width="90" height="16.5" align-x="267" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:id xml:space="preserve">prod</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="f1">t</ml:id> <ml:id xml:space="preserve" subscript="f2">t</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>0.021531727076413449</ml:real> </result> </ml:eval> </math> <rendering item-idref="33"/> </region> <region region-id="380" left="192" top="560.25" width="244.5" height="12" align-x="192" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> The productivity in 2 CSTRs in series was 0.027 g/(L<f family="Symbol" charset="2"></f>h) </text> </region> <region region-id="373" left="6" top="578.25" width="25.5" height="12" align-x="6" align-y="588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> profile </text> </region> <region region-id="701" left="42" top="568.5" width="79.5" height="45.75" align-x="67.5" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define 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region-id="392" left="6" top="750" width="436.5" height="9.75" align-x="6" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="37" display-width="435" display-height="8.25"/> </picture> <rendering item-idref="38"/> </region> <region region-id="393" left="6" top="764.25" width="432" height="24" align-x="6" align-y="774" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> The product is encoded in a plasmid. 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Optimal profile </text> </region> <region region-id="763" left="78" top="1268.25" width="84.75" height="62.25" align-x="103.5" align-y="1302" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:matrix rows="4" cols="1"> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:matrix> <ml:apply> <ml:id xml:space="preserve">xysp</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="f1">t</ml:id> <ml:id xml:space="preserve" subscript="f2">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="780" left="6" top="1332" width="177" height="146.25" align-x="6" 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background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Fermentation time for 5-h induction was longer than that for 10-h induction (~32h versus ~20h). Product concentration for 5-h induction was lower than that for 10-h induction (0.236 g/L versus 0.353 g/L).<sp count="2"/>5-h induction led to a fermentor full of nonproductive plasmid-free cells, the fraction of nonproductive plasmid-free cells being 0.777 for 5-h induction versus 0.022 for 10-h induction. </text> </region> <region region-id="799" left="6" top="1712.25" width="80.25" height="12" align-x="6" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Sub optimal profile </text> </region> <region region-id="800" left="102" top="1713" width="33" height="16.5" align-x="118.5" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" 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xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:matrix> <ml:apply> <ml:id xml:space="preserve">xysp</ml:id> <ml:sequence> <ml:id xml:space="preserve" subscript="f1">t</ml:id> <ml:id xml:space="preserve" subscript="f2">t</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="74"/> </region> <region region-id="808" left="6" top="1734" width="177" height="146.25" align-x="6" align-y="1734" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="75"/> <rendering item-idref="76"/> </region> <region region-id="814" left="192" top="1754.25" width="167.25" height="12" align-x="192" align-y="1764" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> product concentration at end of the run </text> </region> <region region-id="815" 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