<p>The use of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase in the food, feed, and industrial sectors is constantly increasing, especially in the context of sustainable development. Modeling starch hydrolysis by commercial <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase with enzyme deactivation was performed for initial concentration of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({20\%}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({30\%}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>30</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({40\%}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>40</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> at 333 K. However, earlier in this study, need to determine the parameters of the starch hydrolysis process using commercial <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase from <i>Bacillus</i> spp. The analysis focused on determining the deactivation energy <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{\text{d}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> in starch hydrolysis while simultaneously deactivating commercial <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylases from <i>Bacillus subtillis</i> and <i>Bacillus licheniformis</i>. The mathematical model applied assumes that the changes in starch concentrations and the deactivation of commercially bacterial <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase are first-order reactions with respect to enzyme concentration. The calculated activation energies <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq13.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{\text{a}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>a</mtext> </msub> </math></EquationSource> </InlineEquation> ranged from <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq14.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">\({22.08 \pm 6.96}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>22.08</mn> <mo>±</mo> <mn>6.96</mn> </mrow> </math></EquationSource> </InlineEquation> kJ <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq15.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {mol}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>mol</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq16"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq16.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">\({70.35 \pm 15.24}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>70.35</mn> <mo>±</mo> <mn>15.24</mn> </mrow> </math></EquationSource> </InlineEquation> kJ <InlineEquation ID="IEq17"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq15.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {mol}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>mol</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>, and the deactivation energies <InlineEquation ID="IEq18"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{\text{d}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> ranged from <InlineEquation ID="IEq19"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq19.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">\({21.30 \pm 1.05}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>21.30</mn> <mo>±</mo> <mn>1.05</mn> </mrow> </math></EquationSource> </InlineEquation> kJ <InlineEquation ID="IEq20"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq15.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {mol}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>mol</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq21"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq21.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="95" /> </InlineMediaObject> <EquationSource Format="TEX">\({163.66 \pm 6.57}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>163.66</mn> <mo>±</mo> <mn>6.57</mn> </mrow> </math></EquationSource> </InlineEquation> kJ <InlineEquation ID="IEq22"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq15.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text {mol}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>mol</mtext> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>. The results obtained in this study were used to model the conversion of starch hydrolysis by commercial <InlineEquation ID="IEq23"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase from <i>Bacillus</i> spp. Additionally, the obtained <InlineEquation ID="IEq24"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq24.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{\text{a}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>a</mtext> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq25"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq25.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{\text{d}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> values from the activity versus temperature were compared to the <InlineEquation ID="IEq26"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq26.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{{\text{a}}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>a</mtext> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq27"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq27.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{{\text{d}}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> values obtained using the Arrhenius methods. The obtained activation energies <InlineEquation ID="IEq28"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq26.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{{\text{a}}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>a</mtext> </msub> </math></EquationSource> </InlineEquation> and deactivation energies <InlineEquation ID="IEq29"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq27.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({E_{{{\text{d}}}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>d</mtext> </msub> </math></EquationSource> </InlineEquation> allow to modeling hydrolysis of starch by <InlineEquation ID="IEq30"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase from <i>Bacillus</i> spp. Presented modeling of starch hydrolysis with commercial <InlineEquation ID="IEq31"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase deactivation is essential to optimize the use of commercial <InlineEquation ID="IEq32"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14800_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-amylase, improve process efficiency and minimize costs in large-scale applications.</p>

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Modeling of starch hydrolysis by commercial \(\alpha\)-amylases with enzyme deactivation

  • Justyna Miłek,
  • Anna Ciaciuch

摘要

The use of \(\alpha\) α -amylase in the food, feed, and industrial sectors is constantly increasing, especially in the context of sustainable development. Modeling starch hydrolysis by commercial \(\alpha\) α -amylase with enzyme deactivation was performed for initial concentration of \({20\%}\) 20 % , \({30\%}\) 30 % and \({40\%}\) 40 % at 333 K. However, earlier in this study, need to determine the parameters of the starch hydrolysis process using commercial \(\alpha\) α -amylase from Bacillus spp. The analysis focused on determining the deactivation energy \({E_{{\text{d}}}}\) E d in starch hydrolysis while simultaneously deactivating commercial \(\alpha\) α -amylases from Bacillus subtillis and Bacillus licheniformis. The mathematical model applied assumes that the changes in starch concentrations and the deactivation of commercially bacterial \(\alpha\) α -amylase are first-order reactions with respect to enzyme concentration. The calculated activation energies \({E_{{\text{a}}}}\) E a ranged from \({22.08 \pm 6.96}\) 22.08 ± 6.96 kJ \(\text {mol}^{-1}\) mol - 1 to \({70.35 \pm 15.24}\) 70.35 ± 15.24 kJ \(\text {mol}^{-1}\) mol - 1 , and the deactivation energies \({E_{{\text{d}}}}\) E d ranged from \({21.30 \pm 1.05}\) 21.30 ± 1.05 kJ \(\text {mol}^{-1}\) mol - 1 to \({163.66 \pm 6.57}\) 163.66 ± 6.57 kJ \(\text {mol}^{-1}\) mol - 1 . The results obtained in this study were used to model the conversion of starch hydrolysis by commercial \(\alpha\) α -amylase from Bacillus spp. Additionally, the obtained \({E_{\text{a}}}\) E a and \({E_{\text{d}}}\) E d values from the activity versus temperature were compared to the \({E_{{{\text{a}}}}}\) E a and \({E_{{{\text{d}}}}}\) E d values obtained using the Arrhenius methods. The obtained activation energies \({E_{{{\text{a}}}}}\) E a and deactivation energies \({E_{{{\text{d}}}}}\) E d allow to modeling hydrolysis of starch by \(\alpha\) α -amylase from Bacillus spp. Presented modeling of starch hydrolysis with commercial \(\alpha\) α -amylase deactivation is essential to optimize the use of commercial \(\alpha\) α -amylase, improve process efficiency and minimize costs in large-scale applications.