Stochastic phenotype transition of a single cell in an intermediate region of gene-state switching

Multiple phenotypic states often arise in a single cell with different gene-expression states that undergo transcription regulation with positive feedback. Recent experiments have shown that at least in E. coli, the gene state switching can be neither extremely slow nor exceedingly rapid as many previous theoretical treatments assumed. Rather it is in the intermediate region which is difficult to handle mathematically.Under this condition, from a full chemical-master-equation description we derive a model in which the protein copy-number, for a given gene state, follow a deterministic mean-field description while the protein synthesis rates fluctuate due to stochastic gene-state switching. The simplified kinetics yields a nonequilibrium landscape function, which, similar to the energy function for equilibrium fluctuation, provides the leading orders of fluctuations around each phenotypic state, as well as the transition rates between the two phenotypic states. This rate formula is analogous to Kramers theory for chemical reactions. The resulting behaviors are significantly different from the two limiting cases studied previously.Comment: 6 pages,4 figure

Numerical inversion of SRNFs for efficient elastic shape analysis of star-shaped objects.

The elastic shape analysis of surfaces has proven useful in several application areas, including medical image analysis, vision, and graphics. This approach is based on defining new mathematical representations of parameterized surfaces, including the square root normal field (SRNF), and then using the L2 norm to compare their shapes. Past work is based on using the pullback of the L2 metric to the space of surfaces, performing statistical analysis under this induced Riemannian metric. However, if one can estimate the inverse of the SRNF mapping, even approximately, a very efficient framework results: the surfaces, represented by their SRNFs, can be efficiently analyzed using standard Euclidean tools, and only the final results need be mapped back to the surface space. Here we describe a procedure for inverting SRNF maps of star-shaped surfaces, a special case for which analytic results can be obtained. We test our method via the classification of 34 cases of ADHD (Attention Deficit Hyperactivity Disorder), plus controls, in the Detroit Fetal Alcohol and Drug Exposure Cohort study. We obtain state-of-the-art results

Mechanistic insight into the regulation of Tec family kinase activity - substrate selection and conformational preferences

This thesis dissertation addresses the regulatory mechanism of Tec family kinases at the molecular level, focusing on two members, Interleukin-2 inducible T cell kinase (Itk) and Bruton\u27s tyrosine kinase (Btk). Itk, expressed in T cell lines, modulates the signal relayed from the T cell receptor on the cellular membrane to the nucleus, which results in expression of the genes essential for T cell immunity upon T cell stimulation. Btk is the counterpart of Itk expressed in B cells and is important for the antibody production. Therefore, the activity of Itk and Btk needs to be maintained in a normal range: too low their activity leads to immunodeficiency while too high activity is responsible for certain autoimmune diseases. Better understanding of the molecular details on how the activity of Itk and Btk is regulated will provide new insights for design of small molecules to rescue the misregulated Tec family kinases in these disease states. Formation of a productive kinase-substrate complex is one prerequisite for efficient catalysis. Generally, protein kinases are quite specific in selecting their substrate, but how the specificity is achieved is less well understood. As for Itk, our lab previously identified a remote docking interaction between the kinase domain of Itk and the C-terminal SH2 domain of PLCγ1, contributing to the recognition of Y783 of PLCγ1 as Itk substrate. In chapter 2, I proceeded on to map the docking interaction surface on Itk kinase domain to the G helix region, using a combination of biochemical and biophysical methods. Elucidation of this substrate recognition surface on Itk provides with an alternative site, other than the kinase active site, that small molecules can target to inhibit Itk activity with the promise of achieving higher specificity. The active protein kinases share several structural features in common, including the formation of a salt bridge between a conserved lysine on the β3 strand and a conserved glutamate on the αC helix. In the kinase inactive states, this salt bridge breaks apart. Taking advantage of this structural signature, in chapter 3, I proposed a novel method of coupling reductive methylation chemistry and NMR spectroscopy to examine the activation status of protein kinases. I demonstrated using a well characterized protein kinase Src that the conformational transition between the inactive state and the active state of Src can be followed by the spectral change of the peak resonances corresponding to the beta 3 strand lysine and another lysine located on the αC helix. This method can be easily applied to other protein kinases, such as Tec family kinases, regardless of their required expression systems. It complements other structural techniques by providing lysine-specific information on the conformations protein kinases sample in solution. For instance, it can be used to screen and classify small molecules that drive the conformational equilibrium of a particular protein kinase towards the active or the inactive state. We are also interested in the motifs that regulate the catalytic activity of Tec family kinases. Chapter 4 describes the discovery of a mutation Y617P in the kinase domain of Btk, which not only improves the solubility but also enhances the catalytic activity of Btk kinase domain. The site of the mutation is remote from the active site and therefore how this mutation impacts on the kinase activity is rather intriguing. Coupling biochemical and computational tools, we investigated the known structural features required by an active protein kinase and our data suggested that Y617P activates Btk activity via stabilization of the regulatory spine in the kinase domain. Discovery of the Y617 allosteric site in Btk also raises the possibility of intervening Btk functionality by targeting this site. In summary, the work presented in this dissertation adds to our knowledge of the molecular mechanism Tec family kinases exploit to attain substrate specificity and catalytic activity. It also provides an experimental tool with potential to facilitate the structure-function study on not only Tec family kinases but also other therapeutically important protein kinases

