Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth.

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued this understanding. Based on this assessment, we review a multiscale, i.e., from the molecular to the gross tumor scale, mathematical and computational "first-principle" approach based on mass conservation and other physical laws, such as employed in reaction-diffusion systems. Model variables describe known characteristics of tumor behavior, and parameters and functional relationships across scales are informed from in vitro, in vivo and ex vivo biology. We review the feasibility of this methodology that, once coupled to tumor imaging and tumor biopsy or cell culture data, should enable prediction of tumor growth and therapy outcome through quantification of the relation between the underlying dynamics and morphological characteristics. In particular, morphologic stability analysis of this mathematical model reveals that tumor cell patterning at the tumor-host interface is regulated by cell proliferation, adhesion and other phenotypic characteristics: histopathology information of tumor boundary can be inputted to the mathematical model and used as a phenotype-diagnostic tool to predict collective and individual tumor cell invasion of surrounding tissue. This approach further provides a means to deterministically test effects of novel and hypothetical therapy strategies on tumor behavior.

Laser-induced transient grating analysis of dynamics of interaction between sensory rhodopsin II D75N and the HtrII transducer.

The interaction between sensory rhodopsin II (SRII) and its transducer HtrII was studied by the time-resolved laser-induced transient grating method using the D75N mutant of SRII, which exhibits minimal visible light absorption changes during its photocycle, but mediates normal phototaxis responses. Flash-induced transient absorption spectra of transducer-free D75N and D75N joined to 120 amino-acid residues of the N-terminal part of the SRII transducer protein HtrII (DeltaHtrII) showed only one spectrally distinct K-like intermediate in their photocycles, but the transient grating method resolved four intermediates (K(1)-K(4)) distinct in their volumes. D75N bound to HtrII exhibited one additional slower kinetic species, which persists after complete recovery of the initial state as assessed by absorption changes in the UV-visible region. The kinetics indicate a conformationally changed form of the transducer portion (designated Tr*), which persists after the photoreceptor returns to the unphotolyzed state. The largest conformational change in the DeltaHtrII portion was found to cause a DeltaHtrII-dependent increase in volume rising in 8 micros in the K(4) state and a drastic decrease in the diffusion coefficient (D) of K(4) relatively to those of the unphotolyzed state and Tr*. The magnitude of the decrease in D indicates a large structural change, presumably in the solvent-exposed HAMP domain of DeltaHtrII, where rearrangement of interacting molecules in the solvent would substantially change friction between the protein and the solvent.

The dynamics of calmodulin signaling revealed using optical methods

The Ca2+-binding protein calmodulin (CaM) is a key transducer of Ca2+ oscillations by virtue of its ability to bind Ca 2+ selectively and then interact specifically with a large number of downstream enzymes and proteins. It remains unclear whether Ca2+ -dependent signaling alone can activate the full range of Ca 2+/CaM regulated processes or whether other regulatory schemes in the cell exist that allow specific targeting of CaM to subsets of Ca 2+/CaM binding sites or regions of the cell. Here we investigate the possibility that alterations of the availability of CaM may serve as a potential cellular mechanism for regulating the activation of CaM-dependent targets. By utilizing sensitive optical techniques with high spatial and temporal resolution, we examine the intracellular dynamics of CaM signaling at a resolution previously unattainable. After optimizing and characterizing both the optical methods and fluorescently labeled probes for intracellular measurements, the diffusion of CaM in the cytoplasm of HEK293 cells was analyzed. It was discovered that the diffusion characteristics of CaM are similar to that of a comparably sized inert molecule. Independent manipulation of experimental parameters, including increases in total concentrations of CaM and intracellular Ca2+ levels, did not change the diffusion of CaM in the cytoplasm. However, changes in diffusion were seen when the concentration of Ca2+/CaM-binding targets was increased in conjunction with elevated Ca2+. This indicates that CaM is not normally limiting for the activation of Ca 2+/CaM-dependent enzymes in HEK293 cells but reveals that the ratio of CaM to CaM-dependent targets is a potential mechanism for changing CaM availability. Next we considered whether cellular compartmentalization may act to regulate concentrations of available Ca2+/CaM in hippocampal neurons. We discovered changes in diffusion parameters of CaM under elevated Ca2+ conditions in the soma, neurite and nucleus which suggest that either the composition of cytoplasm is different in these compartments and/or they are composed of unique families of CaM-binding proteins. Finally, we return to the HEK293 cell and for the first time directly show the intracellular binding of CaM and CaMKII, an important target for CaM critical for neuronal function and plasticity. Furthermore, we analyzed the complex binding stoichiometry of this molecular interaction in the basal, activated and autophosphorylated states of CaMKII and determined the impact of this binding on CaM availability in the cell. Overall these results demonstrate that regulation of CaM availability is a viable cellular mechanism for regulating the output of CaM-dependent processes and that this process is tuned to the specific functional needs of a particular cell type and subcellular compartment. ^