Single-cell behavior and population heterogeneity: Solving an inverse problem to compute the intrinsic physiological state functions

Journal of Biotechnology

Volumn 158, Issue 3, 2012, Pages 80-90

  Spetsieris, Konstantinos ^a   Zygourakis, Kyriacos ^a  

^a Rice University   (United States)

Author keywords

Cell population balance model; Genetic toggle network; Intrinsic physiological state functions; Inverse problem; Phenotypic distributions; Population heterogeneity

Indexed keywords

BIVARIATE; CELL POPULATIONS; CELL SUBPOPULATIONS; COMPUTATIONAL FRAMEWORK; COMPUTATIONAL PROCEDURES; DISCRETIZATIONS; E. COLI; FINITE SAMPLING; INTRINSIC PHYSIOLOGICAL STATE FUNCTIONS; INVERSE SOLUTION; ISOGENIC CELLS; NON-PARAMETRIC; PARAMETRIC ANALYSIS; PHENOTYPIC DISTRIBUTIONS; PHYSIOLOGICAL STATE; POPULATION HETEROGENEITY; PREDICTIVE POWER;

CELL PROLIFERATION; CELLS; ESCHERICHIA COLI; ESTIMATION; INVERSE PROBLEMS; PHYSIOLOGY; REACTION RATES; STAINLESS STEEL;

CELL CULTURE;

ACCURACY; ARTICLE; CELL DIVISION; CELL FUNCTION; CELL SUBPOPULATION; ESCHERICHIA COLI; KNOWLEDGE; MEASUREMENT; PHENOTYPE; PRIORITY JOURNAL; PROBABILITY;

CELL DIVISION; COMPUTER SIMULATION; ESCHERICHIA COLI; MODELS, BIOLOGICAL;

EID: 84858299106     PISSN: 01681656     EISSN: 18734863     Source Type: Journal    
DOI: 10.1016/j.jbiotec.2011.08.018     Document Type: Article

References (65)

