Networked enzymatic logic gates with filtering: New theoretical modeling expressions and their experimental application

Journal of Physical Chemistry B

Volumn 117, Issue 48, 2013, Pages 14928-14939

  Privman, Vladimir ^a   Zavalov, Oleksandr ^a   Halámková, Lenka ^b   Moseley, Fiona ^a   Halámek, Jan ^b   Katz, Evgeny ^a  

^a CLARKSON UNIVERSITY   (United States)

^b STATE UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENZYMATIC PROCESS; ENZYME-CATALYZED REACTIONS; EXPERIMENTAL APPLICATION; FILTERING PROCESS; MODEL APPROACH; PROCESSING SYSTEMS; THEORETICAL EXPRESSION; THEORETICAL MODELING;

PHYSICAL CHEMISTRY; PHYSICS;

NETWORK COMPONENTS;

ENZYME;

ARTICLE; BIOCATALYSIS; BIOLOGICAL MODEL; METABOLISM;

BIOCATALYSIS; ENZYMES; MODELS, BIOLOGICAL;

EID: 84890075439     PISSN: 15206106     EISSN: 15205207     Source Type: Journal    
DOI: 10.1021/jp408973g     Document Type: Article

References (110)

1. Privman, V.; Pedrosa, V.; Melnikov, D.; Pita, M.; Simonian, A.; Katz, E. Enzymatic AND-Gate Based on Electrode-Immobilized Glucose-6-phosphate Dehydrogenase: Towards Digital Biosensors and Biochemical Logic Systems with Low Noise Biosens. Bioelectron. 2009, 25, 695-701
2. Pedrosa, V.; Melnikov, D.; Pita, M.; Halámek, J.; Privman, V.; Simonian, A.; Katz, E. Enzymatic Logic Gates with Noise-Reducing Sigmoid Response Int. J. Unconv. Comput. 2010, 6, 451-460
3. Privman, V.; Zavalov, O.; Simonian, A. Extended Linear Response for Bioanalytical Applications Using Multiple Enzymes Anal. Chem. 2013, 85, 2027-2031
4. Rafael, S. P.; Vallée-Bélisle, A.; Fabregas, E.; Plaxco, K.; Palleschi, G.; Ricci, F. Employing the Metabolic "Branch Point Effect" to Generate an All-or-None, Digital-Like Response in Enzymatic Outputs and Enzyme-Based Sensors Anal. Chem. 2012, 84, 1076-1082
5. Vallée-Bélisle, A.; Ricci, F.; Plaxco, K. W. Engineering Biosensors with Extended, Narrowed, or Arbitrarily Edited Dynamic Range J. Am. Chem. Soc. 2012, 134, 2876-2879
6. Kang, D.; Vallée-Bélisle, A.; Plaxco, K. W.; Ricci, F. Re-engineering Electrochemical Biosensors to Narrow or Extend Their Useful Dynamic Range Angew. Chem., Int. Ed. 2012, 51, 6717-6721
7. Seaton, D. D.; Krishnan, J. Effects of Multiple Enzyme-Substrate Interactions in Basic Units of Cellular Signal Processing. Phys. Biol. 2012, 9, article #045009, 1-17.
8. Alon, U. An Introduction to Systems Biology. Design Principles of Biological Circuits; Chapman & Hall/CRC Press: Boca Raton, FL, 2007.
9. Wang, J.; Katz, E. Digital Biosensors with Built-in Logic for Biomedical Applications-Biosensors Based on Biocomputing Concept Anal. Bioanal. Chem. 2010, 398, 1591-1603
10. Wang, J.; Katz, E. Digital Biosensors with Built-in Logic for Biomedical Applications Isr. J. Chem. 2011, 51, 141-150
11. Katz, E.; Wang, J.; Privman, M.; Halámek, J. Multianalyte Digital Enzyme Biosensors with Built-in Boolean Logic Anal. Chem. 2012, 84, 5463-5469
12. Halámková, L.; Halámek, J.; Bocharova, V.; Wolf, S.; Mulier, K. E.; Beilman, G.; Wang, J.; Katz, E. Analysis of Biomarkers Characteristic of Porcine Liver Injury-From Biomolecular Logic Gates to Animal Model Analyst 2012, 137, 1768-1770
13. Halámek, J.; Bocharova, V.; Chinnapareddy, S.; Windmiller, J. R.; Strack, G.; Chuang, M.-C.; Zhou, J.; Santhosh, P.; Ramirez, G. V.; Arugula, M. A. Multi-enzyme Logic Network Architectures for Assessing Injuries: Digital Processing of Biomarkers Mol. Biosyst. 2010, 6, 2554-2560
