| Summary: | 博士 === 國立陽明大學 === 生物醫學資訊研究所 === 105 === Computational modeling has become a useful and important tool to study and to gain insights
for many biological and chemical processes. In order to model the noise (stochasticity) in
the biochemical processes at the cellular/molecular level, stochastic simulations are often
performed with the Gillespie’s algorithm or the Langevin’s equation. For gene expression,
the noise due to the burst production in mRNA and proteins were mathematically derived
and a Langevin’s equation for modeling the noisy gene expression was developed. We
found that it is possible to include both transcriptional and translational burst effects in one
Langevin’s equation for the gene, where the overall burst size is the product of the burst
sizes of mRNA and protein. Our proposed burst Langevin’s equation to simulate protein’s
fluctuation produces accurate dynamics of protein number’s mean and standard deviation
for expression level as low as ten particles. This scheme allows good-quality simulation,
and it is very efficient in computer time and memory. The Langevin simulation also allows
independent change in deterministic dynamics versus fluctuation, which is useful in the
analysis of noise in biological networks.
We further use the burst Langevin’s formulism to study the noise propagation in a
development network. Functionally similar pathways are often seen in biological systems,
forming feed-forward controls. The robustness in network motifs such as feed-forward loops
(FFLs) has been reported previously. FFLs has the potential to filter the noise, but such noisefiltering
is asymmetric, i.e it works at either the “ON” or the “OFF” states in the target gene.
In the developmental regulatory network of Caenorhabditis elegans (C. elegans) that controls
the timing of distal tip cell (DTC) migration, we found multiple, interlinked FFLs. We further
study the propagated noises and the noise-filtering effect. Using stochastic simulation with
burst Langevin scheme, we show the noise-filtering property of an interlinked FFLs can be
largely derived from that of the individual FFLs. With interlinked FFLs, it is possible to filter
noises in both “ON” and “OFF” states in the output. We also demonstrated molecular basis
of heterogeneous phenotype observed in blmp-1;daf-12 mutant. We observed that positive
feedback loops are helpful in maintaining the desirable activity of the target gene, but it may
enhance intrinsic noise of the genes involved. The post-translational degradation of DRE-1
also plays a crucial role in reducing the propagated noises in final target gene UNC-5. Our analyses allow for better inference from network structures to noise-filtering properties, and
provide insights into the mechanisms behind the precise DTC migration controls in space
and time.
In the kinetic modelling equilibrium approximation method can reduce the parameter
space compared to ODE model. In another project I use equilibrium approximation method
to characterize the acidity of liquid acids by 31P NMR using Trimethyl Phosphine Oxides
(TMPO) as probes. To probe acidity of materials or catalysts, a Lewis base is often employed.
NMR has been a sensitive technique to measure the strength of interaction between the
Lewis base and the proton and chemical shifts (CS) obtained can be tightly correlated to
the proton affinity. TMPO, a Lewis base has been shown to be a unique 31P NMR probe
molecule for acidity characterization of solid catalysts. Recently, such 31P-TMPO NMR
approach has been extended for acidity characterization of 10 liquid acids which range from
weak to strong and superacids. In general, a concave, nearly linear, and convex dependence
of CS vs. acid concentration curve was observed for weak, medium, and strong acids,
respectively. However, the overall dynamic scale for TMPO interaction with standard acids
is not yet established. In this work, we anticipate the system to undergo rapid exchange,
simulations were carried out using models based on chemical equilibrium to characterize the
interactions between TMPO and H2O, HA, and H3O+. Accordingly, related parameters such
as equilibrium constants and 31P CS values, associated with the above interactions derived
through numerical global optimization using constrained nonlinear optimization function
by fitting the data. The parameters obtained from simulations show excellent fit (± ca. 0.2
ppm) to the experimental 31P CS results. The optimized parameters shown that both the
dissociation constants and 31P CS values between TMPO and acid, are well correlated with
the acid strength (pKa). To further understand the dynamic behavior of chemical shift data,
we derive an approximate analytical expression for weak acids. In addition to the TMPO-acid
binding affinities and their chemical shift values, our work also offers a theoretical ground for
the TMPO-acid chemical shift profile, which is useful in future applications of acid strength
determination with TMPO. The unique correlation between the 31P NMR CS and the acidic
strength therefore represents a novel and practical acidity scale surpassing the conventional
pKa and/or pH approaches.
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