1. Anderson E.C., Bell G.I., Petersen D.F., Tobey R.A. Cell growth and division IV Determination of volume growth: rate and division probability. Biophysical Journal 1967, 9:246-263.
2. Aster R.C., Borchers B., Thurber C.H. Parameter Estimation and Inverse Problems 2005, Elsevier Academic Press, Amsterdam.
3. Bæk K., Svenningsen S., Eisen H., Sneppen K., Brown S. Single-cell analysis of λ immunity regulation. Journal of Molecular Biology 2003, 334:363-372.
4. Block D.E., Eitzman P.D., Wangensteen J.D., Srienc F. Slit scanning of Saccharomyces cerevisiae cells: quantification of asymmetric cell division and cell cycle progression in asynchronous culture. Biotechnology Progress 1990, 6:504-512.
5. Bowman A.W., Azzalini A. Applied Smoothing Techniques for Data Analysis. The Kernel Approach with S-Plus Illustrations 1997, Clarendon Press, Oxford.
6. Campbell A. Synchronization of cell division. Bacteriological Reviews 1957, 21:263-272.
7. Chung J.D., Stephanopoulos G. Studies of transcriptional state heterogeneity in sporulating cultures of Bacillus subtilis. Biotechnology and Bioengineering 1995, 47:234-242.
8. Collins J.F., Richmond M.H. Rate of growth of Bacillus cereus between divisions. Journal of General Microbiology 1962, 28:15-33.
9. Delbrück M. Effects of specific antisera on the growth of bacterial viruses (bacteriophages). Journal of Bacteriology 1945, 50:137-150.
10. Eakman J.M., Fredrickson A.G., Tsuchiya H.M. Statistics and dynamics of microbial cell populations. Chemical Engineering Progress Symposium Series 1966, 62:37-49.
11. Elowitz M.B., Levine A.J., Siggia E.D., Swain P.S. Stochastic gene expression in a single cell. Science 2002, 297:1183-1186.
12. Fredrickson A.G., Ramkrishna D., Tsuchiya H.M. Statistics and dynamics of prokaryotic cell populations. Mathematical Biosciences 1967, 1:327-374.
13. 2 theory. Z. Wahrscheinlichkeitstheor. Verw. Geb. 1981, 57:453-476.
14. Gardner T.S., Cantor C.R., Collins J.J. Construction of a genetic toggle switch in Escherichia coli. Nature 2000, 403:339-342.
15. Godin F.B., Cooper D.G., Rey A.D. Numerical methods for a population balance model of a periodic fermentation process. AICHE Journal 1999, 45:1359-1364.
16. Hansen, P.C., 1998 Rank-deficient and discrete ill-posed problems. Numerical aspects of linear inversion. Society for industrial and applied mathematics Philadelphia.
17. Harvey R.J., Marr A.G., Painter P.R. Kinetics of growth of individual cells of Escherichia coli and Azotobacter agilis. Journal of Bacteriology 1967, 93:605-617.
18. Hatzis C., Fredrickson A.G., Srienc F. Cell-cycle analysis in phagotrophic microorganisms from flow cytometric histograms. Journal of Theoretical Biology 1997, 186:131-144.
19. Hofmann B. Regularization for Applied-inverse and Ill-posed Problems 1986, B.G. Teubner, Leipzig.
20. Hofmann B. Regularization of nonlinear problems and the degree of ill-posedness. Mathematical Research 1993, 74:174-188.
21. Izenman A.J. Recent developments in nonparametric density estimation Journal of the American Statistical Association 1991, 86:205-224.
22. Jerri A.J. Introduction to integral equations with applications 1999, John Wiley & Sons, Inc., New York. 2nd ed.
23. Kavousanakis M.E., Mantzaris N.V., Boudouvis A.G. A novel free boundary algorithm for the solution of cell population balance models. Chemical Engineering Science 2009, 64:4247-4261.
24. Kempner E.S., Marr A.G. Growth in volume of Euglena gracilis during the division cycle. Journal of Bacteriology 1979, 101:561-567.
25. Kepler T.B., Elston T.C. Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophysical Journal 2001, 81:3116-3136.
26. Koch A.L. Distribution of cell size in growing cultures of bacteria and the applicability of the Collins-Richmond principle. Journal of General Microbiology 1966, 45:409-417.
27. Kostova T.V. Numerical solutions to equations modeling nonlinearity interacting age-dependent populations. Computational and Applied Mathematics 1990, 19:95-103.
28. Kromenaker S.J., Srienc F. Effect of lactic acid on the kinetics of growth and antibody production in a murine hybridoma: secretion patterns during the cell cycle. Journal of Biotechnology 1994, 34:13-34.
29. Mahoney A.W., Doyle F.J., Doraiswami R. Inverse problems in population balances: growth and nucleation from dynamic data. AICHE Journal 2002, 48:981-990.
30. Maloney P.C., Rotman B. Distribution of suboptimally induced β-d-galactosidase in Escherichia coli: the enzyme content of the individual cell. Journal of Molecular Biology 1972, 73:77-91.
31. Mantzaris N.V. Stochastic and deterministic simulations of heterogeneous cell population dynamics. Journal of Theoretical Biology 2006, 241:690-706.
32. Mantzaris N.V., Daoutidis P., Srienc F. Numerical solution of multi-variable cell population balance models: I Finite difference methods. Computers and Chemical Engineering 2001, 25:1411-1440.