14. Halámek, J.; Windmiller, J. R.; Zhou, J.; Chuang, M.-C.; Santhosh, P.; Strack, G.; Arugula, M. A.; Chinnapareddy, S.; Bocharova, V.; Wang, J. Multiplexing of Injury Codes for the Parallel Operation of Enzyme Logic Gates Analyst 2010, 135, 2249-2259
15. Margulies, D.; Hamilton, A. D. Digital Analysis of Protein Properties by an Ensemble of DNA Quadruplexes J. Am. Chem. Soc. 2009, 131, 9142-9143
16. May, E. E.; Dolan, P. L.; Crozier, P. S.; Brozik, S.; Manginell, M. Towards De Novo Design of Deoxyribozyme Biosensors for GMO Detection IEEE Sens. J. 2008, 8, 1011-1019
17. von Maltzahn, G.; Harris, T. J.; Park, J.-H.; Min, D.-H.; Schmidt, A. J.; Sailor, M. J.; Bhatia, S. N. Nanoparticle Self-Assembly Gated by Logical Proteolytic Triggers J. Am. Chem. Soc. 2007, 129, 6064-6065
18. Niazov, T.; Baron, R.; Katz, E.; Lioubashevski, O.; Willner, I. Concatenated Logic Gates Using Four Coupled Biocatalysts Operating in Series Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 17160-17163
19. Baron, R.; Lioubashevski, O.; Katz, E.; Niazov, T.; Willner, I. Elementary Arithmetic Operations by Enzymes: A Model for Metabolic Pathway Based Computing Angew. Chem., Int. Ed. 2006, 45, 1572-1576
20. Strack, G.; Ornatska, M.; Pita, M.; Katz, E. Biocomputing Security System: Concatenated Enzyme-Based Logic Gates Operating as a Biomolecular Keypad Lock J. Am. Chem. Soc. 2008, 130, 4234-4235
21. Zhou, J.; Arugula, M. A.; Halámek, J.; Pita, M.; Katz, E. Enzyme-Based NAND and NOR Logic Gates with Modular Design J. Phys. Chem. B 2009, 113, 16065-16070
22. Privman, V.; Arugula, M. A.; Halámek, J.; Pita, M.; Katz, E. Network Analysis of Biochemical Logic for Noise Reduction and Stability: A System of Three Coupled Enzymatic AND Gates J. Phys. Chem. B 2009, 113, 5301-5310
23. Katz, E.; Privman, V. Enzyme-Based Logic Systems for Information Processing Chem. Soc. Rev. 2010, 39, 1835-1857
24. Miyamoto, T.; Razavi, S.; DeRose, R.; Inoue, T. Synthesizing Biomolecule-Based Boolean Logic Gates ACS Synth. Biol. 2013, 2, 72-82
25. Ashkenasy, G.; Ghadiri, M. R. Boolean Logic Functions of a Synthetic Peptide Network J. Am. Chem. Soc. 2004, 126, 11140-11141
26. Benenson, Y. Biocomputers: From Test Tubes to Live Cells Mol. Biosyst. 2009, 5, 675-685
27. Stojanovic, M. N. Some Experiments and Directions in Molecular Computing and Robotics Isr. J. Chem. 2011, 51, 99-105
28. Pei, R.; Matamoros, E.; Liu, M.; Stefanovic, D.; Stojanovic, M. N. Training a Molecular Automaton to Play a Game Nat. Nanotechnol. 2010, 5, 773-777
29. Kahan, M.; Gil, B.; Adar, R.; Shapiro, E. Towards Molecular Computers that Operate in a Biological Environment Physica D 2008, 237, 1165-1172
30. Stojanovic, M. N.; Stefanovic, D. Chemistry at a Higher Level of Abstraction J. Comput. Theor. Nanosci. 2011, 8, 434-440
31. Domanskyi, S.; Privman, V. Design of Digital Response in Enzyme-Based Bioanalytical Systems for Information Processing Applications J. Phys. Chem. B 2012, 116, 13690-13695
32. Privman, V. Control of Noise in Chemical and Biochemical Information Processing Isr. J. Chem. 2011, 51, 118-131
33. Privman, V. Error-Control and Digitalization Concepts for Chemical and Biomolecular Information Processing Systems J. Comput. Theor. Nanosci. 2011, 8, 490-502