Low-mass Active Galactic Nuclei on the Fundamental Plane of Black Hole Activity

It is widely known that in active galactic nuclei (AGNs) and black hole X-ray binaries (BHXBs), there is a tight correlation among their radio luminosity ($L_R$), X-ray luminosity ($L_X$) and BH mass (\mbh), the so-called `fundamental plane' (FP) of BH activity. Yet the supporting data are very limited in the \mbh regime between stellar mass (i.e., BHXBs) and 10$^{6.5}$\,\msun\ (namely, the lower bound of supermassive BHs in common AGNs). In this work, we developed a new method to measure the 1.4 GHz flux directly from the images of the VLA FIRST survey, and apply it to the type-1 low-mass AGNs in the \cite{2012ApJ...755..167D} sample. As a result, we obtained 19 new low-mass AGNs for FP research with both \mbh\ estimates (\mbh \approx 10^{5.5-6.5}\,\msun), reliable X-ray measurements, and (candidate) radio detections, tripling the number of such candidate sources in the literature.Most (if not all) of the low-mass AGNs follow the standard radio/X-ray correlation and the universal FP relation fitted with the combined dataset of BHXBs and supermassive AGNs by \citet{2009ApJ...706..404G}; the consistency in the radio/X-ray correlation slope among those accretion systems supports the picture that the accretion and ejection (jet) processes are quite similar in all accretion systems of different \mbh. In view of the FP relation, we speculate that the radio loudness $\mathcal{R}$ (i.e., the luminosity ratio of the jet to the accretion disk) of AGNs depends not only on Eddington ratio, but probably also on \mbh.Comment: ApJ accepte

Multispectral and Hyperspectral Image Fusion by MS/HS Fusion Net

Hyperspectral imaging can help better understand the characteristics of different materials, compared with traditional image systems. However, only high-resolution multispectral (HrMS) and low-resolution hyperspectral (LrHS) images can generally be captured at video rate in practice. In this paper, we propose a model-based deep learning approach for merging an HrMS and LrHS images to generate a high-resolution hyperspectral (HrHS) image. In specific, we construct a novel MS/HS fusion model which takes the observation models of low-resolution images and the low-rankness knowledge along the spectral mode of HrHS image into consideration. Then we design an iterative algorithm to solve the model by exploiting the proximal gradient method. And then, by unfolding the designed algorithm, we construct a deep network, called MS/HS Fusion Net, with learning the proximal operators and model parameters by convolutional neural networks. Experimental results on simulated and real data substantiate the superiority of our method both visually and quantitatively as compared with state-of-the-art methods along this line of research.Comment: 10 pages, 7 figure

Stabilizing Queuing Networks with Model Data-Independent Control

Classical queuing network control strategies typically rely on accurate knowledge of model data, i.e., arrival and service rates. However, such data are not always available and may be time-variant. To address this challenge, we consider a class of model data-independent (MDI) control policies that only rely on traffic state observation and network topology. Specifically, we focus on the MDI control policies that can stabilize multi-class Markovian queuing networks under centralized and decentralized policies. Control actions include routing, sequencing, and holding. By expanding the routes and constructing piecewise-linear test functions, we derive an easy-to-use criterion to check the stability of a multi-class network under a given MDI policy. For stabilizable multi-class networks, we show that a centralized, stabilizing MDI policy exists. For stabilizable single-class networks, we further show that a decentralized, stabilizing MDI policy exists. In addition, for both settings, we construct explicit policies that attain maximal throughput and present numerical examples to illustrate the results.Comment: Accepted by IEEE Transactions on Control of Network System