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Article(id=1217845641879933496, tenantId=1146029695717560320, journalId=1149652044408987649, issueId=1217845635080962613, articleNumber=null, orderNo=null, doi=10.19812/j.cnki.jfsq11-5956/ts.20250512002, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1746979200000, receivedDateStr=2025-05-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1768286627502, onlineDateStr=2026-01-13, pubDate=1756051200000, pubDateStr=2025-08-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1768286627502, onlineIssueDateStr=2026-01-13, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1768286627502, creator=13701087609, updateTime=1768286627502, updator=13701087609, issue=Issue{id=1217845635080962613, tenantId=1146029695717560320, journalId=1149652044408987649, year='2025', volume='16', issue='16', pageStart='1', pageEnd='324', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=1, specialIssue=null, createTime=1768286625881, creator=13701087609, updateTime=1768287480278, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1217849218753024879, tenantId=1146029695717560320, journalId=1149652044408987649, issueId=1217845635080962613, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1217849218753024880, tenantId=1146029695717560320, journalId=1149652044408987649, issueId=1217845635080962613, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=21, endPage=27, ext={EN=ArticleExt(id=1217845642328724043, articleId=1217845641879933496, tenantId=1146029695717560320, journalId=1149652044408987649, language=EN, title=Construction of a growth kinetics model for Escherichia coli in braised chicken legs under fluctuating temperatures based on the Huang model, columnId=1151895322692776479, journalTitle=Journal of Food Safety & Quality, columnName=Special Topic: Analysis and Monitoring of Toxic and Harmful Substances in Food, runingTitle=null, highlight=null, articleAbstract=

Objective To construct a predictive model for bacterial growth in braised chicken legs under variable temperature conditions during actual circulation. Methods Based on the one-step method of the Huang model, the growth process of foodborne Escherichia coli (E. coli) in braised chicken legs was studied. Kinetic parameters for E. coli growth and survival were determined through multiple sets of isothermal experiments, ultimately yielding a second-order model describing the relationship between instantaneous colony count, temperature, time and initial colony count. The model was validated using simulation experiments. Results A significance analysis of differences was conducted between the measured growth colony counts of E. coli strains cultured under fluctuating temperatures and the predicted colony counts obtained by the model. The test showed that P=0.926>0.05, indicated that there was no significant difference between the predicted values and the measured values. Conclusion The second-order model constructed in this study can effectively simulate E. coli growth under fluctuating temperatures and is sufficiently reliable. The model, integrated with the R programming language, allows for rapid prediction of E. coli growth under fluctuating temperature conditions, providing a rapid and effective tool for risk assessment of braised meat products in actual circulation.

, correspAuthors=Hua JI, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, authorCompany=null, fund=null, authors=null, authorsList=Ying-Jiao LI, Zhi-Quan HAN, Zi-Yu LIU, Hua JI, Yan-Fei WAN), CN=ArticleExt(id=1217845644023222963, articleId=1217845641879933496, tenantId=1146029695717560320, journalId=1149652044408987649, language=CN, title=基于Huang模型的波动温度下卤鸡腿中大肠杆菌生长动力学模型构建, columnId=1151923892102197877, journalTitle=食品安全质量检测学报, columnName=专题：食品中有毒有害物质分析与监测, runingTitle=null, highlight=null, articleAbstract=

目的 构建实际流通过程中即变温条件下卤鸡腿中细菌的生长预测模型。方法 基于Huang模型的一步法, 以食源大肠杆菌在卤鸡腿中的生长过程为研究对象, 通过多组恒温试验确定大肠杆菌生长和存活的动力学参数, 最终得到描述即时菌落数与温度、时间和初始菌落数之间关系的二级模型, 并运用模拟试验对模型进行验证。结果 将波动温度下培养得到的大肠杆菌菌株的生长菌落数实测值与用模型预测得到的菌落数预测值进行差异显著性分析, 经检验显示P=0.926>0.05, 预测值和实测值无显著差异。结论 本研究构建的二级模型能够较好地拟合波动温度下大肠杆菌的生长, 具有较充分的可靠性。本模型的使用过程结合R编程语言, 可快速预测大肠杆菌在波动温度条件下的生长情况, 为实际流通中卤肉制品的风险评估提供一种迅速而有效的工具。

, correspAuthors=姬华, authorNote=null, correspAuthorsNote=
* 姬华(1980—), 女, 博士, 教授, 主要研究方向为食品微生物学。E-mail:
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李英娇(1982—), 女, 博士, 主要研究方向为食品微生物学。E-mail:

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李英娇(1982—), 女, 博士, 主要研究方向为食品微生物学。E-mail:

