Kinetic single-cell models

While clever experimental design may make it possible to test predictions of single-cell models without recourse to measurements of f, direct experimental access to the frequency function is often desirable and sometimes necessary in order to evaluate single-cell control and kinetic properties using the strategy just outlined. 

We can also use chemical kinetics to attempt to model populations of living systems such as single-celled organisms or plant, animal, and human populations. We describe the density of individuals (species A) as Ca, which might be in individualsA olume in a three-dimensional... 

Model Fitting to Mixing-Cell Data Multiple-site kinetic models have been used to describe pesticide and herbicide movement in soils (15,16,17), cesium migration in columns (18), and strontium migration in a sandy aquifer over a twenty-year time period (1L). The results of the selective extraction procedures in all experiments discussed here suggest that a multi-site model should provide a better fit of the data than a single-site model. This hypothesis is supported by the variances in Table I, with the possible exception of selenium. 

In the second part of this article (Section III), various tumor models, which can mimic several characteristics of human tumors, are summarized and compared. These models include single cells, multicell spheroids, and experimental solid tumors. The most obvious and observable characteristic of neoplastic diseases is uncontrolled growth, invasion, and metastasis. As a result, attempts to model growth kinetics of tumor are discussed briefly in this section. 

The value of combinations of steady-state and transient experiments In formulating and testing models of single cell kinetics and controls will be apparent In the examples which follow. 

Franco has designed this model to coimect within a nonequilibrium thermodynamics framework atomistic phenomena (elementary kinetic processes) with macroscopic electrochemical observables (e.g., I-V curves, EIS, Uceii(t)) with reasonable computational efforts. The model is a transient, multiscale, and multiphysics single electrochemical cell model accounting for the coupling between physical mechanistic descriptions of the phenomena taking place in the different component and material scales. For the case of PEMFCs, the modeling approach can account for detailed descriptions of the electrochemical and transport mechanisms in the electrodes, the membrane, the gas diffusion layers and the channels H2, O2, N2, and vapor... 

In this code, a 1-dimensional electrochemical element is defined, which represents a finite volume of active unit cell. This 1-D sub-model can be validated with appropriate single-cell data and established 1-D codes. This 1-D element is then used in FLUENT, a commercially available product, to carry out 3-D similations of realistic fuel cell geometries. One configuration studied was a single tubular solid oxide fuel cell (TSOFC) including a support tube on the cathode side of the cell. Six chemical species were tracked in the simulation H2, CO2, CO, O2, H2O, and N2. Fluid dynamics, heat transfer, electrochemistry, and the potential field in electrode and interconnect regions were all simulated. Voltage losses due to chemical kinetics, ohmic conduction, and diffusion were accounted for in the model. Because of a lack of accurate and detailed in situ characterization of the SOFC modeled, a direct validation of the model results was not possible. However, the results are consistent with input-output observations on experimental cells of this type. 

Figure 4. The Brownian ratchet model of lamellar protrusion (Peskin et al., 1993). According to this hypothesis, the distance between the plasma membrane (PM) and the filament end fluctuates randomly. At a point in time when the PM is most distant from the filament end, a new monomer is able to add on. Consequently, the PM is no longer able to return to its former position since the filament is now longer. The filament cannot be pushed backwards by the returning PM as it is locked into the mass of the cell cortex by actin binding proteins. In this way, the PM is permitted to diffuse only in an outward direction. The maximum force which a single filament can exert (the stalling force) is related to the thermal energy of the actin monomer by kinetic theory according to the following equation ...

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