Determining microbial kinetic parameters using nonlinear regression analysis. Advantages and limitations in microbial ecology

Microbial ecologists, and biologists in general, have come to appreciate the power of the quantitative approach in their research. It is no longer enough to describe the organisms that occupy a given habitat; the rates at which they carry out metabolic functions of ecological importance must be estimated. Only when quantitative information of metabolic activities is coupled with knowledge of organismal types can our understanding of the concerted actions of the members of a community be considered complete.

[1]  William K. W. Li.  Consideration of errors in estimating kinetic parameters based on Michaelis‐Menten formalism in microbial ecology , 1983 .

[2]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[3]  Graeme Bonham-Carter,et al.  Computer Simulation in Geology , 1970 .

[4]  David M. Ward,et al.  Oxygen Microelectrode That Is Insensitive to Medium Chemical Composition: Use in an Acid Microbial Mat Dominated by Cyanidium caldarium , 1983, Applied and environmental microbiology.

[5]  Derek R. Lovley,et al.  Kinetic Analysis of Competition Between Sulfate Reducers and Methanogens for Hydrogen in Sediments , 1982, Applied and environmental microbiology.

[6]  W. Cleland,et al.  The statistical analysis of enzyme kinetic data. , 1967, Advances in enzymology and related areas of molecular biology.

[7]  J J DiStefano,et al.  Optimized blood sampling protocols and sequential design of kinetic experiments. , 1981, The American journal of physiology.

[8]  L. Meyer-Reil,et al.  Biomass and Metabolic Activity of Heterotrophic Marine Bacteria , 1982 .

[9]  J. DiStefano,et al.  Optimal nonuniform sampling interval and test-input design for identification of physiological systems from very limited data , 1979 .

[10]  Stuart L. Meyer,et al.  Data analysis for scientists and engineers , 1975 .

[11]  P. J. Huber.  The 1972 Wald Lecture Robust Statistics: A Review , 1972 .

[12]  D. S. Riggs,et al.  A COMPARISON OF ESTIMATES OF MICHAELIS-MENTEN KINETIC CONSTANTS FROM VARIOUS LINEAR TRANSFORMATIONS. , 1965, The Journal of biological chemistry.

[13]  Louis J. Thibodeaux,et al.  Chemodynamics, environmental movement of chemicals in air, water, and soil , 1979 .

[14]  A. Cornish-Bowden.  Fundamentals of Enzyme Kinetics , 1979 .

[15]  Dammkoehler Ra.  A computational procedure for parameter estimation applicable to certain nonlinear models of enzyme kinetics. , 1966 .

[16]  B. Efron,et al.  The Jackknife: The Bootstrap and Other Resampling Plans. , 1983 .

[17]  B. Jørgensen,et al.  Photosynthesis of benthic microflora measured with high spatial resolution by the oxygen microprofile method: Capabilities and limitations of the method1 , 1983 .

[18]  J. Tiedje,et al.  Kinetic Explanation for Accumulation of Nitrite, Nitric Oxide, and Nitrous Oxide During Bacterial Denitrification , 1981, Applied and environmental microbiology.

[19]  F. A. Lootsma,et al.  Numerical methods for non-linear optimization , 1974 .

[20]  M. H. Quenouille.  NOTES ON BIAS IN ESTIMATION , 1956 .

[21]  A Cornish-Bowden,et al.  Evaluation of rate constants for enzyme-catalysed reactions by the jackknife technique. Application to liver alcohol dehydrogenase. , 1978, The Biochemical journal.

[22]  A. Cornish-Bowden,et al.  Evaluation of distribution-free confidence limits for enzyme kinetic parameters. , 1978, Journal of theoretical biology.

[23]  G. Thomas,et al.  Calculus and Analytical Geometry , 1972 .

[24]  R. Kohberger.  Statistical evaluation of the direct linear plot method for estimation of enzyme kinetic parameters. , 1980, Analytical biochemistry.

[25]  P. Gerhardt.  Manual of methods for general bacteriology. , 1981 .

[26]  C. Taylor.  Growth of a Bacterium Under a High-Pressure Oxy-Helium Atmosphere , 1979, Applied and environmental microbiology.