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Brazilian Journal of Microbiology, 2021, 52(2): 837-846., articleTitle=Attachment and survival of bacteria on apples with the creation of a kinetic mathematical model, refAbstract=null), Reference(id=1217864264841351985, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, doi=null, pmid=null, pmcid=null, year=2021, volume=13, issue=8, pageStart=1468, pageEnd=null, url=null, language=null, rfNumber=[30], rfOrder=37, authorNames=YOLOCUAUHTLI S, EMMANUEL R, AP V, journalName=Symmetry, refType=null, unstructuredReference=YOLOCUAUHTLI S, EMMANUEL R, AP V, et al. Primary model for biomass growth prediction in batch fermentation[J]. Symmetry, 2021, 13(8): 1468., articleTitle=Primary model for biomass growth prediction in batch fermentation, refAbstract=null), Reference(id=1217864264954598200, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[31], rfOrder=38, authorNames=陈雨, journalName=进口动物源性食品中致病菌生长预测模型的建立及乳酸结合壳聚糖杀菌效果的初步研究, refType=null, unstructuredReference=陈雨. 进口动物源性食品中致病菌生长预测模型的建立及乳酸结合壳聚糖杀菌效果的初步研究[D]. 南京: 南京农业大学, 2021., articleTitle=null, refAbstract=null), Reference(id=1217864265097204543, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, doi=null, pmid=null, pmcid=null, year=2021, volume=null, issue=null, pageStart=null, pageEnd=null, url=null, language=null, rfNumber=[31], rfOrder=39, authorNames=CHEN Y, journalName=Establishment of a predictive model for the growth of pathogenic bacteria in imported animal-derived foods and preliminary study on the bactericidal effect of lactic acid combined with chitosan, refType=null, unstructuredReference=CHEN Y. Establishment of a predictive model for the growth of pathogenic bacteria in imported animal-derived foods and preliminary study on the bactericidal effect of lactic acid combined with chitosan[D]. Nanjing: Nanjing Agricultural University, 2021., articleTitle=null, refAbstract=null), Reference(id=1217864265239810892, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, doi=null, pmid=null, pmcid=null, year=2020, volume=9, issue=3, pageStart=331, pageEnd=331, url=null, language=null, rfNumber=[32], rfOrder=40, authorNames=QUINTO JE, MARÍN MJ, CARO I, journalName=Foods, refType=null, unstructuredReference=QUINTO JE, MARÍN MJ, CARO I, et al. Modelling growth and decline in a two-species model system: Pathogenic Escherichia coli O157: H7 and Psychrotrophic spoilage bacteria in milk[J]. 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journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Fig.1, caption=Growth curves of E. coli cultured in braised chicken legs under different incubation temperatures, figureFileSmall=khNzCUX32JOeR6z0ca8hCw==, figureFileBig=WIixhYiSPNjlS5axOJ1Ypw==, tableContent=null), ArticleFig(id=1217864253613199565, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=图1, caption=不同培养温度下卤鸡腿中培养大肠杆菌的生长曲线, figureFileSmall=khNzCUX32JOeR6z0ca8hCw==, figureFileBig=WIixhYiSPNjlS5axOJ1Ypw==, tableContent=null), ArticleFig(id=1217864253722251477, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Fig.2, caption=Inactivation model of E. coli under 4 ℃ low temperature storage was obtained by fitting Reduced Huang Model, figureFileSmall=30Ing9R/Jm939R/834wFvA==, figureFileBig=hJVYT91wkpcClzkxLNw/gQ==, tableContent=null), ArticleFig(id=1217864253835497696, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=图2, caption=Reduced Huang Model拟合得到4 ℃低温贮藏条件下大肠杆菌失活模型, figureFileSmall=30Ing9R/Jm939R/834wFvA==, figureFileBig=hJVYT91wkpcClzkxLNw/gQ==, tableContent=null), ArticleFig(id=1217864253982298345, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Fig.3, caption=Linear relationship between λ、µmax and T, figureFileSmall=KMLTdXZNvrVIVsc45fTYwQ==, figureFileBig=dDnkR0usbycvJvy9umFX+g==, tableContent=null), ArticleFig(id=1217864254108127475, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=图3, caption=λ、µmax与T的线性关系, figureFileSmall=KMLTdXZNvrVIVsc45fTYwQ==, figureFileBig=dDnkR0usbycvJvy9umFX+g==, tableContent=null), ArticleFig(id=1217864254233956606, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Fig.4, caption=Change of bacteria number in 70 h of braised chicken legs inoculated with E. coli under fluctuating temperature from the finished product to before consumption, figureFileSmall=xevKBoeeEO0WYN009cCOKg==, figureFileBig=7khshPzBI+tiQIB+Xotiaw==, tableContent=null), ArticleFig(id=1217864254355591433, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=图4, caption=接种大肠杆菌的卤鸡腿在供应链及食用前波动温度下, 70 h的菌数变化, figureFileSmall=xevKBoeeEO0WYN009cCOKg==, figureFileBig=7khshPzBI+tiQIB+Xotiaw==, tableContent=null), ArticleFig(id=1217864254498197779, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Table 1, caption=