34. MacVittie, K.; Halámek, J.; Privman, V.; Katz, E. A Bioinspired Associative Memory System Based on Enzymatic Cascades Chem. Commun. 2013, 49, 6962-6964
35. Bocharova, V.; MacVittie, K.; Chinnapareddy, S.; Halámek, J.; Privman, V.; Katz, E. Realization of Associative Memory in an Enzymatic Process: Toward Biomolecular Networks with Learning and Unlearning Functionalities J. Phys. Chem. Lett. 2012, 3, 1234-1237
36. Privman, M.; Tam, T. K.; Pita, M.; Katz, E. Switchable Electrode Controlled by Enzyme Logic Network System: Approaching Physiologically Regulated Bioelectronics J. Am. Chem. Soc. 2009, 131, 1314-1321
37. Katz, E.; Bocharova, V.; Privman, M. Electronic Interfaces Switchable by Logically Processed Multiple Biochemical and Physiological Signals J. Mater. Chem. 2012, 22, 8171-8178
38. Bocharova, V.; Katz, E. Switchable Electrode Interfaces Controlled by Physical, Chemical and Biological signals Chem. Rec. 2012, 12, 114-130
39. Privman, M.; Tam, T. K.; Bocharova, V.; Halámek, J.; Wang, J.; Katz, E. Responsive Interface Switchable by Logically Processed Physiological Signals-Towards "Smart" Actuators for Signal Amplification and Drug Delivery ACS Appl. Mater. Interfaces 2011, 3, 1620-1623
40. Zhou, M.; Dong, S. J. Bioelectrochemical Interface Engineering: Toward the Fabrication of Electrochemical Biosensors, Biofuel Cells, and Self-Powered Logic Biosensors Acc. Chem. Res. 2011, 44, 1232-1243
41. Kim, K.-W.; Kim, B. C.; Lee, H. J.; Kim, J.; Oh, M.-K. Enzyme Logic Gates Based on Enzyme-Coated Carbon Nanotubes Electroanalysis 2011, 23, 980-986
42. Zhou, M.; Wang, J. Biofuel Cells for Self-Powered Electrochemical Biosensing and Logic Biosensing Electroanalysis 2012, 24, 197-209
43. Zhou, M.; Zhou, N. D.; Kuralay, F.; Windmiller, J. R.; Parkhomovsky, S.; Valdes-Ramirez, G.; Katz, E.; Wang, J. A Self-Powered "Sense-Act- Treat" System that is Based on a Biofuel Cell and Controlled by Boolean Logic Angew. Chem., Int. Ed. 2012, 51, 2686-2689
44. Krämer, M.; Pita, M.; Zhou, J.; Ornatska, M.; Poghossian, A.; Schöning, M. J.; Katz, E. Coupling of Biocomputing Systems with Electronic Chips: Electronic Interface for Transduction of Biochemical Information J. Phys. Chem. C 2009, 113, 2573-2579
45. Minko, S.; Katz, E.; Motornov, M.; Tokarev, I.; Pita, M. Materials with Built-in Logic J. Comput. Theor. Nanosci. 2011, 8, 356-364
46. Pita, M.; Minko, S.; Katz, E. Enzyme-Based Logic Systems and Their Applications for Novel Multi-Signal-Responsive Materials J. Mater. Sci.: Mater. Med. 2009, 20, 457-462
47. Bocharova, V.; Zavalov, O.; MacVittie, K.; Arugula, M. A.; Guz, N. V.; Dokukin, M. E.; Halámek, J.; Sokolov, I.; Privman, V.; Katz, E. Biochemical Logic Approach to Biomarker-Activated Drug Release J. Mater. Chem. 2012, 22, 19709-19717
48. Bychkova, V.; Shvarev, A.; Zhou, J.; Pita, M.; Katz, E. Enzyme Logic Gate Associated with a Single Responsive Microparticle: Scaling Biocomputing to Microsize Systems Chem. Commun. 2010, 46, 94-96
49. Tokarev, I.; Gopishetty, V.; Zhou, J.; Pita, M.; Motornov, M.; Katz, E.; Minko, S. Stimuli-Responsive Hydrogel Membranes Coupled with Biocatalytic Processes ACS Appl. Mater. Interfaces 2009, 1, 532-536
50. Motornov, M.; Zhou, J.; Pita, M.; Tokarev, I.; Gopishetty, V.; Katz, E.; Minko, S. An Integrated Multifunctional Nanosystem from Command Nanoparticles and Enzymes Small 2009, 5, 817-820
