Use my Search Websuite to scan PubMed, PMCentral, Journal Hosts and Journal Archives, FullText. Kick-your-searchterm to multiple Engines kick-your-query now !>

A dictionary by aggregated review articles of nephrology, medicine and the life sciences Your one-stop-run pathway from word to the immediate pdf of peer-reviewed on-topic knowledge.

10.3389/fphys.2016.00089 http://scihub22266oqcxt.onion/10.3389/fphys.2016.00089 C4805594!4805594!27047384     free     free     free Warning: file_get_contents(https://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=pubmed&id=27047384&cmd=llinks): Failed to open stream: HTTP request failed! HTTP/1.1 429 Too Many Requests in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 215 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 211.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 245.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 245.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 245.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 245.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 245.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 245.2 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 278.79999999999995 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Warning: imagejpeg(C:\Inetpub\vhosts\kidney.de\httpdocs\phplern\27047384.jpg): Failed to open stream: No such file or directory in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 117       Front+Physiol 2016 ; 7 (�): � Nephropedia Template TP {{tp|p=27047384|t=2016. An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations |pdf=|usr=}}{{27047384}} gab.com Text An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations JO: Front Physiol http://www.kidney.de/pget.php?&tw=1&pmid=27047384 #FOAvip Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. Twit Text FOAVip An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations ????Front Physiol http://www.kidney.de/pget.php?&tw=1&pmid=27047384 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=27047384 #FOAvip English Wikipedia <ref>{{Cite pmid|27047384}}</ref> An Analytical Framework for Studying Small-Number Effects in Catalytic Reaction Networks: A Probability Generating Function Approach to Chemical Master Equations #MMPMID27047384 Nakagawa M; Togashi Y Front Physiol 2016[]; 7 (�): � PMID27047384show ga Cell activities primarily depend on chemical reactions, especially those mediated by enzymes, and this has led to these activities being modeled as catalytic reaction networks. Although deterministic ordinary differential equations of concentrations (rate equations) have been widely used for modeling purposes in the field of systems biology, it has been pointed out that these catalytic reaction networks may behave in a way that is qualitatively different from such deterministic representation when the number of molecules for certain chemical species in the system is small. Apart from this, representing these phenomena by simple binary (on/off) systems that omit the quantities would also not be feasible. As recent experiments have revealed the existence of rare chemical species in cells, the importance of being able to model potential small-number phenomena is being recognized. However, most preceding studies were based on numerical simulations, and theoretical frameworks to analyze these phenomena have not been sufficiently developed. Motivated by the small-number issue, this work aimed to develop an analytical framework for the chemical master equation describing the distributional behavior of catalytic reaction networks. For simplicity, we considered networks consisting of two-body catalytic reactions. We used the probability generating function method to obtain the steady-state solutions of the chemical master equation without specifying the parameters. We obtained the time evolution equations of the first- and second-order moments of concentrations, and the steady-state analytical solution of the chemical master equation under certain conditions. These results led to the rank conservation law, the connecting state to the winner-takes-all state, and analysis of 2-molecules M-species systems. A possible interpretation of the theoretical conclusion for actual biochemical pathways is also discussed. �An Analytical Framework for Studying Small-Number Effects in Catalytic(epmc).pdf DeepDyve Pubget Overpricing