Fitting parameters for growth model of E. coli in braised chicken legs obtained by Huang model fitting

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温度/℃ Y0 Ymax lag/h μmax/h-1 MSE AIC
10 3.040 4.474 19.494 0.057 0.001 -74.660
15 3.510 7.654 15.256 0.114 0.001 -18.521
18 3.050 7.528 7.027 0.082 0.035 -19.977
25 3.050 7.728 4.512 0.393 0.008 -61.879
35 3.078 7.775 0.800 0.515 0.011 -77.002
37 3.990 8.918 7.779 1.897 0.001 -41.987
), ArticleFig(id=1217864255831986465, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=表1, caption=

Huang模型拟合得到的卤鸡腿中培养大肠杆菌的生长模型的拟合参数

, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃ Y0 Ymax lag/h μmax/h-1 MSE AIC
10 3.040 4.474 19.494 0.057 0.001 -74.660
15 3.510 7.654 15.256 0.114 0.001 -18.521
18 3.050 7.528 7.027 0.082 0.035 -19.977
25 3.050 7.728 4.512 0.393 0.008 -61.879
35 3.078 7.775 0.800 0.515 0.011 -77.002
37 3.990 8.918 7.779 1.897 0.001 -41.987
), ArticleFig(id=1217864255978787114, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Table 2, caption=

Inactivation model parameters and statistical analysis of E. coli under 4 ℃ low temperature storage

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温度
/℃		 Y0 lag/h µmax/h-1 R2 MSE AIC
4 4.210 0.397 -0.019 0.951 0.014 -17.085
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4 ℃低温贮藏条件下大肠杆菌的失活模型参数及统计分析

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温度
/℃		 Y0 lag/h µmax/h-1 R2 MSE AIC
4 4.210 0.397 -0.019 0.951 0.014 -17.085
), ArticleFig(id=1217864256268194111, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Table 3, caption=

Independent sample nonparametric test value table of predicted and measured value

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个案数 中位数 四分
位距		 秩平
均值		 秩总和 统计量 P
实测值 72 7.4250 3.31 74.17 5414.50 2615.500 0.848
预测值 72 7.4400 3.34 72.83 5316.50
), ArticleFig(id=1217864256398217545, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=表3, caption=

预测值与实测值独立样本非参数检验数值表

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个案数 中位数 四分
位距		 秩平
均值		 秩总和 统计量 P
实测值 72 7.4250 3.31 74.17 5414.50 2615.500 0.848
预测值 72 7.4400 3.34 72.83 5316.50
), ArticleFig(id=1217864256498880850, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Table 4, caption=

Nonparametric test table for independent samples of measured and predicted values under verification temperature

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个案数 中位数 四分
位距		 秩平
均值		 秩总和 统计量 P
实测值 15 9.2300 2.23 16.20 243.00 102.000 0.683
预测值 15 9.1900 2.27 14.80 222.00
), ArticleFig(id=1217864256599544152, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=表4, caption=

验证温度下实测值与预测值独立样本非参数检验数值表

, figureFileSmall=null, figureFileBig=null, tableContent=
个案数 中位数 四分
位距		 秩平
均值		 秩总和 统计量 P
实测值 15 9.2300 2.23 16.20 243.00 102.000 0.683
预测值 15 9.1900 2.27 14.80 222.00
), ArticleFig(id=1217864256716984675, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Table 5, caption=

Number of colonies of E. coli strains in braised chicken legs under fluctuating temperatures from the finished product to before consumption

, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃ 时间/h 菌落数实测值/(logCFU/g) 菌落数预测值/(logCFU/g)
1 25 2.0 3.06 3.08
2 35 2.0 4.09 4.16
3 25 8.0 7.11 7.12
4 4 12.0 6.59 6.61
5 25 2.0 6.60 6.63
6 35 0.5 6.61 6.68
7 25 1.0 6.58 6.66
8 4 6.0 6.40 6.42
9 25 2.0 6.39 6.44
10 4 12.0 5.88 5.93
11 25 2.0 5.91 5.96
12 4 6.0 5.70 5.72
13 25 1.0 5.69 5.72
14 4 12.0 5.18 5.21
), ArticleFig(id=1217864256939282799, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=表5, caption=

卤鸡腿中大肠杆菌菌株从成品到食用前波动温度下的菌落数

, figureFileSmall=null, figureFileBig=null, tableContent=
温度/℃ 时间/h 菌落数实测值/(logCFU/g) 菌落数预测值/(logCFU/g)
1 25 2.0 3.06 3.08
2 35 2.0 4.09 4.16
3 25 8.0 7.11 7.12
4 4 12.0 6.59 6.61
5 25 2.0 6.60 6.63
6 35 0.5 6.61 6.68
7 25 1.0 6.58 6.66
8 4 6.0 6.40 6.42
9 25 2.0 6.39 6.44
10 4 12.0 5.88 5.93
11 25 2.0 5.91 5.96
12 4 6.0 5.70 5.72
13 25 1.0 5.69 5.72
14 4 12.0 5.18 5.21
), ArticleFig(id=1217864257039946106, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=EN, label=Table 6, caption=

