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1.  Mathematical modeling of left ventricular dimensional changes in mice during aging 
BMC Systems Biology  2012;6(Suppl 3):S10.
Cardiac aging is characterized by diastolic dysfunction of the left ventricle (LV), which is due in part to increased LV wall stiffness. In the diastolic phase, myocytes are relaxed and extracellular matrix (ECM) is a critical determinant to the changes of LV wall stiffness. To evaluate the effects of ECM composition on cardiac aging, we developed a mathematical model to predict LV dimension and wall stiffness changes in aging mice by integrating mechanical laws and our experimental results. We measured LV dimension, wall thickness, LV mass, and collagen content for wild type (WT) C57/BL6J mice of ages ranging from 7.3 months to those of 34.0 months. The model was established using the thick wall theory and stretch-induced tissue growth to an isotropic and homogeneous elastic composite with mixed constituents. The initial conditions of the simulation were set based on the data from the young mice. Matlab simulations of this mathematical model demonstrated that the model captured the major features of LV remodeling with age and closely approximated experimental results. Specifically, the temporal progression of the LV interior and exterior dimensions demonstrated the same trend and order-of-magnitude change as our experimental results. In conclusion, we present here a validated mathematical model of cardiac aging that applies the thick-wall theory and stretch-induced tissue growth to LV remodeling with age.
doi:10.1186/1752-0509-6-S3-S10
PMCID: PMC3524011  PMID: 23281647
2.  Mathematical modeling and stability analysis of macrophage activation in left ventricular remodeling post-myocardial infarction 
BMC Genomics  2012;13(Suppl 6):S21.
Background
About 6 million Americans suffer from heart failure and 70% of heart failure cases are caused by myocardial infarction (MI). Following myocardial infarction, increased cytokines induce two major types of macrophages: classically activated macrophages which contribute to extracellular matrix destruction and alternatively activated macrophages which contribute to extracellular matrix construction. Though experimental results have shown the transitions between these two types of macrophages, little is known about the dynamic progression of macrophages activation. Therefore, the objective of this study is to analyze macrophage activation patterns post-MI.
Results
We have collected experimental data from adult C57 mice and built a framework to represent the regulatory relationships among cytokines and macrophages. A set of differential equations were established to characterize the regulatory relationships for macrophage activation in the left ventricle post-MI based on the physical chemistry laws. We further validated the mathematical model by comparing our computational results with experimental results reported in the literature. By applying Lyaponuv stability analysis, the established mathematical model demonstrated global stability in homeostasis situation and bounded response to myocardial infarction.
Conclusions
We have established and validated a mathematical model for macrophage activation post-MI. The stability analysis provided a possible strategy to intervene the balance of classically and alternatively activated macrophages in this study. The results will lay a strong foundation to understand the mechanisms of left ventricular remodelling post-MI.
doi:10.1186/1471-2164-13-S6-S21
PMCID: PMC3481436  PMID: 23134700
3.  Virtual Screening Using Molecular Simulations 
Proteins  2011;79(6):1940-1951.
Effective virtual screening relies on our ability to make accurate prediction of protein-ligand binding, which remains a great challenge. In this work, utilizing the molecular-mechanics Poisson-Boltzmann (or Generalized Born) Surface Area approach, we have evaluated the binding affinity of a set of 156 ligands to seven families of proteins, trypsin β, thrombin α, cyclin-dependent kinase (CDK), cAMP-dependent kinase (PKA), urokinase-type plasminogen activator, β-glucosidase A and coagulation factor Xa. The effect of protein dielectric constant in the implicit-solvent model on the binding free energy calculation is shown to be important. The statistical correlations between the binding energy calculated from the implicit-solvent approach and experimental free energy are in the range 0.56~0.79 across all the families. This performance is better than that of typical docking programs especially given that the latter is directly trained using known binding data while the molecular mechanics is based on general physical parameters. Estimation of entropic contribution remains the barrier to accurate free energy calculation. We show that the traditional rigid rotor harmonic oscillator approximation is unable to improve the binding free energy prediction. Inclusion of conformational restriction seems to be promising but requires further investigation. On the other hand, our preliminary study suggests that implicit-solvent based alchemical perturbation, which offers explicit sampling of configuration entropy, can be a viable approach to significantly improve the prediction of binding free energy. Overall, the molecular mechanics approach has the potential for medium to high-throughput computational drug discovery.
doi:10.1002/prot.23018
PMCID: PMC3092865  PMID: 21491494
molecular mechanics; MM-GBSA; MM-PBSA; dielectric constant; configurational entropy; alchemical free energy calculation
4.  Bayesian parameter estimation for nonlinear modelling of biological pathways 
BMC Systems Biology  2011;5(Suppl 3):S9.
