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Eugene V Koonin - One of the best experts on this subject based on the ideXlab platform.
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birth and death of protein domains a simple model of evolution explains power Law Behavior
BMC Evolutionary Biology, 2002Co-Authors: Georgy P Karev, Yuri I Wolf, Andrey Rzhetsky, Faina S Berezovskaya, Eugene V KooninAbstract:Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power Laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power Laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power Law distributions has the potential of revealing non-trivial aspects of genome evolution. A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a b irth, d eath and i nnovation m odel (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power Law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, are considered in details and the distributions of the equilibrium frequencies of domain families of different size are determined for each case. We apply the BDIM formalism to the analysis of the domain family size distributions in prokaryotic and eukaryotic proteomes and show an excellent fit between these empirical data and a particular form of the model, the second-order balanced linear BDIM. Calculation of the parameters of these models suggests surprisingly high innovation rates, comparable to the total domain birth (duplication) and elimination rates, particularly for prokaryotic genomes. We show that a straightforward model of genome evolution, which does not explicitly include selection, is sufficient to explain the observed distributions of domain family sizes, in which power Laws appear as asymptotic. However, for the model to be compatible with the data, there has to be a precise balance between domain birth, death and innovation rates, and this is likely to be maintained by selection. The developed approach is oriented at a mathematical description of evolution of domain composition of proteomes, but a simple reformulation could be applied to models of other evolving networks with preferential attachment.
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birth and death of protein domains a simple model of evolution explains power Law Behavior
BMC Evolutionary Biology, 2002Co-Authors: Georgy P Karev, Yuri I Wolf, Andrey Rzhetsky, Faina S Berezovskaya, Eugene V KooninAbstract:Background Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power Laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power Laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power Law distributions has the potential of revealing non-trivial aspects of genome evolution.
Jae Hyun Park - One of the best experts on this subject based on the ideXlab platform.
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apparent power Law Behavior of water s isothermal compressibility and correlation length upon supercooling
Physical Chemistry Chemical Physics, 2019Co-Authors: Alexander Späh, Fivos Perakis, Daniel Mariedahl, Jonas A. Sellberg, Harshad Pathak, Katrin Amannwinkel, Tetsuo Katayama, Jae Hyun Park, Anders NilssonAbstract:The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-Law in the temperature ...
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Apparent power-Law Behavior of water's isothermal compressibility and correlation length upon supercooling
Physical Chemistry Chemical Physics, 2018Co-Authors: Alexander Späh, Fivos Perakis, Daniel Mariedahl, Katrin Amann-winkel, Jonas A. Sellberg, Harshad Pathak, Jae Hyun ParkAbstract:The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-Law in the temperature range from 280 K down to the temperature of maximum compressibility at 229 K. Although the increase in thermodynamic response functions is not towards a critical point, it is still possible to obtain an apparent power Law all the way to the maximum values with best-fit exponents of γ = 0.40 ± 0.01 for the isothermal compressibility and ν = 0.26 ± 0.03 for the correlation length. The ratio between these exponents is close to a value of ≈0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of γ obtained from experiment with molecular dynamics simulations on the iAMOEBA water model shows that it would be located at pressures in the neighborhood of 1 kbar. The high value and sharpness of the compressibility maximum observed in the experiment are not reproduced by any of the existing classical water models, thus inviting further development of simulation models of water.
Georgy P Karev - One of the best experts on this subject based on the ideXlab platform.
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birth and death of protein domains a simple model of evolution explains power Law Behavior
BMC Evolutionary Biology, 2002Co-Authors: Georgy P Karev, Yuri I Wolf, Andrey Rzhetsky, Faina S Berezovskaya, Eugene V KooninAbstract:Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power Laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power Laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power Law distributions has the potential of revealing non-trivial aspects of genome evolution. A simple model of evolution of the domain composition of proteomes was developed, with the following elementary processes: i) domain birth (duplication with divergence), ii) death (inactivation and/or deletion), and iii) innovation (emergence from non-coding or non-globular sequences or acquisition via horizontal gene transfer). This formalism can be described as a b irth, d eath and i nnovation m odel (BDIM). The formulas for equilibrium frequencies of domain families of different size and the total number of families at equilibrium are derived for a general BDIM. All asymptotics of equilibrium frequencies of domain families possible for the given type of models are found and their appearance depending on model parameters is investigated. It is proved that the power Law asymptotics appears if, and only if, the model is balanced, i.e. domain duplication and deletion rates are asymptotically equal up to the second order. It is further proved that any power asymptotic with the degree not equal to -1 can appear only if the hypothesis of independence of the duplication/deletion rates on the size of a domain family is rejected. Specific cases of BDIMs, namely simple, linear, polynomial and rational models, are considered in details and the distributions of the equilibrium frequencies of domain families of different size are determined for each case. We apply the BDIM formalism to the analysis of the domain family size distributions in prokaryotic and eukaryotic proteomes and show an excellent fit between these empirical data and a particular form of the model, the second-order balanced linear BDIM. Calculation of the parameters of these models suggests surprisingly high innovation rates, comparable to the total domain birth (duplication) and elimination rates, particularly for prokaryotic genomes. We show that a straightforward model of genome evolution, which does not explicitly include selection, is sufficient to explain the observed distributions of domain family sizes, in which power Laws appear as asymptotic. However, for the model to be compatible with the data, there has to be a precise balance between domain birth, death and innovation rates, and this is likely to be maintained by selection. The developed approach is oriented at a mathematical description of evolution of domain composition of proteomes, but a simple reformulation could be applied to models of other evolving networks with preferential attachment.
