Browsing by Author "Li, Xin"
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Item A New Theoretical Approach to Analyze Complex Processes in Cytoskeleton Proteins(American Chemical Society, 2014) Li, Xin; Kolomeisky, Anatoly B.; Center for Theoretical Biological PhysicsCytoskeleton proteins are filament structures that support a large number of important biological processes. These dynamic biopolymers exist in non-equilibrium conditions stimulated by hydrolysis chemical reactions in their monomers. Current theoretical methods provide a comprehensive picture of biochemical and biophysical processes in cytoskeleton proteins. However, the description is only qualitative at biologically relevant conditions because utilized theoretical mean-field models neglect correlations. We develop a new theoretical method to describe dynamic processes in cytoskeleton proteins that takes into account spatial correlations in the chemical composition of these biopolymers. Our approach is based on analysis of probabilities of different clusters of subunits. It allows us to obtain exact analytical expressions for a variety of dynamic properties of cytoskeleton filaments. By comparing theoretical predictions with Monte Carlo computer simulations it is shown that our method provides a fully quantitative description of complex dynamic phenomena in cytoskeleton proteins at all conditions.Item Mechanisms and topology determination of complex chemical and biological network systems from first-passage theoretical approach(American Institute of Physics, 2013) Li, Xin; Kolomeisky, Anatoly B.; Center for Theoretical Biological PhysicsThe majority of chemical and biological processes can be viewed as complex networks of states connected by dynamic transitions. It is fundamentally important to determine the structure of these networks in order to fully understand the mechanisms of underlying processes. A new theoretical method of obtaining topologies and dynamic properties of complex networks, which utilizes a first-passage analysis, is developed. Our approach is based on a hypothesis that full temporal distributions of events between two arbitrary states contain full information on number of intermediate states, pathways, and transitions that lie between initial and final states. Several types of network systems are analyzed analytically and numerically. It is found that the approach is successful in determining structural and dynamic properties, providing a direct way of getting topology and mechanisms of general chemical network systems. The application of the method is illustrated on two examples of experimental studies of motor protein systems.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 Robust dynamic energy use and climate change(Wiley, 2016) Li, Xin; Narajabad, Borghan; Temzelides, Ted; James A. Baker III Institute for Public PolicyWe study a dynamic stochastic general equilibrium model in which agents are concerned about model uncertainty regarding climate change. An externality from greenhouse gas emissions damages the economy's capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, as opposed to risk, and we use robust control to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality and characterize dynamic optimal taxation. The optimal tax that restores the socially optimal allocation is Pigouvian. We study optimal output growth in the presence and in the absence of concerns about model uncertainty, and find that these can lead to substantially different conclusions regarding the optimal emissions and the optimal mix of fossil fuel. In particular, the optimal use of coal will be significantly lower on a robust path, while the optimal use of oil/gas will edge down.Item Robust Dynamic Energy Use and Climate ChangeLi, Xin; Narajabad, Borghan; Loch-Temzelides, Ted P.; James A. Baker III Institute for Public PolicyWe study a dynamic stochastic general equilibrium model in which agents are concerned about model uncertainty regarding climate change. An externality from greenhouse gas emissions damages the economyメs capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, as opposed to risk, and we use robust control theory to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality and characterize dynamic optimal taxation. The optimal tax that restores the socially optimal allocation is Pigouvian. We study optimal output growth in the presence and in the absence of concerns about model uncertainty and find that these can lead to substantially different conclusions regarding the optimal emissions and the optimal mix of fossil fuel.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 The Role of Multifilament Structures and Lateral Interactions in Dynamics of Cytoskeleton Proteins and Assemblies(American Chemical Society, 2015) Li, Xin; Kolomeisky, Anatoly B.; Center for Theoretical Biological PhysicsMicrotubules and actin filaments are biopolymer molecules that are major components of cytoskeleton networks in biological cells. They play important roles in supporting fundamental cellular processes such as cell division, signaling, locomotion, and intracellular transport. In cells, cytoskeleton proteins function under nonequilibrium conditions that are powered by hydrolysis of adenosine triphosphate (ATP) or guanosine triphosphate (GTP) molecules attached to them. Although these biopolymers are critically important for all cellular processes, the mechanisms that govern their complex dynamics and force generation remain not well explained. One of the most difficult fundamental issues is to understand how different components of cytoskeleton proteins interact together. We develop an approximate theoretical approach for analyzing complex processes in cytoskeleton proteins that takes into account the multifilament structure, lateral interactions between parallel protofilaments, and the most relevant biochemical transitions during the biopolymer growth. It allows us to fully evaluate collective dynamic properties of cytoskeleton filaments as well as the effect of external forces on them. It is found that for the case of strong lateral interactions the stall force of the multifilament protein is a linear function of the