136. On the chemical kinetics of autosynthetic systems

Hinshelwood, Cyril Norman

doi:10.1039/jr9520000745

Cited by 55 publications

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“…It has been shown that, in a constant environment, such autosynthetic systems will ultimately settle down into so-called ' steady states ' in which the amounts of all components increase at a common exponential rate (Hinshelwood, 1952;1953a, b).…”

Section: Discussionmentioning

confidence: 99%

“…The foundations of the general theory of open systems have been presented, discussed, and some aspects analysed in detail, by Burton (1936Burton ( , 1939, Reiner & Spiegelman (1944), Spiegelman & Reiner (1945), Hinshelwood (1946Hinshelwood ( , 1952Hinshelwood ( , 1953a, Denbigh, Hicks & Page (1948), Denbigh (1951Denbigh ( , 1952 and Dean & Hinshelwood (1955) in papers which provide references to the works of many other authors. Specific applications of the theory to continuous chemical reactions and continuous culture have also been published by Denbigh (1944Denbigh ( , 1947, Monod (1950) ~ Novick & Szilard (1950), Danckwerts (1954), Denbigh & Page (1954), Spicer (1955), Herbert, Elsworth & Telling (1956), Perret (1956Perret ( , 1957) and Moser (1957).…”

Section: Open Systemsmentioning

confidence: 99%

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A New Kinetic Model of a Growing Bacterial Population

Perret

1960

Journal of General Microbiology

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SUMMARY:A chemical open system of fixed volume in a constant environment tends towards a steady s t a t e in which its mass remains unchanged. Such a system is not a satisfactory kinetic model of a growing bacterial population, which increases its mass and volume, or grows, logarithmically, in a constant environment. However, when the material limiting the volume of an open system is itself one of the dynamic components the system can then grow logarithmically of its own accord. If the surface-area-to-volume ratio of such an 'expanding system' remains unchanged logarithmic growth can continue indefinitely, and in a constant environment the system enters a time-dependent 'exponential state '. Autocatalysis is not involved in the Iogarithmic growth of an expanding system ; but when an autocatalytic stage is included the growth curve can exhibit a typical log-phase during which growth rate is virtually independent of concentrations of source material above a threshold level. The properties of expanding systems are deduced from those of open systems by non-mathematical arguments, and some of the implications of the expanding system concept in practical and theoretical microbiology are discussed. It is suggested that the spontaneous occurrence of expanding systems in a non-living environment might be the first step towards the evolution of living organisms. Throughout the paper all reactions are treated as reversible, since there seems to be no justification for the concept of an irreversible chemical change. The reactions are also assumed to be homogeneous, unimolecular, and of the first order, except where otherwise stated. Those assumptions are made in order to keep the examples in the text as simple as possible; but the * Present address :

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Section: Discussionmentioning

confidence: 99%

Section: Open Systemsmentioning

confidence: 99%

A New Kinetic Model of a Growing Bacterial Population

Perret

1960

Journal of General Microbiology

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“…This model gives insight into some of the complex nonlinear relationships between energy utilization and ribosomal and nonribosomal production as a function of cell growth conditions. growth laws | fitness landscape | energy efficiency | yield | bacterial metabolism S ince the work of Monod in the 1940s, there has been interest in understanding the principles of bacterial growth laws (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). Monod observed that increasing glucose increases Escherichia coli's growth rate, up to a maximum rate beyond which the cells cannot replicate any faster (1).…”

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confidence: 99%

Bacterial growth laws reflect the evolutionary importance of energy efficiency

Maitra

Dill

2014

Proc. Natl. Acad. Sci. U.S.A.

