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Clerc MG, Tirapegui E, Trejo M. Pattern formation and localized structures in reaction-diffusion systems with non-Fickian transport. PHYSICAL REVIEW LETTERS 2006; 97:176102. [PMID: 17155485 DOI: 10.1103/physrevlett.97.176102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2005] [Indexed: 05/12/2023]
Abstract
We study the robust dynamical behaviors of reaction-diffusion systems where the transport gives rise to non-Fickian diffusion. A prototype model describing the deposition of molecules in a surface is used to show the generic appearance of Turing structures which can coexist with homogeneous states giving rise to localized structures through the pinning mechanism. The characteristic lengths of these structures are in the nanometer region in agreement with recent experimental observations.
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Affiliation(s)
- M G Clerc
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile
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2
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Lerch HP, Rigler R, Mikhailov AS. Functional conformational motions in the turnover cycle of cholesterol oxidase. Proc Natl Acad Sci U S A 2005; 102:10807-12. [PMID: 16046535 PMCID: PMC1182465 DOI: 10.1073/pnas.0504995102] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2005] [Indexed: 11/18/2022] Open
Abstract
Reexamining experimental data of single-molecule fluorescence correlation spectroscopy for cholesterol oxidase, we find that the existing Michaelis-Menten models with dynamical disorder cannot explain strong correlations between subsequent turnover cycles revealed in the diagonal feature in the joint statistical distribution of adjacent "on" times of this enzyme. We suggest that functional conformational motions representing ordered sequences of transitions between a set of conformational substates are involved, along with equilibrium conformational fluctuations in the turnover cycle of cholesterol oxidase. A two-channel model of single-enzyme dynamics, including a slow functional conformational motion in one of the channels, is proposed that allows us to reproduce such strong correlations.
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Affiliation(s)
- Hans-Philipp Lerch
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany.
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3
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Konkoli Z. Interplay between chemical reactions and transport in structured spaces. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:011917. [PMID: 16090011 DOI: 10.1103/physreve.72.011917] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2005] [Revised: 06/02/2005] [Indexed: 05/03/2023]
Abstract
The main motivation behind this study is to understand the interplay between the reactions and transport in a geometries that are not compact. Typical examples of compact geometries are a box or a sphere. A network made of containers C(1) , C(2),..., C(N) and tubes is an example of the space that is structured and noncompact. In containers, particles react with the rate lambda. Tubes connecting containers allow for the exchange of chemicals with the transport rate D. A situation is considered where a number of reactants is small and kinetics is noise dominated. A method is presented that can be used to calculate the average and higher moments of the reaction time. A number of different chemical reactions are studied and their performance compared in various ways. Two schemes are discussed in general, the reaction on a fixed geometry ensemble (ROGE) and the geometry on a fixed reaction ensemble, examples are given in the ROGE case. The most important findings are as follows. (i) There is a large number of reactions that run faster in a networklike geometry. Such reactions contain antagonistic catalytic influences in the intermediate stages of a reaction scheme that are best dealt with in a networklike structure. (ii) Antagonistic catalytic influences are hard to identify since they are strongly connected to the pattern of injected molecules (inject pattern) and depend on the choice of molecules that have to be synthesized at the end (task pattern). (iii) The reaction time depends strongly on the details of the inject and task patterns.
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Affiliation(s)
- Zoran Konkoli
- Department of Applied Physics, Chalmers University of Technology and Göteborg University, Sweden.
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4
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Berry H. Nonequilibrium phase transition in a self-activated biological network. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:031907. [PMID: 12689101 DOI: 10.1103/physreve.67.031907] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2002] [Revised: 12/16/2002] [Indexed: 05/18/2023]
Abstract
We present a lattice model for a two-dimensional network of self-activated biological structures with a diffusive activating agent. The model retains basic and simple properties shared by biological systems at various observation scales, so that the structures can consist of individuals, tissues, cells, or enzymes. Upon activation, a structure emits a new mobile activator and remains in a transient refractory state before it can be activated again. Varying the activation probability, the system undergoes a nonequilibrium second-order phase transition from an active state, where activators are present, to an absorbing, activator-free state, where each structure remains in the deactivated state. We study the phase transition using Monte Carlo simulations and evaluate the critical exponents. As they do not seem to correspond to known values, the results suggest the possibility of a separate universality class.
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Affiliation(s)
- Hugues Berry
- Equipe de Recherche sur les Relations Matrice Extracellulaire-Cellules (ERRMECe), Département de Biologie, Université de Cergy-Pontoise, Boîte Postale 222, 2 Avenue A. Chauvin, 95302 Cergy-Pontoise Cedex, France.