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birth and death of protein domains a simple model of evolution explains power Law Behavior
BMC Evolutionary Biology, 2002Co-Authors: Georgy P Karev, Yuri I Wolf, Andrey Rzhetsky, Faina S Berezovskaya, Eugene V KooninAbstract:Background Power distributions appear in numerous biological, physical and other contexts, which appear to be fundamentally different. In biology, power Laws have been claimed to describe the distributions of the connections of enzymes and metabolites in metabolic networks, the number of interactions partners of a given protein, the number of members in paralogous families, and other quantities. In network analysis, power Laws imply evolution of the network with preferential attachment, i.e. a greater likelihood of nodes being added to pre-existing hubs. Exploration of different types of evolutionary models in an attempt to determine which of them lead to power Law distributions has the potential of revealing non-trivial aspects of genome evolution.
Ramon Ferrericancho - One of the best experts on this subject based on the ideXlab platform.
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distinct flavors of zipf s Law and its maximum likelihood fitting rank size and size distribution representations
Physical Review E, 2020Co-Authors: Alvaro Corral, Isabel Serra, Ramon FerrericanchoAbstract:In recent years, researchers have realized the difficulties of fitting power-Law distributions properly. These difficulties are higher in Zipfian systems, due to the discreteness of the variables and to the existence of two representations for these systems, i.e., two versions depending on the random variable to fit: rank or size. The discreteness implies that a power Law in one of the representations is not a power Law in the other, and vice versa. We generate synthetic power Laws in both representations and apply a state-of-the-art fitting method to each of the two random variables. The method (based on maximum likelihood plus a goodness-of-fit test) does not fit the whole distribution but the tail, understood as the part of a distribution above a cutoff that separates non-power-Law Behavior from power-Law Behavior. We find that, no matter which random variable is power-Law distributed, using the rank as the random variable is problematic for fitting, in general (although it may work in some limit cases). One of the difficulties comes from recovering the ``hidden'' true ranks from the empirical ranks. On the contrary, the representation in terms of the distribution of sizes allows one to recover the true exponent (with some small bias when the underlying size distribution is a power Law only asymptotically).
Alexander Späh - One of the best experts on this subject based on the ideXlab platform.
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apparent power Law Behavior of water s isothermal compressibility and correlation length upon supercooling
Physical Chemistry Chemical Physics, 2019Co-Authors: Alexander Späh, Fivos Perakis, Daniel Mariedahl, Jonas A. Sellberg, Harshad Pathak, Katrin Amannwinkel, Tetsuo Katayama, Jae Hyun Park, Anders NilssonAbstract:The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-Law in the temperature ...
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Apparent power-Law Behavior of water's isothermal compressibility and correlation length upon supercooling
Physical Chemistry Chemical Physics, 2018Co-Authors: Alexander Späh, Fivos Perakis, Daniel Mariedahl, Katrin Amann-winkel, Jonas A. Sellberg, Harshad Pathak, Jae Hyun ParkAbstract:The isothermal compressibility and correlation length of supercooled water obtained from small-angle X-ray scattering (SAXS) were analyzed by fits based on an apparent power-Law in the temperature range from 280 K down to the temperature of maximum compressibility at 229 K. Although the increase in thermodynamic response functions is not towards a critical point, it is still possible to obtain an apparent power Law all the way to the maximum values with best-fit exponents of γ = 0.40 ± 0.01 for the isothermal compressibility and ν = 0.26 ± 0.03 for the correlation length. The ratio between these exponents is close to a value of ≈0.5, as expected for a critical point, indicating the proximity of a potential second critical point. Comparison of γ obtained from experiment with molecular dynamics simulations on the iAMOEBA water model shows that it would be located at pressures in the neighborhood of 1 kbar. The high value and sharpness of the compressibility maximum observed in the experiment are not reproduced by any of the existing classical water models, thus inviting further development of simulation models of water.