[27]  H. Jannasch,et al.  Assimilatory Sulfur Metabolism in Marine Microorganisms: Considerations for the Application of Sulfate Incorporation into Protein as a Measurement of Natural Population Protein Synthesis , 1982, Applied and environmental microbiology.

[28]  R I Jennrich,et al.  Fitting nonlinear models to data. , 1979, Annual review of biophysics and bioengineering.

[29]  R. Duggleby,et al.  Experimental designs for estimating the kinetic parameters for enzyme-catalysed reactions. , 1979, Journal of theoretical biology.

[30]  A. L. Koch,et al.  Multistep kinetics: choice of models for the growth of bacteria. , 1982, Journal of theoretical biology.

[31]  J. Tiedje,et al.  Kinetic Parameters of the Conversion of Methane Precursors to Methane in a Hypereutrophic Lake Sediment , 1978, Applied and environmental microbiology.

[32]  G. Atkins,et al.  A comparison of two methods for fitting the integrated Michaelis-Menten equation. , 1974, The Biochemical journal.

[33]  N. Wolfe,et al.  Structure-Activity Relationships in Microbial Transformation of Phenols , 1982, Applied and environmental microbiology.

[34]  J. Suflita,et al.  Kinetics of Microbial Dehalogenation of Haloaromatic Substrates in Methanogenic Environments , 1983, Applied and environmental microbiology.

[35]  A. Cornish-Bowden,et al.  The direct linear plot. A new graphical procedure for estimating enzyme kinetic parameters. , 1974, The Biochemical journal.

[36]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[37]  D. Hinkley.  Jackknifing in Unbalanced Situations , 1977 .

[38]  Robert A. Berner,et al.  Early Diagenesis: A Theoretical Approach , 1980 .

[39]  George A. F. Seber,et al.  Linear regression analysis , 1977 .

[40]  T. Blackburn,et al.  Distribution of oxygen in marine sediments measured with microelectrodes1 , 1980 .

[41]  A. Goldberger.  Topics in regression analysis , 1969 .

[42]  J. Hobbie,et al.  RESPIRATION CORRECTIONS FOR BACTERIAL UPTAKE OF DISSOLVED ORGANIC COMPOUNDS IN NATURAL WATERS1 , 1969 .

[43]  R. Cukier,et al.  Application of nonlinear sensitivity analysis to enzyme mechanisms , 1981 .

[44]  N. W. F. Kossen,et al.  On the statistical analysis of batch data , 1981 .

[45]  Rupert G. Miller.  The jackknife-a review , 1974 .

[46]  James G. Ferry,et al.  Kinetics of Formate Metabolism in Methanobacterium formicicum and Methanospirillum hungatei , 1982, Applied and environmental microbiology.

[47]  G. N. Wilkinson.  Statistical estimations in enzyme kinetics. , 1961, The Biochemical journal.

[48]  Bengt Mannervik,et al.  Error Structure of Enzyme Kinetic Experiments , 1976 .

[49]  J. A. Robinson,et al.  Kinetics of Hydrogen Consumption by Rumen Fluid, Anaerobic Digestor Sludge, and Sediment , 1982, Applied and environmental microbiology.

[50]  F. F. Blackman.  Optima and Limiting Factors , 1905 .

[51]  The chemostat and blackman kinetics. , 1982, Biotechnology and bioengineering.

[52]  J. A. Robinson,et al.  Nonlinear estimation of Monod growth kinetic parameters from a single substrate depletion curve , 1983, Applied and environmental microbiology.

[53]  R. K. Finn,et al.  Equations of substrate‐limited growth: The case for blackman kinetics , 1973, Biotechnology and bioengineering.

[54]  T. Capizzi,et al.  Application of jackknife procedures to inter-experiment comparisons of parameter estimates for the Michaelis-Menten equation. , 1981, The Biochemical journal.

[55]  G L Atkins,et al.  Current trends in the estimation of Michaelis-Menten parameters. , 1980, Analytical biochemistry.

[56]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[57]  DiStefano Jj rd.  Design and optimization of tracer experiments in physiology and medicine. , 1980 .

[58]  H. M. Tsuchiya,et al.  On the accuracy of determining rate constants in enzymatic reactions , 1967 .