Test of between-subjects effects for predicted and measured values of E. coli colony number under fluctuating temperatures

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源 III 类平方和 自由度 均方 F 显著性
分组 0.011 1 0.011 0.009 0.926
误差 31.579 26 1.215
总计 31.59 27
), ArticleFig(id=1217864257153192326, tenantId=1146029695717560320, journalId=1149652044408987649, articleId=1217845641879933496, language=CN, label=表6, caption=

波动温度下大肠杆菌菌落数预测值和实测值两组数据主体间效应检验

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源 III 类平方和 自由度 均方 F 显著性
分组 0.011 1 0.011 0.009 0.926
误差 31.579 26 1.215
总计 31.59 27
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基于Huang模型的波动温度下卤鸡腿中大肠杆菌生长动力学模型构建
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李英娇 1 , 韩志全 2 , 刘子与 3 , 姬华 4, * , 王艳斐 1
食品安全质量检测学报 | 专题：食品中有毒有害物质分析与监测 2025,16(16): 21-27
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食品安全质量检测学报 | 专题：食品中有毒有害物质分析与监测 2025, 16(16): 21-27
基于Huang模型的波动温度下卤鸡腿中大肠杆菌生长动力学模型构建
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李英娇1 , 韩志全2, 刘子与3, 姬华4, * , 王艳斐1
作者信息
  • 1 新疆石河子职业技术学院食品工程学院, 石河子 832000
  • 2 石河子大学理学院, 石河子 832000
  • 3 南开大学软件学院, 天津 300000
  • 4 石河子大学食品学院, 石河子 832000

    • 李英娇(1982—), 女, 博士, 主要研究方向为食品微生物学。E-mail:

通讯作者:

* 姬华(1980—), 女, 博士, 教授, 主要研究方向为食品微生物学。E-mail:
Construction of a growth kinetics model for Escherichia coli in braised chicken legs under fluctuating temperatures based on the Huang model
Ying-Jiao LI1 , Zhi-Quan HAN2, Zi-Yu LIU3, Hua JI4, * , Yan-Fei WAN1
Affiliations
  • 1 College of Food Engineering, Xinjiang Shihezi Vocational Technical College, Shihezi 832000, China
  • 2 School of Science, Shihezi University, Shihezi 832000, China
  • 3 School of Software, Nankai University, Tianjin 300000, China
  • 4 College of Food Science, Shihezi University, Shihezi 832000, China
出版时间: 2025-08-25 doi: 10.19812/j.cnki.jfsq11-5956/ts.20250512002
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摘要
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目的 构建实际流通过程中即变温条件下卤鸡腿中细菌的生长预测模型。方法 基于Huang模型的一步法, 以食源大肠杆菌在卤鸡腿中的生长过程为研究对象, 通过多组恒温试验确定大肠杆菌生长和存活的动力学参数, 最终得到描述即时菌落数与温度、时间和初始菌落数之间关系的二级模型, 并运用模拟试验对模型进行验证。结果 将波动温度下培养得到的大肠杆菌菌株的生长菌落数实测值与用模型预测得到的菌落数预测值进行差异显著性分析, 经检验显示P=0.926>0.05, 预测值和实测值无显著差异。结论 本研究构建的二级模型能够较好地拟合波动温度下大肠杆菌的生长, 具有较充分的可靠性。本模型的使用过程结合R编程语言, 可快速预测大肠杆菌在波动温度条件下的生长情况, 为实际流通中卤肉制品的风险评估提供一种迅速而有效的工具。

卤鸡腿  /  大肠杆菌  /  生长动力学模型  /  波动温度

Objective To construct a predictive model for bacterial growth in braised chicken legs under variable temperature conditions during actual circulation. Methods Based on the one-step method of the Huang model, the growth process of foodborne Escherichia coli (E. coli) in braised chicken legs was studied. Kinetic parameters for E. coli growth and survival were determined through multiple sets of isothermal experiments, ultimately yielding a second-order model describing the relationship between instantaneous colony count, temperature, time and initial colony count. The model was validated using simulation experiments. Results A significance analysis of differences was conducted between the measured growth colony counts of E. coli strains cultured under fluctuating temperatures and the predicted colony counts obtained by the model. The test showed that P=0.926>0.05, indicated that there was no significant difference between the predicted values and the measured values. Conclusion The second-order model constructed in this study can effectively simulate E. coli growth under fluctuating temperatures and is sufficiently reliable. The model, integrated with the R programming language, allows for rapid prediction of E. coli growth under fluctuating temperature conditions, providing a rapid and effective tool for risk assessment of braised meat products in actual circulation.