Background
The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data.
Results
We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC) method. We applied this approach to the biological pathways involved in the left ventricle (LV) response to myocardial infarction (MI) and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly parameterized dynamic systems.
Conclusions
Our proposed Bayesian algorithm successfully estimated parameters in nonlinear mathematical models for biological pathways. This method can be further extended to high order systems and thus provides a useful tool to analyze biological dynamics and extract information using temporal data.
doi:10.1186/1752-0509-5-S3-S9
PMCID: PMC3287577  PMID: 22784628
5.  Strand-specific PCR of UV radiation-damaged genomic DNA revealed an essential role of DNA-PKcs in the transcription-coupled repair 
BMC Biochemistry  2011;12:2.
Background
In eukaryotic cells, there are two sub-pathways of nucleotide excision repair (NER), the global genome (gg) NER and the transcription-coupled repair (TCR). TCR can preferentially remove the bulky DNA lesions located at the transcribed strand of a transcriptional active gene more rapidly than those at the untranscribed strand or overall genomic DNA. This strand-specific repair in a suitable restriction fragment is usually determined by alkaline gel electrophoresis followed by Southern blotting transfer and hybridization with an indirect end-labeled single-stranded probe. Here we describe a new method of TCR assay based on strand-specific-PCR (SS-PCR). Using this method, we have investigated the role of DNA-dependent protein kinase catalytic subunit (DNA-PKcs), a member of the phosphatidylinositol 3-kinase-related protein kinases (PIKK) family, in the TCR pathway of UV-induced DNA damage.
Results
Although depletion of DNA-PKcs sensitized HeLa cells to UV radiation, it did not affect the ggNER efficiency of UV-induced cyclobutane pyrimidine dimers (CPD) damage. We postulated that DNA-PKcs may involve in the TCR process. To test this hypothesis, we have firstly developed a novel method of TCR assay based on the strand-specific PCR technology with a set of smart primers, which allows the strand-specific amplification of a restricted gene fragment of UV radiation-damaged genomic DNA in mammalian cells. Using this new method, we confirmed that siRNA-mediated downregulation of Cockayne syndrome B resulted in a deficiency of TCR of the UV-damaged dihydrofolate reductase (DHFR) gene. In addition, DMSO-induced silencing of the c-myc gene led to a decreased TCR efficiency of UV radiation-damaged c-myc gene in HL60 cells. On the basis of the above methodology verification, we found that the depletion of DNA-PKcs mediated by siRNA significantly decreased the TCR capacity of repairing the UV-induced CPDs damage in DHFR gene in HeLa cells, indicating that DNA-PKcs may also be involved in the TCR pathway of DNA damage repair. By means of immunoprecipitation and MALDI-TOF-Mass spectrometric analysis, we have revealed the interaction of DNA-PKcs and cyclin T2, which is a subunit of the human transcription elongation factor (P-TEFb). While the P-TEFb complex can phosphorylate the serine 2 of the carboxyl-terminal domain (CTD) of RNA polymerase II and promote transcription elongation.
Conclusion
A new method of TCR assay was developed based the strand-specific-PCR (SS-PCR). Our data suggest that DNA-PKcs plays a role in the TCR pathway of UV-damaged DNA. One possible mechanistic hypothesis is that DNA-PKcs may function through associating with CyclinT2/CDK9 (P-TEFb) to modulate the activity of RNA Pol II, which has already been identified as a key molecule recognizing and initializing TCR.
doi:10.1186/1471-2091-12-2
PMCID: PMC3022811  PMID: 21214942

Results 1-5 (5)