number of protofilaments. However, for weak lateral interactions, deviations from the linearity are observed. We also show that stall forces, mean velocities, and dispersions are increasing functions of the lateral interactions. Physicalヨchemical explanations of these phenomena are presented. Our theoretical predictions are supported by extensive Monte Carlo computer simulations.Item Theoretical Analysis of Microtubule Dynamics at All Times(American Chemical Society, 2014) Li, Xin; Kolomeisky, Anatoly B.; Center for Theoretical Biological PhysicsMicrotubules are biopolymers consisting of tubulin dimer subunits. As a major component of cytoskeleton they are essential for supporting most important cellular processes such as cell division, signaling, intracellular transport and cell locomotion. The hydrolysis of guanosine triphosphate (GTP) molecules attached to each tubulin subunit supports the nonequilibrium nature of microtubule dynamics. One of the most spectacular properties of microtubules is their dynamic instability when their growth from continuous attachment of tubulin dimers stochastically alternates with periods of shrinking. Despite the critical importance of this process to all cellular activities, its mechanism remains not fully understood. We investigated theoretically microtubule dynamics at all times by analyzing explicitly temporal evolution of various length clusters of unhydrolyzed subunits. It is found that the dynamic behavior of microtubules depends strongly on initial conditions. Our theoretical findings provide a microscopic explanation for recent experiments which found that the frequency of catastrophes increases with the lifetime of microtubules. It is argued that most growing microtubule configurations cannot transit in one step into a shrinking state, leading to a complex overall temporal behavior. Theoretical calculations combined with Monte Carlo computer simulations are also directly compared with experimental observations, and good agreement is found.Item Three Essays on Sovereign Default and Robust Policy Design(2014-04-23) Li, Xin; Loch-Temzelides, Ted; Narajabad, Borghan N.; El-Gamal, Mahmoud A.; Fang, SongyingChapter 1 discusses the optimal fiscal response of a small open economy to business cycle fluctuations at the presence of sovereign default risks. The most recent sovereign debt crisis in Europe has demonstrated that the risk of sovereign default is not a problem in developing economies only. However, empirical studies show that fiscal policy tends to be countercyclical or acyclical in developed small open economies and procyclical in developing countries. This chapter presents a general equilibrium model with endogenous government spending, external debt financing, and sovereign default decisions for a small open economy. The model shows that developed countries’ acyclical fiscal response to productivity fluctuations can be motivated by their larger size of public sectors, lower demand elasticity of public goods, and lower volatilities of domestic investments relative to foreign investments, compared to their developing counterparts. Along this line, the recently observed fiscal policy graduation in some Latin American countries can be rationalized by the shifts in the characteristics of their public sectors towards developed countries. The model also implies that fiscal austerity is always optimal for countries with sufficiently high debt-to-output ratio, and the optimal consolidation consists of tax hikes, cuts in public consumption but not in public investment. Based on Chapman, Fang, Li and Stone (2013), Chapter 2 studies the effect of new official bailouts on capital markets when borrowing countries economic state is private information. We first analyze a game-theoretical model of crisis lending that incorporates bargaining, compliance and enforcement. The presence of asymmet- ric information yields two interesting scenarios. There are conditions under which lending reduces the risk of a deepening crisis and reduces the risk premium demanded by market actors. On the other hand, the political interests that make lenders willing to lend weaken the credibility of commitments to reform, and the act of accepting an agreement reveals unfavorable information about the state of the borrower’s economy. The net “catalytic” effect on the price of private borrowing depends on whether these effects dominate the beneficial effects of the liquidity the loan provides. Decomposing the contradictory effects of crisis lending provides an explanation for the discrepant empirical findings about market reactions, especially with regard to IMF programs. We test the implications of our theory by examining how sovereign bond yields are affected by IMF program announcements, loan size, the scope of conditions attached to loans, and measures of the geopolitical interests of the United States, a key IMF principal. Based on Li, Narajabad, and Temzelides (2013), Chapter 3 turns to the study of robust policy design when decision makers are concerned about model uncertainty. We study a dynamic stochastic general equilibrium model where agents are concerned about model uncertainty regarding climate change. An externality from greenhouse gas emissions adversely affects the economy’s capital stock. We assume that the mapping from climate change to damages is subject to uncertainty, and we adapt and use techniques from robust control theory in order to study efficiency and optimal policy. We obtain a sharp analytical solution for the implied environmental externality, and we characterize dynamic optimal taxation. A small increase in the concern about model uncertainty can cause a significant drop in optimal energy extraction. The optimal tax which restores the social optimal allocation is Pigouvian. Under more general assumptions, we develop a recursive method and solve the model computationally. We find that the introduction of uncertainty matters qualitatively and quantitatively. We study optimal output growth in the presence and in the absence of concerns about uncertainty and find that these can lead to substantially different conclusions.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.