169

208

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We are interested in the balance of energy and protein synthesis in bacterial growth. How has evolution optimized this balance? We describe an analytical model that leverages extensive literature data on growth laws to infer the underlying fitness landscape and to draw inferences about what evolution has optimized in Escherichia coli. Is E. coli optimized for growth speed, energy efficiency, or some other property? Experimental data show that at its replication speed limit, E. coli produces about four mass equivalents of nonribosomal proteins for every mass equivalent of ribosomes. This ratio can be explained if the cell's fitness function is the the energy efficiency of cells under fast growth conditions, indicating a tradeoff between the high energy costs of ribosomes under fast growth and the high energy costs of turning over nonribosomal proteins under slow growth. This model gives insight into some of the complex nonlinear relationships between energy utilization and ribosomal and nonribosomal production as a function of cell growth conditions. Monod observed that increasing glucose increases Escherichia coli's growth rate, up to a maximum rate beyond which the cells cannot replicate any faster (1). On the one hand, such growth laws are experimentally observable. On the other hand, growth laws, per se, do not give insight into the evolutionary driving forces that lead to them.Evolutionary principles are expressed by fitness landscapes (13), which are mathematical surfaces that represent how the organism's fitness depends on some cellular property that can be altered by evolution over time. Peaks on fitness landscapes represent states of maximal fitness. To understand why a cell has a particular growth law, we need a mathematical model that relates its growth law (how the growth rate of the cellular population depends on food concentration) to its underlying fitness landscape (how the cell's growth parameters can be altered through evolution). Thus far, this is relatively uncharted territory for cellular modeling. Here, we develop a model to explore how bacteria balance their fluxes of energy and ribosomal (RPs) and nonribosomal proteins (NRPs). By comparing the model with data, we can explore possible fitness objectives for bacterial replication. Are bacteria evolutionarily optimized to maximize their duplication speed? Or, are bacteria evolutionarily optimized to maximize the energy efficiency of their duplication processes? Or, something else? By "evolutionarily optimized," we mean the tradeoffs that a cell must make. By evaluating extensive growth data on E. coli through the lens of the present model, which relates growth observables to fitness landscapes, we conclude that a principal evolutionary driving force for bacteria is the energy efficiency of the fastest-growing cells. Fig. 1 shows our kinetic model of bacteria growing in the exponential phase. This model defines relationships among four dynamical quantities: the rate of synthesis of ribosomal proteins, the synthesis and degradation rates of NRP...

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“…While this may be true for the problem on a molecular scale, it does not follow, ip8o facto, that an investigation cannot be made at a Iiigher level of organisation. Hinshelwood (1952) has pointed out, for example, that the three-body problem in mechanics cannot be solved, altho-Ligh the kinetic theory can explain the behaviour of a large number of bodies. He has shown that bacterial growth can be understood in terms of certain simple mathematical relationships, in spite of the fact that the molecular mechanisms involved are extraordinarily complicated.…”

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confidence: 99%

“…We note that the present simple theory accounts for the existence of the steady state in differentiated organisms. In any system in which a large number of chemical reactions occur in a stepwise sequence, the products of one reaction being utihzed by the next, as occurs in a series of enzymatic reactions in a uniceRular orgamsm, the growth curve should obey an exponential law (Hinshelwood, 1952), i.e., the rate of growth is proportioned to the number of ceRs present.…”

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confidence: 99%

A Physical Approach to the Problem of Cancer

Ej¹

1954

Br J Cancer

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(1952). But it will help for the purposes of the present communicatioii to provide a summary of the results.(a) Chemical carcinogens.-The first chemical compound to be identified as a carcinogenic agent was 1:2:5:6-dibenzanthracene (Cook, Hieger, Kennaway and Mayneord, 1932). Since that time, the polycyclic hydrocarbons have been investigated systematically from this point of view. A certain degree of specificity has been observed and it has been correlated to some extent with the presence of a region of high electron density (K region, Schmidt, 1939), within the molecule. Some recent work has suggested, however, that the carcinogenic activity of the polycyclic hydrocarbons may be related in part to their ability to undergo autooxidation and liberate free radicals (Alexander, 1952).The second class of carcinogenic compounds includes mustard gas (Heston, 1950), nitrogen mustards (Boyland and Horning, 1949)

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136. On the chemical kinetics of autosynthetic systems

Cited by 55 publications

References 0 publications

A New Kinetic Model of a Growing Bacterial Population

A New Kinetic Model of a Growing Bacterial Population

Bacterial growth laws reflect the evolutionary importance of energy efficiency

A Physical Approach to the Problem of Cancer

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