51. Radhakrishnan, K.; Tripathy, J.; Raichur, A. M. Dual Enzyme Responsive Microcapsules Simulating an "OR" Logic Gate for Biologically Triggered Drug Delivery Applications Chem. Commun. 2013, 49, 5390-5392
52. Halámek, J.; Zavalov, O.; Halámková, L.; Korkmaz, S.; Privman, V.; Katz, E. Enzyme-Based Logic Analysis of Biomarkers at Physiological Concentrations: AND Gate with Double-Sigmoid "Filter" Response J. Phys. Chem. B 2012, 116, 4457-4464
53. Zavalov, O.; Bocharova, V.; Privman, V.; Katz, E. Enzyme-Based Logic: OR Gate with Double-Sigmoid Filter Response J. Phys. Chem. B 2012, 116, 9683-9689
54. Zavalov, O.; Bocharova, V.; Halámek, J.; Halámková, L.; Korkmaz, S.; Arugula, M. A.; Chinnapareddy, S.; Katz, E.; Privman, V. Two-Input Enzymatic Logic Gates Made Sigmoid by Modifications of the Biocatalytic Reaction Cascades Int. J. Unconv. Comput. 2012, 8, 347-365
55. Bakshi, S.; Zavalov, O.; Halámek, J.; Privman, V.; Katz, E. Modularity of Biochemical Filtering for Inducing Sigmoid Response in Both Inputs in an Enzymatic AND Gate J. Phys. Chem. B 2013, 117, 9857-9865
56. Privman, V.; Fratto, B. E.; Zavalov, O.; Halámek, J.; Katz, E. Enzymatic AND Logic Gate with Sigmoid Response Induced by Photochemically Controlled Oxidation of the Output J. Phys. Chem. B 2013, 117, 7559-7568
57. Privman, V.; Strack, G.; Solenov, D.; Pita, M.; Katz, E. Optimization of Enzymatic Biochemical Logic for Noise Reduction and Scalability: How Many Biocomputing Gates Can be Interconnected in a Circuit? J. Phys. Chem. B 2008, 112, 11777-11784
58. Melnikov, D.; Strack, G.; Pita, M.; Privman, V.; Katz, E. Analog Noise Reduction in Enzymatic Logic Gates J. Phys. Chem. B 2009, 113, 10472-10479
59. Biomolecular Computing-From Logic Systems to Smart Sensors and Actuators; Katz, E., Ed.; Willey-VCH: Weinheim, 2012.
60. Benenson, Y. Biomolecular Computing Systems: Principles, Progress and Potential Nat. Rev. Genet. 2012, 13, 455-468
61. Molecular and Supramolecular Information Processing-From Molecular Switches to Unconventional Computing; Katz, E., Ed.; Wiley-VCH: Weinheim, 2012.
62. De Silva, A. P.; Uchiyama, S.; Vance, T. P.; Wannalerse, B. A Supramolecular Chemistry Basis for Molecular Logic and Computation Coord. Chem. Rev. 2007, 251, 1623-1632
63. Szacilowski, K. Digital Information Processing in Molecular Systems Chem. Rev. 2008, 108, 3481-3548
64. Credi, A. Molecules that Make Decisions Angew. Chem., Int. Ed. 2007, 46, 5472-5475
65. Pischel, U. Chemical Approaches to Molecular Logic Elements for Addition and Subtraction Angew. Chem., Int. Ed. 2007, 46, 4026-4040
66. Andreasson, J.; Pischel, U. Smart Molecules at Work-Mimicking Advanced Logic Operations Chem. Soc. Rev. 2010, 39, 174-188
67. Unconventional Computation. Lecture Notes in Computer Science; Calude, C. S.; Costa, J. F.; Dershowitz, N.; Freire, E.; Rozenberg, G., Eds.; Springer: Berlin, 2009; Vol. 5715.
68. Unconventional Computing 2007; Adamatzky, A.; Bull, L.; De Lacy Costello, B.; Stepney, S.; Teuscher, C., Eds.; Luniver Press: Bristol, UK, 2007.
69. Ashkenazi, G.; Ripoll, D. R.; Lotan, N.; Scheraga, H. A. A Molecular Switch for Biochemical Logic Gates: Conformational Studies Biosens. Bioelectron. 1997, 12, 85-95
70. Unger, R.; Moult, J. Towards Computing with Proteins Proteins 2006, 63, 53-64
