Kinetics stochastic nature

Each survival curve clearly shows that at smaller supercooling temperatures (i.e., higher experimental temperatures) all runs remained unfrozen, while at larger supercooling temperatures (i.e., lower experimental temperatures) all runs were frozen. From these survival curves, Wilson et al. (2003, 2005) defined the nucleation temperature for a given sample, also called the SCP, or kinetic freezing point, as the temperature at which half the runs of the same sample have frozen (T50). The inherent width of each survival curve was considered as an indication of the stochastic nature of nucleation, with the 10-90 width (i.e., the range of temperature from 10% samples unfrozen to 90% samples frozen) to be an indicator of the error bars for the SCP. 

Yet, the largest future challenge goes beyond time-independent descriptions, to irreversible thermodynamics, or kinetics. We know very little about a kinetic mechanism founded on hydrate measurements. Due to the stochastic nature of nucleation, experimentalists have dealt with the deterministic growth process. 

Genetic circuits must integrate specific components or network motifs that make them robust to fluctuations in the kinetics of biochemical reactions. Gene expression tends to be noisy because of the stochastic nature of the constituent biochemical reactions (Elowitz et al., 2002 McAdams and Arkin, 1997). In addition, fluctuations in environmental conditions, such as temperature and nutrient levels, affect cellular metabolism and consequently the operation of genetic circuits. Circuits that achieve reproducible, reliable behavior must do so despite components whose behavior fluctuates considerably. Mitigating the effects of gene expression noise will probably require a solution that incorporates positive and negative feedback loops. 

First, we will describe the fluorescence kinetics after excitation with an ultrafast excitation pulse that can be approximated by a 5-pulse in the absence of nonradiative processes that could deplete the excited state (idealized case of time-resolved fluorescence decay measurements) [11, 12]. In a system of equivalent fluorophores (embedded in a homogeneous medium and interacting equally with the microenvironment), all the excited molecules have the same probability of emission of a photon but, due to the stochastic nature of the spontaneous emission, only the relationships concerning large numbers of fluorophores can be formulated. It is obvious that the number of photons released per unit time (rate of emission, or fluorescence intensity, F (xdNp/dt) in the system without competing nonradiative processes equals the total rate of de-excitation (depletion of the excited state), —dN/dt, which is proportional to the number of fluorophores excited at a given time, N t). Hence, we can write — dN/dt = N(t), where is the rate constant of... 

In several theoretical models for small systems [77,79,80-81] the stochastic nature of the biochemical processes under certain circumstances reveals itself as the apparent violation of the Second Law of Thermodynamics. We consider below some of these models, demonstrating that the description of such processes in small systems based on averaging (nonlocal) formalism can often be misleading. These models demonstrate several unusual thermodynamic and kinetic properties that contradict the conventional laws of chemical thermodynamics and kinetics, described as a rule in terms of the average concentrations of the reagents and chemical intermediates. 

Cabaniss, S., Madey, G., Leff, L., Maurice, R, and Wetzel, R. (2005). A stochastic model for the synthesis and degradation of natural organic matter. Part I. Data structures and reaction kinetics. Bio geochemistry 76, 319-347. 

When mechanistic information is available or obtainable for the components of a system, it is possible to develop detailed analyses and simulations of that system. Such analyses and simulations may be deterministic or stochastic in nature. (Stochastic systems are the subject of Chapter 11.) In either case, the overriding philosophy is to apply mechanistic rules to predict behavior. Often, however, the information required to develop mechanistic models accounting for details such as enzyme and transporter kinetics and precisely predicting biochemical states is not available. Instead, all that may be known reliably about certain large-scale systems is the stoichiometry of the participating reactions. As we shall see in this chapter, this stoichiometric information is sometimes enough to make certain concrete determinations about the feasible operation of biochemical networks. 

Thus far, we have described the time-dependent nature of polymerizing environments both through stochastic [49-51] and lattice [52,53] models capable of addressing this kind of dynamics in a complex environment. The current article focuses on the former approach, but now rephrases the earlier justification of the use of the irreversible Langevin equation, iGLE, to the polymerization problem in the context of kinetic models, and specifically the chemical stochastic equation. The nonstationarity in the solvent response due to the collective polymerization of the dense solvent now appears naturally. This leads to a clear recipe for the construction of the requisite terms in the iGLE. Namely the potential of mean force and the friction kernel as described in Section 3. With these tools in hand, the iGLE is used... 

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