braised chicken leg  /  Escherichia coli  /  growth kinetic model  /  fluctuating temperature
李英娇, 韩志全, 刘子与, 姬华, 王艳斐. 基于Huang模型的波动温度下卤鸡腿中大肠杆菌生长动力学模型构建. 食品安全质量检测学报, 2025 , 16 (16) : 21 -27 . DOI: 10.19812/j.cnki.jfsq11-5956/ts.20250512002
Ying-Jiao LI, Zhi-Quan HAN, Zi-Yu LIU, Hua JI, Yan-Fei WAN. Construction of a growth kinetics model for Escherichia coli in braised chicken legs under fluctuating temperatures based on the Huang model[J]. Journal of Food Safety & Quality, 2025 , 16 (16) : 21 -27 . DOI: 10.19812/j.cnki.jfsq11-5956/ts.20250512002
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0 引言
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微生物在肉类中的生长预测模型是食品安全风险评估和货架期管理的核心工具, 而变温条件下的生长动力学研究更是该领域的重点难点。在实际的肉类生产、运输、储存和销售过程中, 温度波动是普遍存在的现象, 这种非恒定温度环境会显著影响微生物的生长行为, 尤其是大肠杆菌(Escherichia coli, E. coli)等食源性致病菌的响应机制更为复杂。食源性病原微生物的生长预测模型主要分为一级模型(描述菌落数量随时间的变化)、二级模型(描述环境参数如温度对生长参数的影响)和三级模型(整合前两者并包含更多变量)[1]。
近年来, 动态温度条件下的生长模型开发已成为食品安全工程的前沿研究方向。在变温条件下, 大肠杆菌的生长动力学呈现非线性特征, 如在低温向高温转换时可能出现“延滞期缩短-指数期加速”的双重响应, 而在高温突降时可能出现生长停滞现象[1-2]。这种动态响应机制使得传统恒定温度模型的预测准确性显著下降。因此, 构建能够适应温度动态变化的预测模型, 对于精确评估食品风险、优化冷链管理及减少食源性疾病暴发具有重要意义。
市售卤肉制品生产一般呈小作坊形式。卫生设施欠缺, 生产环境易受污染, 且大都无外包装。运输过程难以保证冷链, 销售时较难保证冷藏环境, 容易造成卤肉制品污染及变质。而仅仅构建恒温生长模型不适用于实际变温流通过程中的生长预测。本研究模拟市售卤鸡腿从成品到食用前的波动温度条件, 构建其中大肠杆菌菌株的生长预测模型。以期快速预测大肠杆菌在波动温度条件下的生长情况, 为实际流通中卤肉制品的风险评估提供一种迅速而有效的工具。
1 材料与方法
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1.1 试验材料
1.1.1 菌种与试验原料
大肠杆菌菌株分离自生鲜鸡肉, 石河子大学食品微生物学试验室保存(菌株编号为DC026)。
1.1.2 材料、试剂与仪器
生姜、花椒、桂皮、八角、清油、老抽、盐、新鲜生鸡腿均在当地超市购买。
胰酪大豆胨肉汤、伊红美蓝琼脂、结晶紫中性红胆盐MUG琼脂(青岛海博生物技术有限公司)。
HD-MT10 细菌麦氏浊度仪(杭州华端生物科技有限公司); SPX-150B恒温恒湿培养箱(绍兴市苏珀仪器有限公司); ZF-5手提式暗箱紫外分析仪(西安立科环保科技有限公司); Friocell 55 L可编程培养箱(德国MMM集团); SW-CJ-2D洁净工作台(苏州苏洁净化设备有限公司); XYJ-A电动离心机(金坛市恒丰仪器厂); LDZX-30KBS立式压力灭菌锅(上海申安医疗器械厂); DGG-9070A电热恒温鼓风干燥箱(上海森信试验仪器有限公司)。
1.2 试验方法
1.2.1 卤鸡腿制作方法
超市购买新鲜生鸡腿; 清水清洗表面; 冷水下锅用大火煮开; 弃沫; 加入生姜(4片); 加入花椒10粒、桂皮1块、八角2个、清油5 mL、老抽5 mL; 中火煮至8成熟放盐适量; 继续煮15 min即可。
1.2.2 接种与计数
(1)菌株复壮
将目标菌株取出, 在室温下放置30 min。再接种至TSB培养液中, 复壮3代, 以得到活力旺盛的足量接种物。
(2)菌悬液制备
用麦氏浊度仪将复壮后的大肠杆菌菌株调至成0.5麦氏浊度的菌悬液, 其浓度相应约为1.5×108 CFU/mL, 连续稀释至103~104 CFU/mL备用。
(3)接种
