Browsing by Author "Valleriani, Angelo"
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Item Pathway structure determination in complex stochastic networks with non-exponential dwell times(AIP Publishing, 2014) Li, Xin; Kolomeisky, Anatoly B.; Valleriani, Angelo; Center for Theoretical Biological PhysicsAnalysisᅠof complexᅠnetworksᅠhas been widely used as a powerful tool for investigating various physical, chemical, and biological processes. To understand the emergentᅠpropertiesᅠof these complex systems, one of the most basic issues is to determine the structure andᅠtopologyᅠof the underlyingᅠnetworks.ᅠRecently, a newᅠtheoreticalᅠapproach based on first-passageᅠanalysisᅠhas been developed for investigating the relationship between structure and dynamicᅠpropertiesᅠforᅠnetworkᅠsystems with exponential dwell time distributions. However, many real phenomena involve transitions with non-exponential waiting times. We extend the first-passage method to uncover the structure of distinct pathways in complexᅠnetworksᅠwith non-exponential dwell time distributions. It is found that theᅠanalysisᅠof early time dynamics provides explicit information on the length of the pathways associated to their dynamicᅠproperties.ᅠIt reveals a universal relationship that we have condensed in one general equation, which relates the number of intermediate states on the shortest path to the early time behavior of the first-passage distributions. Ourᅠtheoreticalᅠpredictions are confirmed by extensiveᅠMonte Carlo simulations.Item Stochastic Kinetics on Networks: When Slow Is Fast(American Chemical Society, 2014) Li, Xin; Kolomeisky, Anatoly B.; Valleriani, Angelo; Center for Theoretical Biological PhysicsMost chemical and biological processes can be viewed as reaction networks in which different pathways often compete kinetically for transformation of substrates into products. An enzymatic process is an example of such phenomena when biological catalysts create new routes for chemical reactions to proceed. It is typically assumed that the general process of product formation is governed by the pathway with the fastest kinetics at all time scales. In contrast to the expectation, here we show theoretically that at time scales sufficiently short, reactions are predominantly determined by the shortest pathway (in the number of intermediate states), regardless of the average turnover time associated with each pathway. This universal phenomenon is demonstrated by an explicit calculation for a system with two competing reversible (or irreversible) pathways. The time scales that characterize this regime and its relevance for single-molecule experimental studies are also discussed.Item Unveiling the hidden structure of complex stochastic biochemical networks(AIP Publishing LLC, 2014) Valleriani, Angelo; Li, Xin; Kolomeisky, Anatoly B.; Center for Theoretical Biological PhysicsComplex Markov models is a widely used and powerful predictive tool to analyze stochastic biochemical processes. When, however, the network of states is unknown, it is necessary to extract information from the data to partially build the network and to give estimates about the rates. The short-time behavior of the first-passage time distributions between two states in linear chains has been shown recently to behave as a power of time with an exponent equal to the number of intermediate states. For a general Markov network system we derive here the complete Taylor expansion of the first passage time distribution in terms of absorption times. By combining algebraic methods and graph theoretical approaches it is shown that the first term of the Taylor expansion is determined by the shortest path from the initial state to the absorbing state. When this path is unique, we prove that the coefficient of the first term can be written in terms of the product of the transition rates along the path. It is argued that the application of our results to first-return times may be used to estimate the dependence of rates from external parameters in experimentally measured time distributions.