71. Ezziane, Z. DNA Computing: Applications and Challenges Nanotechnology 2006, 17, R27-R39
72. Stojanovic, M. N.; Mitchell, T. E.; Stefanovic, D. Deoxyribozyme-Based Logic Gates J. Am. Chem. Soc. 2002, 124, 3555-3561
73. Benenson, Y. RNA-Based Computation in Live Cells Curr. Opin. Biotechnol. 2009, 20, 471-478
74. Simpson, M. L.; Sayler, G. S.; Fleming, J. T.; Applegate, B. Whole-Cell Biocomputing Trends Biotechnol. 2001, 19, 317-323
75. Li, Z.; Rosenbaum, M. A.; Venkataraman, A.; Tam, T. K.; Katz, E.; Angenent, L. T. Bacteria-Based AND Logic Gate: A Decision-Making and Self-Powered Biosensor Chem. Commun. 2011, 47, 3060-3062
76. Arugula, M. A.; Halámek, J.; Katz, E.; Melnikov, D.; Pita, M.; Privman, V.; Strack, G. Optimization of Enzymatic Logic Gates and Networks for Noise Reduction and Stability, In Proceedings of Conference CENICS 2009; IEEE Comp. Soc. Conf. Publ. Serv.; Los Alamitos, CA, 2009; 1-7.
77. Halámek, J.; Zhou, J.; Halamkova, L.; Bocharova, V.; Privman, V.; Wang, J.; Katz, E. Biomolecular Filters for Improved Separation of Output Signals in Enzyme Logic Systems Applied to Biomedical Analysis Anal. Chem. 2011, 83, 8383-8386
78. Pita, M.; Privman, V.; Arugula, M. A.; Melnikov, D.; Bocharova, V.; Katz, E. Towards Biochemical Filter with Sigmoidal Response to pH Changes: Buffered Biocatalytic Signal Transduction Phys. Chem. Chem. Phys. 2011, 13, 4507-4513
79. Privman, V.; Halámek, J.; Arugula, M. A.; Melnikov, D.; Bocharova, V.; Katz, E. Biochemical Filter with Sigmoidal Response: Increasing the Complexity of Biomolecular Logic J. Phys. Chem. B 2010, 114, 14103-14109
80. Zhang, Z.; Jaffrezic-Renault, N.; Bessueille, F.; Leonard, D.; Xia, S.; Wang, X.; Chen, L.; Zhao, J. Development of a Conductometric Phosphate Biosensor Based on Tri-layer Maltose Phosphorylase Composite Films Anal. Chim. Acta 2008, 615, 73-79
81. Pyeshkova, V. M.; Saiapina, O. Y.; Soldatkin, O. O.; Dzyadevych, S. V. Enzyme Conductometric Biosensor for Maltose Determination Biopolym. Cell 2009, 25, 272-278
82. Shirokane, Y.; Ichikawa, K.; Suzuki, M. A Novel Enzymic Determination of Maltose Carbohydr. Res. 2000, 329, 699-702
83. Reiss, M.; Heibges, A.; Metzger, J.; Hartmeier, W. Determination of BOD-Values of Starch-Containing Waste Water by a BOD-Biosensor Biosens. Bioelectron. 1998, 13, 1083-1090
84. Vrbová, E.; Pecková, J.; Marek, M. Biosensor for Determination of Starch Starch 1993, 45, 341-344
85. Strack, G.; Chinnapareddy, S.; Volkov, D.; Halámek, J.; Pita, M.; Sokolov, I.; Katz, E. Logic Networks Based on Immunorecognition Processes J. Phys. Chem. B 2009, 113, 12154-12159
86. Chen, G. S.; Segel, I. H. Purification and Properties of Glycogen Phosphorylase from Escherichia coli Arch. Biochem. Biophys. 1968, 127, 175-186
87. Warmadewanthi; Liu, J. C Selective Precipitation of Phosphate from Semiconductor Wastewater J. Environ. Eng. 2009, 135, 1063-1070
88. Taylor, A. W.; Frazier, A. W.; Gurney, E. L.; Smith, J. P. Solubility Products of Di- and Trimagnesium Phosphates and the Dissociation of Magnesium Phosphate Solutions Trans. Faraday Soc. 1963, 59, 1585-1589
89. Garrett, R. H.; Grisham, C. M. Biochemistry; Brooks/Cole, Cengage Learning: Belmont, CA, 2013.
90. Hidaka, Y.; Hatada, Y.; Akita, M.; Yoshida, M.; Nakamura, N.; Takada, M.; Nakakuki, T.; Ito, S.; Horikoshi, K. Maltose Phosphorylase from a Deep-Sea Paenibacillus sp.: Enzymatic Properties and Nucleotide and Amino-Acid Sequences Enzyme Microbial Technol. 2005, 37, 185-194