在无菌操作下将新卤好的鸡腿切成肉片放入按上述过程制备好的大肠杆菌菌液中, 完全浸没15 s。制备21份, 每份25 g肉样。
(4)肉样培养
分别在无菌操作下取25 g按上述接种操作后的肉片放入无菌均质袋中。拍打均质后分别放入4、10、15、18、25、35和37 ℃的条件下保藏。于35 ℃、37 ℃下恒温培养的样品每隔2 h取出计数; 于10、15、18、25 ℃下恒温培养的样品每隔6 h取出计数; 于4 ℃中恒温培养的样品每隔12 h取出计数, 每个培养温度得到3个平行试验数据, 取平均值用于后续数据分析。
(5)微生物计数
菌落计数单位为CFU/g, 计数方法参照GB 4789.38—2012《食品安全国家标准 大肠埃希氏菌计数》中的大肠埃希氏菌平板计数法(第二法)。
1.2.3 卤鸡腿中大肠杆菌菌株恒温生长模型的建立
(1)生长模型拟合
根据试验过程得到的卤鸡腿肉片分别在4、10、15、18、25、35和37 ℃恒定温度下培养的大肠杆菌的生长数据, 运用美国农业部IPMP 2013软件, 将计数结果代入Huang模型, 进行数据拟合。计算见公式(1)~(2)[5,7]:
$Y(t)=Y_{0}+Y_{\max }-\ln \left[e^{Y_{0}}+\left(e^{Y_{\max }}-e^{Y_{0}}\right) \times e^{-\mu_{\max } B(t)}\right]$
$B(t)=t+\frac{1}{4} \ln \frac{1+e^{-4(t-\lambda)}}{1+e^{4 \lambda}}$
式中: Y0为接种时的大肠杆菌的菌种数量, log10CFU/g; Y(t)为t时刻的大肠杆菌的菌种数量, log10CFU/g; Ymax为大肠杆菌达到最大生长浓度时的菌种数量, log10CFU/g; μmax为大肠杆菌最大比生长速率, h-1; λ为迟滞期, h; t为时间, h; B(t)为调整后的时间变量, 由t和λ计算得到。
(2)恒温生长模型的数学检验
运用相关统计学方法, 用均方误差(mean squared error, MSE)评价预测模型数据的变化程度, 用赤池系数(Akike coefficient, AIC)对预测模型的复杂度和拟合数据的优良性进行衡量。计算见公式(3):
$\mathrm{MSE}=\frac{\sum\left(N_{\mathrm{obs}}-N_{\mathrm{pred}}\right)^{2}}{n}$
式中: Npred和Nobs分别为大肠杆菌菌落数的预测值和实际值; n为取样次数。
(3)恒温生长模型的统计学检验
将10、15、18、25、35和37 ℃恒定温度下培养得到的大肠杆菌菌株的生长数据与用Huang模型预测得到的数据进行差异显著性分析, 所用软件为SPASS 26.0。
(4)低温贮藏条件下大肠杆菌失活模型的建立
用Reduced Huang Model对4 ℃低温贮藏下目标大肠杆菌的生长情况进行拟合, 得到4 ℃低温贮藏下目标大肠杆菌的失活模型。计算见公式(4)[5]:
$Y(t)=Y_{0}+\mu_{\max }\left[t+\frac{1}{4} \ln \left(\frac{1+e^{-4(t-\lambda)}}{1+e^{4 \lambda}}\right)\right]$
1.2.4 波动温度下卤鸡腿中大肠杆菌菌株生长预测模型建立
(1)肉样培养
将卤鸡腿从成品到食用前分为预冷期-储藏期-处理包装期-成品储藏期-运输期-销售期-购买后到餐桌期-家庭存放期, 每个时期预设温度和时间。称取25 g已接种大肠杆菌菌株的卤鸡腿肉片于无菌袋中, 放入可编程培养箱中, 设定程序培养。
(2)微生物计数方法
参照GB 4789.38—2012中的平板计数法。
1.3 数据处理
用EXCEL 2013、SPSS 26.0、R 3.6.2 处理数据, 进行统计学分析和绘图。
2 结果与分析
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2.1 卤鸡腿中大肠杆菌菌株恒温生长模型的建立
2.1.1 恒温生长模型的拟合
采用一级生长模型Huang模型对10、15、18、25、35和37 ℃下恒温培养的食源大肠杆菌菌株生长情况进行拟合, 结果见图1。并由此得到相应的模型拟合参数(见表1)。
将食源大肠杆菌菌株接种在卤鸡腿中进行恒温培养, 用Huang模型建立生长的一级模型, 揭示了该菌的生长规律。如表1所示, 一级模型的均方误差MSE均小于0.5, 说明模型数据的误差较小, 较小的AIC值说明模型可以较好地拟合该菌的生长。
2.1.2 失活模型结果
在4 ℃贮藏条件下, 目标大肠杆菌的生长趋势如图2所示。将食源大肠杆菌菌株在4 ℃恒温培养, 用Reduced Huang Model拟合得到该菌株的失活模型(具体参数见表2)。该失活模型的R2>0.95, 说明该失活模型可以较好地拟合食源大肠杆菌菌株在4 ℃的生长趋势。由该模型可知, 在4 ℃贮藏条件, 目标菌株菌落数呈现显著减少趋势。