[59]  D. Hinkley,et al.  Jackknifing in Nonlinear Regression , 1980 .

[60]  H J Fromm,et al.  A computer program for fitting and statistically analyzing initial rate data applied to bovine hexokinase type III isozyme. , 1975, Archives of biochemistry and biophysics.

[61]  A. Cornish-Bowden,et al.  Fitting of enzyme kinetic data without prior knowledge of weights. , 1981, The Biochemical journal.

[62]  Claudio Cobelli,et al.  Minimal sampling schedules for identification of dynamic models of metabolic systems of clinical interest: case studies for two liver function tests , 1983 .

[63]  Yadolah Dodge,et al.  Mathematical Programming In Statistics , 1981 .

[64]  J. Hobbie,et al.  Use of Glucose and Acetate by Bacteria and Algae in Aquatic Ecosystems , 1966 .

[65]  H. L. Lucas,et al.  DESIGN OF EXPERIMENTS IN NON-LINEAR SITUATIONS , 1959 .

[66]  J. Suflita,et al.  Reductive Dehalogenations of Halobenzoates by Anaerobic Lake Sediment Microorganisms , 1983, Applied and environmental microbiology.

[67]  I. Nimmo,et al.  The nature of the random experimental error encountered when acetylcholine hydrolase and alcohol dehydrogenase are assayed. , 1979, Analytical biochemistry.

[68]  R G Duggleby,et al.  A nonlinear regression program for small computers. , 1981, Analytical biochemistry.

[69]  D Garfinkel,et al.  Systems analysis in enzyme kinetics. , 1977, CRC critical reviews in bioengineering.

[70]  A. Holmberg.  On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities , 1982 .

[71]  W. Silvert.  Practical curve fitting , 1979 .

[72]  W. Dixon.  BMD : biomedical computer programs , 1967 .

[73]  P Koeppe,et al.  A program for non-linear regression analysis to be used on desk-top computers. , 1980, Computer programs in biomedicine.

[74]  W R Porter,et al.  Improved non-parametric statistical methods for the estimation of Michaelis-Menten kinetic parameters by the direct linear plot. , 1977, The Biochemical journal.

[75]  J. Tiedje,et al.  Response of electron-capture detector to hydrogen, oxygen, nitrogen, carbon dioxide, nitric oxide and nitrous oxide , 1980 .

[76]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[77]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[78]  G. Atkins,et al.  The reliability of Michaelis constants and maximum velocities estimated by using the integrated Michaelis-Menten equation. , 1973, The Biochemical journal.

[79]  M. Alexander,et al.  Models for mineralization kinetics with the variables of substrate concentration and population density , 1984, Applied and environmental microbiology.

[80]  S. J. Pirt,et al.  Principles of microbe and cell cultivation , 1975 .

[81]  J. Morrison,et al.  The analysis of progress curves for enzyme-catalysed reactions by non-linear regression. , 1977, Biochimica et biophysica acta.

[82]  A. Downing,et al.  DETERMINATION OF KINETIC CONSTANTS FOR NITRIFYING BACTERIA IN MIXED CULTURE, WITH THE AID OF AN ELECTRONIC COMPUTER. , 1965, Journal of general microbiology.

[83]  Peter D. H. Hill,et al.  A Review of Experimental Design Procedures for Regression Model Discrimination , 1978 .

[84]  Yonathan Bard,et al.  Comparison of Gradient Methods for the Solution of Nonlinear Parameter Estimation Problems , 1970 .

[85]  Frederick Mosteller,et al.  Data Analysis and Regression , 1978 .

[86]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[87]  D. J. Currie.  Estimating Michaelis-Menten Parameters: Bias, Variance and Experimental Design , 1982 .

[88]  A. Cornish-Bowden,et al.  The nature of experimental error in enzyme kinetic measurments. , 1975, The Biochemical journal.

[89]  N. D. Villiers,et al.  A Continuation Method for Nonlinear Regression , 1981 .

[90]  L. Endrenyi,et al.  Optimal design of experiments for the estimation of precise hyperbolic kinetic and binding parameters. , 1981, Journal of theoretical biology.