91. Fedichkin, L.; Katz, E.; Privman, V. Error Correction and Digitalization Concepts in Biochemical Computing J. Comput. Theor. Nanosci. 2008, 5, 36-43
92. Huwel, S.; Haalck, L.; Conrath, N.; Spener, F. Maltose Phosphorylase from Lactobacillus Brevis: Purification, Characterization, and Application in a Biosensor for Ortho-Phosphate Enzyme Microbial Technol. 1997, 21, 413-420
93. Wilson, R.; Turner, A. P. F. Glucose Oxidase: An Ideal Enzyme Biosens. Bioelectron. 1992, 7, 165-185
94. Dunford, H. B. Peroxidases and Catalases: Biochemistry, Biophysics, Biotechnology and Physiology; Wiley: Hoboken NJ, 2010.
95. Claeyssen, E.; Rivoal, J. Isozymes of Plant Hexokinase: Occurrence, Properties and Functions Phytochemistry 2007, 68, 709-731
96. Nelson, D. L.; Cox, M. M. Lehninger Principles of Biochemistry, 5 th ed.; W. H. Freeman & Company: New York, 2008.
97. Purich, D. L. Enzyme Kinetics: Catalysis & Control; Elsevier: London, UK, 2010.
98. Schulz, A. R. Enzyme Kinetics: From Diastase to Multi-Enzyme Systems; Cambridge University Press: Cambridge, UK, 1994.
99. Melnikov, D.; Strack, G.; Zhou, J.; Windmiller, J. R.; Halámek, J.; Bocharova, V.; Chuang, M.-C.; Santhosh, P.; Privman, V.; Wang, J. Enzymatic AND Logic Gates Operated under Conditions Characteristic of Biomedical Applications J. Phys. Chem. B 2010, 114, 12166-12174
100. Baron, R.; Lioubashevski, O.; Katz, E.; Niazov, T.; Willner, I. Two Coupled Enzymes Perform in Parallel the "AND" and "InhibAND" Logic Gates Operations Org. Biomol. Chem. 2006, 4, 989-991
101. Baron, R.; Lioubashevski, O.; Katz, E.; Niazov, T.; Willner, I. Logic Gates and Elementary Computing by Enzymes J. Phys. Chem. A 2006, 110, 8548-8553
102. Strack, G.; Pita, M.; Ornatska, M.; Katz, E. Boolean Logic Gates Using Enzymes as Input Signals ChemBioChem 2008, 9, 1260-1266
103. Marquez, L. A.; Dunford, H. B. Mechanism of the Oxidation of 3,5,3′,5′-Tetramethylbenzidine by Myeloperoxidase Determined by Transient- and Steady-State Kinetics Biochemistry 1997, 36, 9349-9355
104. Josephy, P. D. Oxidative Activation of Benzidine and Its Derivatives by Peroxidases Environ. Health Perspect. 1985, 64, 171-178
105. Ricci, F.; Vallée-Bélisle, A.; Plaxco, K. W. High-Precision, in Vitro Validation of the Sequestration Mechanism for Generating Ultrasensitive Dose-Response Curves in Regulatory Networks. PLoS Comput. Biol. 2011, 7, article #e1002171.
106. Kurganov, B. I.; Lobanov, A. V.; Borisov, I. A.; Reshetilov, A. N. Criterion for Hill Equation Validity for Description of Biosensor Calibration Curves Anal. Chim. Acta 2001, 427, 11-19
107. Heidel, J.; Maloney, J. When Can Sigmoidal Data be Fit to a Hill Curve? J. Austral. Math. Soc. B 1999, 41, 83-92
108. Menon, A.; Mehrotra, K.; Mohan, C. K.; Ranka, S. Characterization of a Class of Sigmoid Functions with Applications to Neural Networks Neural Networks 1996, 9, 819-835
109. Qian, H.; Shi, P.-Z. Fluctuating Enzyme and Its Biological Functions: Positive Cooperativity without Multiple States J. Phys. Chem. B 2009, 113, 2225-2230
110. Rabinowitz, J. D.; Hsiao, J. J.; Gryncel, K. R.; Kantrowitz, E. R.; Feng, X.-J. Dissecting Enzyme Regulation by Multiple Allosteric Effectors: Nucleotide Regulation of Aspartate Transcarbamoylase Biochemistry 2008, 47, 5881-5888