2.1.3 二级模型建立
由2.1.1建立的多组恒温模型得到的Ymax, μmax, λ(lag)和对应的培养温度T以及培养时间t值可确定细菌生长和存活的动力学参数, 从而得到描述环境因子(温度)和一级模型参数之间的变化关系。分析如下。
(1)分析菌落数最大值Ymax与T、菌落初始值Y0之间的多线性相关性
首先判断两个自变量T和Y0之间是否存在多重共线性, 用SPSS 26.0处理数据得出容差=0.996, 方差膨胀因子(variance inflation factor, VF)=1.004, 不符合存在多重共线性的条件(容差小于0.1, VF大于10)。因此判断两个自变量Y0和T之间不存在多重共线性。将Ymax同T以及Y0作多元线性回归得出显著性值为P=0.038 (<0.05), 建立的模型有效。其中Ymax与T相关的P为0.014, Ymax与Y0相关的P为0.993。剔除自变量Y0后模型的R2从0.553升高至0.617, 标准估计的误差由2.57降至2.37。因此剔除自变量Y0, 得出Ymax与T存在线性相关, 即:
$Y_{\max }=0.283 T+10.34$
(2)分析λ和μmax同T之间的线性相关性
分析方法同2.1.3(1), 得出λ和μmax同T相关的线性方程:
$\lambda=0.0346 T^{2}-2.2143 T+36.115$
$\mu_{\max }=0.0052 T^{2.15}$
式(6)和(7)的关系如图3所示(lag=λ):
2.1.4 食源大肠杆菌菌株恒定温度下生长预测模型的统计学检验
将10、15、18、25、35和37 ℃恒定温度下培养得到的大肠杆菌菌株的生长数据与用Huang模型预测得到的数据进行差异显著性分析。
初步分析显示实测组与预测组数据配对差值不明显满足正态分布, 因此选用Mann-Whitney检验对模型预测值与实测值的一致性进行检验分析。原假设为配对样本无显著差异。
结果如表3所示, Mann-Whitney检验结果显示P=0.848>0.05, 接受原假设, 预测值和实测值无显著差异。Huang模型能较好的预测食源大肠杆菌菌株在10、15、18、25、35和37 ℃恒定温度下的生长状况。
2.1.5 构建模型的验证
将验证温度(21 ℃和29 ℃)下数据代入由Huang模型建立的预测模型中, 得到21 ℃和29 ℃的预测值, 与食源大肠杆菌菌株的生长菌落数实际值比较, 选用Mann-Whitney检验对模型预测值与实测值的一致性进行检验分析。结果如表4所示。
结果分析, Mann-Whitney检验结果显示P(双侧渐近显著性) 0.683>0.05, 说明验证温度(21 ℃和29 ℃)下食源大肠杆菌菌株的生长菌落数实测值与通过Huang模型预测的值无显著差异。
2.2 食源大肠杆菌菌株在波动温度下的生长模型
将式(5)~(7)式分别代入式(1)和(2), 即Huang模型中,得到菌落数Y(t)与初始菌落数Y0和时间t以及温度T的函数, 该函数可用于大肠杆菌在波动温度(10~40 ℃)下的菌落生长规律研究。如式(8)所示。
$\begin{matrix} & Y\left( t \right)={{Y}_{0}}+(0.283T+10.34)- \\ & \text{ }\ln [{{e}^{{{Y}_{0}}}}+({{e}^{(0.283T+10.34)}}-{{e}^{{{Y}_{0}}}})\times \\ & \text{ }{{e}^{-0.0052\times {{T}^{2.15}}\times [t+\frac{1}{4}\ln \frac{1+{{e}^{-4(t-0.0346{{T}^{2}}+2.2143T-36.115)}}}{1+{{e}^{4(0.0346{{T}^{2}}-2.2143T+36.115)}}}]}}] \\ \end{matrix}$
将式(6)和(7)代入式(4), 即失活模型Reduced Huang Model中, 可得到菌落数Y(t)与初始菌落数Y0和时间t以及温度T的函数, 该函数可用于大肠杆菌在4 ℃下的菌落生长规律研究。如式(9)所示。
$\begin{aligned} Y(t)= & Y_{0}+0.0052 T^{2.15} \\ & {\left[t+\frac{1}{4} \ln \frac{1+e^{-4\left(t-0.0346 T^{2}+2.2143 T-36.115\right)}}{1+e^{4\left(0.0346 T^{2}-2.2143 T+36.115\right)}}\right] } \end{aligned}$
将式(8)和式(9)用R语言编程后, 输入不同的初始菌落数Y0和培养温度T以及培养时间t, 即可得出该菌的预测生长菌落数Y(t)。
2.3 接种在卤鸡腿上的食源大肠杆菌菌株在波动温度下菌落数的生长变化(预测模型的应用)