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5
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Lerch HP, Mikhailov AS, Hess B. Conformational-relaxation models of single-enzyme kinetics. Proc Natl Acad Sci U S A 2002; 99:15410-5. [PMID: 12429859 PMCID: PMC137730 DOI: 10.1073/pnas.232376799] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2002] [Indexed: 11/18/2022] Open
Abstract
Fluorescent spectroscopy experiments with single-enzyme molecules yield a large volume of statistical data that can be analyzed and interpreted using stochastic models of enzyme action. Here, we present two models, each based on the mechanism that an enzyme molecule must pass through a sequence of conformational transformations to complete its catalytic turnover cycle. In the simplest model, only one path leading to the release of product is present. In contrast to this, two different catalytic paths are possible in the second considered model. If a cycle is started from an active state, immediately after the previous product release, it follows a different conformational route and is much shorter. Our numerical investigations show that both models generate non-Markovian molecular statistics. However, their memory landscapes and distributions of cycle times are significantly different. The memory landscape of the double-path model bears strong similarity to the recent experimental data for horseradish peroxidase.
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Affiliation(s)
- Hans-Philipp Lerch
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany
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6
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Wang H, Ouyang Q, Lei YA. Microscopic Self-Organization in Biochemical Reactions: A Lattice Model. J Phys Chem B 2001. [DOI: 10.1021/jp010239h] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hongli Wang
- Department of Physics, Mesoscopic Physics Laboratory, Peking University, Beijing 100871, People's Republic of China
| | - Qi Ouyang
- Department of Physics, Mesoscopic Physics Laboratory, Peking University, Beijing 100871, People's Republic of China
| | - Yi-an Lei
- Department of Physics, Mesoscopic Physics Laboratory, Peking University, Beijing 100871, People's Republic of China
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7
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Strömberg A, Karlsson A, Ryttsén F, Davidson M, Chiu DT, Orwar O. Microfluidic device for combinatorial fusion of liposomes and cells. Anal Chem 2001; 73:126-30. [PMID: 11195496 DOI: 10.1021/ac000528m] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We describe an electrofusion-based technique for combinatorial synthesis of individual liposomes. A prototype device with containers for liposomes of different compositions and a fusion container was constructed. The sample containers had fluid contact with the fusion container through microchannels. Optical trapping was used to transport individual liposomes and cells through the microchannels into the fusion container. In the fusion container, selected pairs of liposomes were fused together using microelectrodes. A large number of combinatorially synthesized liposomes with complex compositions and reaction systems can be obtained from small sets of precursor liposomes. The order of different reaction steps can be specified and defined by the fusion sequence. This device could also facilitate single cell-cell electrofusions (hybridoma production). This is exemplified by fusion of transported red blood cells.
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Affiliation(s)
- A Strömberg
- Department of Chemistry, Göteborg University, Sweden
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Stange P, Mikhailov AS, Hess B. Coherent Intramolecular Dynamics of Enzymic Reaction Loops in Small Volumes. J Phys Chem B 2000. [DOI: 10.1021/jp992641q] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Pedro Stange
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany, and Max-Planck-Institut für Molekulare Physiologie, Otto-Hahn-Strasse 11, D-44227 Dortmund, Germany
| | - Alexander S. Mikhailov
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany, and Max-Planck-Institut für Molekulare Physiologie, Otto-Hahn-Strasse 11, D-44227 Dortmund, Germany
| | - Benno Hess
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany, and Max-Planck-Institut für Molekulare Physiologie, Otto-Hahn-Strasse 11, D-44227 Dortmund, Germany
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Berry H, Larreta-Garde V. Oscillatory behavior of a simple kinetic model for proteolysis during cell invasion. Biophys J 1999; 77:655-65. [PMID: 10423415 PMCID: PMC1300361 DOI: 10.1016/s0006-3495(99)76921-3] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022] Open
Abstract
Extracellular proteolysis during cell invasion is thought to be tightly organized, both temporally and spatially. This work presents a simple kinetic model that describes the interactions between extracellular matrix (ECM) proteins, proteinases, proteolytic fragments, and integrins. Nonmonotonous behavior arises from enzyme de novo synthesis consecutive to integrin binding to fragments or entire proteins. The model has been simulated using realistic values for kinetic constants and protein concentrations, with fibronectin as the ECM protein. The simulations show damped oscillations of integrin-complex concentrations, indicating alternation of maximal adhesion periods with maximal mobility periods. Comparisons with experimental data from the literature confirm the similarity between this system behavior and cell invasion. The influences on the system of cryptic functions of ECM proteins, proteinase inhibitors, and soluble antiadhesive peptides were examined. The first critical parameter for oscillation is the discrepancy between integrin affinity for intact ECM proteins and the respective proteolytic fragments, thus emphasizing the importance of cryptic functions of ECM proteins in cell invasion. Another critical parameter is the ratio between proteinase and the initial ECM protein concentration. These results suggest new insights into the organization of the ECM degradation during cell invasion.
