A hierarchical model to predict the probability of germination of bacterial spores

Statistical hierarchical modelling is a powerful strategy to model complicated processes by a sequence of relatively simple models placed in a hierarchy. A hierarchical model includes the specification of the conditional probability density functions of response variables given candidate predictor variables, along with the specification of the probability density function of each single variable. We developed a statistical hierarchical model of the probability that a bacterial spore germinates, and used this model to predict the number of germinant spores as function of number of bacterial cells, nutrients concentration and amount of germination activation agents.

[1]  R. Losick,et al.  The transcriptional profile of early to middle sporulation in Bacillus subtilis. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[2]  S. Ben-Yehuda,et al.  The Molecular Timeline of a Reviving Bacterial Spore , 2015, Molecular cell.

[3]  A. T. Carter,et al.  Diversity of the Germination Apparatus in Clostridium botulinum Groups I, II, III, and IV , 2016, Front. Microbiol..

[4]  H. D. Jong,et al.  Qualitative simulation of the initiation of sporulation in Bacillus subtilis , 2004, Bulletin of mathematical biology.

[5]  A. Moir,et al.  How do spores germinate? , 2006, Journal of applied microbiology.

[6]  E J Schantz,et al.  Properties and use of botulinum toxin and other microbial neurotoxins in medicine. , 1992, Microbiological reviews.

[7]  I. Mura,et al.  The pattern of growth observed for Clostridium botulinum type A1 strain ATCC 19397 is influenced by nutritional status and quorum sensing: a modelling perspective , 2015, Pathogens and disease.

[8]  A. T. Carter,et al.  Functional Characterisation of Germinant Receptors in Clostridium botulinum and Clostridium sporogenes Presents Novel Insights into Spore Germination Systems , 2014, PLoS pathogens.

[9]  B. Halle,et al.  The physical state of water in bacterial spores , 2009, Proceedings of the National Academy of Sciences.

[10]  Stanley Brul,et al.  Live Cell Imaging of Germination and Outgrowth of Individual Bacillus subtilis Spores; the Effect of Heat Stress Quantitatively Analyzed with SporeTracker , 2013, PloS one.

[11]  P. Bonventre,et al.  Physiology of toxin production by Clostridium botulinum types A and B. III. Effect of pH and temperature during incubation on growth, autolysis. and toxin production. , 1959, Applied microbiology.

[12]  Ji Yu,et al.  Germination proteins in the inner membrane of dormant Bacillus subtilis spores colocalize in a discrete cluster , 2011, Molecular microbiology.

[13]  D. Paredes-Sabja,et al.  Germination of spores of Bacillales and Clostridiales species: mechanisms and proteins involved. , 2011, Trends in microbiology.

[14]  P. Setlow,et al.  Characterization of bacterial spore germination using phase-contrast and fluorescence microscopy, Raman spectroscopy and optical tweezers , 2011, Nature Protocols.

[15]  Anthony C. Atkinson,et al.  Robust Diagnostic Regression Analysis , 2000 .

[16]  I. Mura,et al.  Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics , 2016, Front. Microbiol..

[17]  Victor A. Bloomfield,et al.  Using R for Numerical Analysis in Science and Engineering , 2014 .

[18]  G C Barker,et al.  Quantitative risk assessment for hazards that arise from non-proteolytic Clostridium botulinum in minimally processed chilled dairy-based foods. , 2011, Food microbiology.

[19]  M. Heyndrickx,et al.  The Importance of Endospore-Forming Bacteria Originating from Soil for Contamination of Industrial Food Processing , 2011 .

[20]  Frédéric Carlin,et al.  Origin of bacterial spores contaminating foods. , 2011, Food microbiology.

[21]  Gary C. Barker,et al.  An Integrative Approach to Computational Modelling of the Gene Regulatory Network Controlling Clostridium botulinum Type A1 Toxin Production , 2016, PLoS Comput. Biol..

[22]  I. Mura,et al.  New Elements To Consider When Modeling the Hazards Associated with Botulinum Neurotoxin in Food , 2015, Journal of bacteriology.

[23]  P. Setlow,et al.  Factors Influencing Germination of Bacillus subtilis Spores via Activation of Nutrient Receptors by High Pressure , 2005, Applied and Environmental Microbiology.

[24]  T. Montville,et al.  Time-to-detection, percent-growth-positive and maximum growth rate models for Clostridium botulinum 56A at multiple temperatures. , 2002, International journal of food microbiology.

[25]  P. Fratamico,et al.  Foodborne Pathogens and Disease to Be Published Six Times per Year , 2008 .

[26]  P. J. Clark,et al.  Distance to Nearest Neighbor as a Measure of Spatial Relationships in Populations , 1954 .

[27]  M. Peck Biology and genomic analysis of Clostridium botulinum. , 2009, Advances in microbial physiology.

[28]  G. Barker,et al.  Germination and growth from spores: variability and uncertainty in the assessment of food borne hazards. , 2005, International journal of food microbiology.

[29]  Peter Setlow,et al.  Kinetics of Germination of Individual Spores of Geobacillus stearothermophilus as Measured by Raman Spectroscopy and Differential Interference Contrast Microscopy , 2013, PloS one.

[30]  Gary C. Barker,et al.  Computational modelling and analysis of the molecular network regulating sporulation initiation in Bacillus subtilis , 2014, BMC Systems Biology.