食源大肠杆菌菌株接种在卤鸡腿上, 在波动温度下(4~35 ℃)(初始菌落数Y0=3.05 logCFU/g), 70 h内菌落数的变化如表5所示。
用R语言绘图, 得到接种食源大肠杆菌菌株的卤鸡腿在供应链及食用前波动温度下, 70 h的菌落数实测值变化图(图4)。由图4可知, 试验70 h内有48 h卤鸡腿是在4 ℃冷藏状态, 但最终菌落数比最高菌落数降低不足2个对数级。培养40 h后, 大肠杆菌菌株的菌落数降低了一个对数级; 培养70 h后, 最终菌落数仍比最初菌落数升高了2个对数级。提示熟肉制品在预冷期-储藏期-处理包装期-成品储藏期-运输期-销售期-购买后到餐桌期-家庭存放期过程中的食品安全性存在较大风险。
同时将试验初始菌落数Y0和培养温度T以及培养时间t代入用R语言编程后的预测模型中, 得出该菌的菌落数预测值(表5)。
2.4 食源大肠杆菌菌株在波动温度下生长预测模型的统计学检验
将波动温度下培养得到的大肠杆菌菌株的生长菌落数实测值与用模型预测得到的菌落数预测值进行差异显著性分析。方差齐性检验结果显示数据满足方差齐性, 且残差满足均值为零的正态分布。因此选用两因素方差分析对模型预测值与实测值的一致性进行检验分析(表6)。原假设为预测值和实测值两组数据无显著差异。
检验结果显示P=0.926>0.05, 接受原假设, 预测值和实测值无显著差异。该模型能较好的预测食源大肠杆菌菌株在波动温度下的生长状况。
3 结论与讨论
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细菌的生长呈现迟滞期、对数期和稳定期3个阶段, Huang模型基于细菌在新环境下的适应性, 以显式的形式简便且明确地定义了迟滞期这一参数, 从而使模型能够从迟滞阶段平稳过渡到指数阶段。
本研究选择Huang模型作为描述菌株生长规律的初级模型。考察不同恒定温度(4~35 ℃)条件下食源大肠杆菌菌株在卤鸡腿中的生长特性。除4 ℃外, 10~35 ℃条件下大肠杆菌菌株的生长曲线均呈现出迟滞期、对数期及稳定期3个阶段, 显示基于Huang模型的一步法适用于卤鸡肉中大肠杆菌菌株的生长曲线分析。
本研究基于该一步法, 通过多组恒温试验确定细菌生长和存活的动力学参数, 得到Ymax, μmax, λ(lag)和对应的温度之间的线性关系。对参数进一步分析, 得到描述即时菌落数Y(t) 与温度T、时间t和初始菌落数Y0之间关系的二级模型, 结合R编程语言得到大肠杆菌在波动温度条件下的生长规律。
有研究显示, 温度从4 ℃突升至25 ℃时, 大肠杆菌延滞期会缩短至恒定温度下的50%[3], 导致安全窗口期大幅缩短。本研究假设的波动温度涵盖了多次温度从4 ℃至25 ℃之间的突升, 模型可量化温度跃升对大肠杆菌的激活效应。
本模型能够较好地拟合波动温度下大肠杆菌的生长, 具有一定的可靠性。该模型框架可迁移应用至其他卤制肉品(如卤鸭、卤牛肉等)。迁移应用时, 需针对不同产品的水分活度、盐分浓度等调整参数(如高盐分可能延长延滞期)。在模型中适当引入水分活度或盐分浓度等作为协变量, 以期为实际物流过程中卤肉制品的风险评估提供一种迅速而有效的工具。
基金
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  • 国家自然科学基金项目(32260621)
  • 石河子大学基础研究计划项目(MSPY202403)
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2025年第16卷第16期
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doi: 10.19812/j.cnki.jfsq11-5956/ts.20250512002
  • 接收时间：2025-05-12
  • 首发时间：2026-01-13
  • 出版时间：2025-08-25
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  • 收稿日期：2025-05-12
基金
国家自然科学基金项目(32260621)
石河子大学基础研究计划项目(MSPY202403)
作者信息
    1 新疆石河子职业技术学院食品工程学院, 石河子 832000
    2 石河子大学理学院, 石河子 832000
    3 南开大学软件学院, 天津 300000
    4 石河子大学食品学院, 石河子 832000

通讯作者:

* 姬华(1980—), 女, 博士, 教授, 主要研究方向为食品微生物学。E-mail:
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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