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Affiliation(s)
- H Berry
- ERRMECE, University of Cergy-Pontoise, 95302 Cergy-Pontoise Cedex, France
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Stange P, Mikhailov AS, Hess B. Mutual Synchronization of Molecular Turnover Cycles in Allosteric Enzymes II. Product Inhibition. J Phys Chem B 1999. [DOI: 10.1021/jp9900640] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- P. Stange
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4−6, D-14195 Berlin, Germany, and Max-Planck-Institut für molekulare Physiologie, Otto-Hahn-Str. 11 D-44227 Dortmund, Germany2
| | - A. S. Mikhailov
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4−6, D-14195 Berlin, Germany, and Max-Planck-Institut für molekulare Physiologie, Otto-Hahn-Str. 11 D-44227 Dortmund, Germany2
| | - B. Hess
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4−6, D-14195 Berlin, Germany, and Max-Planck-Institut für molekulare Physiologie, Otto-Hahn-Str. 11 D-44227 Dortmund, Germany2
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11
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Norris V. Modelling Escherichia coli. The concept of competitive coherence. COMPTES RENDUS DE L'ACADEMIE DES SCIENCES. SERIE III, SCIENCES DE LA VIE 1998; 321:777-87. [PMID: 9809206 DOI: 10.1016/s0764-4469(98)80018-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
Many of the characteristics of life are plainly evident. Others are not. In principle, computer models might be devised to test whether a hypothetical characteristic is likely to be a characteristic of real life. Here, I propose that the bacterium Escherichia coli can be considered as passing through a series of states in which a distinct set of its constituent molecules or 'elements' are active. The activity of these elements is determined by a competition between two processes. One of these processes depends on the previous cell state whilst the other depends on the internal coherence of the developing state. The simultaneous operation of these two processes I term 'competitive coherence'. To clarify and eventually test these related hypotheses, a possible computer model is outlined.
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Affiliation(s)
- V Norris
- IFR systèmes intégrés, faculté des sciences et techniques, université de Rouen, Mont-Saint-Aignan, France.
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12
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Stange P, Mikhailov AS, Hess B. Mutual Synchronization of Molecular Turnover Cycles in Allosteric Enzymes. J Phys Chem B 1998. [DOI: 10.1021/jp9813185] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Pedro Stange
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany, and Max-Planck-Institut für medizinische Forschung, Jahnstrasse 29, D-69120 Heidelberg, Germany
| | - Alexander S. Mikhailov
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany, and Max-Planck-Institut für medizinische Forschung, Jahnstrasse 29, D-69120 Heidelberg, Germany
| | - Benno Hess
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany, and Max-Planck-Institut für medizinische Forschung, Jahnstrasse 29, D-69120 Heidelberg, Germany
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Abstract
Strong diffusional mixing and short delivery times typical for micrometer and sub-micrometer reaction volumes lead to a special situation where the turnover times of individual enzyme molecules become the largest characteristic time scale of the chemical kinetics. Under these conditions, populations of cross-regulating allosteric enzymes form molecular networks that exhibit various kinds of self-organized coherent collective dynamics.
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Affiliation(s)
- P Stange
- Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin, Germany
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14
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Wyskovsky W. Enzymatic reactions in small spatial volumes: comment on a model of Hess and Mikhailov. Biophys Chem 1998; 71:73-81; discussion 83-5. [PMID: 17027453 DOI: 10.1016/s0301-4622(98)00091-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/1997] [Revised: 09/29/1997] [Accepted: 12/05/1997] [Indexed: 10/17/2022]
Abstract
Recently Hess and Mikhailov pointed out that in small subcellular compartments diffusion is so fast that mixing is instantaneous on the time scale of many enzymatic reactions. This opens the possibility for synchronizing individual reaction events. To illustrate this fact they discuss as example an irreversible enzymatic reaction with allosteric product activation. Under appropriate conditions their model shows coherent spiking in the number of product molecules, caused by the strong correlation between reaction events. In this model only substrate binding is an indeterministic process, all other subsequent transitions between different enzyme states being deterministic, contrary to real processes. The purpose of the present paper was to investigate this interesting phenomenon by means of a more realistic modification of the original model, with only probabilistic transitions. In an attempt to obtain spiking, which was not observed under these conditions, the model was extended to make a clear distinction between allosteric high and low affinity substrate binding, in contrast to the original model using a product dependent mean binding probability. However no periodic signal was detectable in the indeterministic version of the Hess Mikhailov model or the extended version, either by means of direct visualization or on autocorrelation or Fourier analysis. Reasons why spiking is not observed in indeterministic enzyme models are discussed.
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Affiliation(s)
- W Wyskovsky
- Pharmakologisches Institut der Universität Wien Währingerstr. 13 A, A-1090 Vienna, Austria
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Mikhailov A, Hess B. Fluctuations of molecular turnover times in enzymatic reactions: reply to W. Wyskovsky. Biophys Chem 1998. [DOI: 10.1016/s0301-4622(98)00092-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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