33. Mantzaris N.V., Daoutidis P., Srienc F. Numerical solution of multi-variable cell population balance models: II. Spectral methods. Computers and Chemical Engineering 2001, 25:1441-1462.
34. Mantzaris N.V., Daoutidis P., Srienc F. Numerical solution of multi-variable cell population balance models: III. Finite element methods. Computers and Chemical Engineering 2001, 25:1463-1481.
35. Muralidar R., Ramkrishna D. An inverse problem in agglomeration kinetics. Journal of Colloid and Interface Science 1986, 112:348-361.
36. Muralidar R., Ramkrishna D. Inverse problem of agglomeration kinetics II. Binary clustering coefficients from self-preserving spectra. Journal of Colloid and Interface Science 1989, 131:503-513.
37. Neumann J.V. Various techniques used in connection with random digits. Monte Carlo methods. National Bureau of Standards 1951, 12:36-38.
38. Novick A., Weiner M. Enzyme induction as an all-or-none phenomenon. Proceedings of the National Academy of Sciences of the United States of America 1957, 43:553-566.
39. Painter P.R., Marr A.G. Mathematics of microbial populations. Annual Review of Microbiology 1968, 22:519-548.
40. Patruno L.E., Dorao C.A., Dupuy P.M., Svendsen H.F., Jakobsen H.A. Identification of droplet breakage kernel for population balance modeling. Chemical Engineering Science 2008, 64:638-645.
41. Patruno L.E., Dorao C.A., Svendsen H.F., Jakobsen H.A. Analysis of breakage kernels for population balance modeling. Chemical Engineering Science 2009, 64:501-508.
42. Powell E.O. Growth rate and generation time of bacteria, with special reference to continuous culture. Journal of General Microbiology 1956, 15:492-511.
43. Powell E.O. A note on Koch and Schaechter's hypothesis about growth and fission of bacteria. Journal of General Microbiology 1964, 37:231-249.
44. Ramkrishna D. Toward a self-similar theory of microbial populations. Biotechnology and Bioengineering 1994, 43:138-148.
45. Ramkrishna D. Population Balances: Theory and Applications to Particulate Systems in Engineering 2000, Academic Press, San Diego, CA.
46. Ramkrishna D., Fredrickson A.G., Tsuchiya H.M. On relationships between various distribution functions in balanced unicellular growth. Bulletin of Mathematical Biophysics 1968, 30:319-323.
47. Ramkrishna D., Schell J. On self-similar growth. Journal of Biotechnology 1999, 71:255-258.
48. Robert C.P., Casella G. Monte Carlo Statistical Methods 2004, Springer-Verlag, New York.
49. Russo-Marie F., Roederer M., Sager B., Herzenberg L.A., Kaiser D. β-Galactosidase activity in single differentiating bacterial cells. Proceedings of the National Academy of Sciences of the United States of America 1993, 90:8194-8198.
50. Sathyagal A.N., Ramkrishna D., Narsimhan G. Solution of inverse problems in population balances-II. Particle break-up. Computers and Chemical Engineering 1995, 19:437-451.
51. Silverman B.W. Density estimation for statistics and data analysis 1986, Chapman & Hall, London. 1st ed.
52. Spetsieris K., Zygourakis K., Mantzaris N.V. A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteria. Biotechnology and Bioengineering 2009, 102:598-615.
53. Spudich J.L., Koshland D.E. Non-genetic individuality: chance in the single cell. Nature 1976, 262:467-476.
54. Srienc F., Dien B.S. Kinetics of the cell cycle of Saccharomyces cerevisiae. Annals of the New York Academy of Sciences 1992, 655:59-71.
55. Stocker B.A.D. Measurements of rate mutation of flagellar antigenic phase in Salmonella typhimurium. Journal of Hygiene Cambridge 1949, 47:398-413.
56. Subramanian G., Ramkrishna D. On the solution of statistical models of cell populations. Mathematical Biosciences 1971, 10:1-23.
57. Sulsky D. Numerical solution of structured population balance models. II Mass structure. Journal of Mathematical Biology 1994, 32:491-514.
58. Sweeney P.J., Srienc F., Fredrickson A.G. Measurement of unequal DNA partitioning in Tetrahymena pyriformis using slit-scanning flow cytometry. Biotechnology Progress 1994, 10:19-25.
59. Thompson J.R., Tapia R.A. Nonparametric Function Estimation, Modeling, and Simulation 1990, Society for Industrial and Applied Mathematics, Philadelphia.
60. Tikhonov A.N., Arsenin V.Y. Solutions of Ill-posed Problems 1977, Winston and Sons, Washington, DC.
61. Tsuchiya H.M., Fredrickson A.G., Aris R. Dynamics of microbial cell populations. Advances in Chemical Engineering 1966, 6:125-206.
62. Wand M.P., Jones M.C. Kernel Smoothing 1995, Chapman & Hall, London. 1st ed.
63. Wright H., Ramkrishna D. Solutions of inverse problems in population balances: I. Aggregation kinetics. Computers and Chemical Engineering 1992, 16:1019-1038.
64. Zahrt J.D. A Primer on Integral Equations of the First Kind. The Problem of Deconvolution and Unfolding 1991, Society of Industrial and Applied Mathematics, Philadelphia.
65. Zusman D., Gottlieb P., Rosenberg E. Division cycle of Myxococcus xanthus. 3 Kinetics of cell growth and protein synthesis. Journal of Bacteriology 1971, 105:811-819.