Browsing by Subject "Autoregulation"

One of the key mechanisms that mediate renal autoregulation is the tubuloglomerular feedback (TGF) system, which is a negative feedback loop in the kidney that balances glomerular filtration with tubular reabsorptive capacity. In this dissertation, we develop several mathematical models of the TGF system to study TGF-mediated model dynamics.

First, we develop a mathematical model of compliant thick ascending limb (TAL) of a short loop of Henle in the rat kidney, called TAL model, to investigate the effects of spatial inhomogeneous properties in TAL on TGF-mediated dynamics. We derive a characteristic equation that corresponds to a linearized TAL model, and conduct a bifurcation analysis by finding roots of that equation. Results of the bifurcation analysis are also validated via numerical simulations of the full model equations.

We then extend the TAL model to explicitly represent an entire short-looped nephron including the descending segments and having compliant tubular walls, developing a short-looped nephron model. A bifurcation analysis for the TGF loop-model equations is similarly performed by computing parameter boundaries, as functions of TGF gain and delay, that separate differing model behaviors. We also use the loop model to better understand the effects of transient as well as sustained flow perturbations on the TGF system and on distal NaCl delivery.

To understand the impacts of internephron coupling on TGF dynamics, we further develop a mathematical model of a coupled-TGF system that includes any finite number of nephrons coupled through their TGF systems, coupled-nephron model. Each model nephron represents a short loop of Henle having compliant tubular walls, based on the short-looped nephron model, and is assumed to interact with nearby nephrons through electrotonic signaling along the pre-glomerular vasculature. The characteristic equation is obtained via linearization of the loop-model equations as in TAL model. To better understand the impacts of parameter variability on TGF-mediated dynamics, we consider special cases where the relation between TGF delays and gains among two coupled nephrons is specifically chosen. By solving the characteristic equation, we determine parameter regions that correspond to qualitatively differing model behaviors.

TGF delays play an essential role in determining qualitatively and quantitatively different TGF-mediated dynamic behaviors. In particular, when noise arising from external sources of system is introduced, the dynamics may become significantly rich and complex, revealing a variety of model behaviors owing to the interaction with delays. In our next study, we consider the effect of the interactions between time delays and noise, by developing a stochastic model. We begin with a simple time-delayed transport equation to represent the dynamics of chloride concentration in the rigid-TAL fluid. Guided by a proof for the existence and uniqueness of the steady-state solution to the deterministic Dirichlet problem, obtained via bifurcation analysis and the contraction mapping theorem, an analogous proof for stochastic system with random boundary conditions is presented. Finally we conduct multiscale analysis to study the effect of the noise, specifically when the system is in subcritical region, but close enough to the critical delay. To analyze the solution behaviors in long time scales, reduced equations for the amplitude of solutions are derived using multiscale method.

Abstract

Hfq is a pleiotropic posttranscriptional regulator and RNA chaperone that facilitates annealing of trans-encoded sRNA/mRNA pairs. It regulates many different cellular pathways including environmental stress responses, quorum sensing, virulence and maintenance of membrane integrity. Hfq is a member of the Sm/LSm family and forms a homohexamer that has two faces, termed proximal and distal. Hfq preferentially binds A/U rich regions that are near stem loop structures. Crystal structures have shown that poly-A sequences tend to bind the distal face while poly-U sequences bind the proximal face. Currently crystal structures reveal the binding mechanisms for short RNA sequences however; physiologically relevant RNA sequences are typically longer and more structured. To study how these more complex RNA sequences interact with Hfq, a tryptophan fluorescence quenching (TFQ) assay has been developed. Here it is presented that TFQ can correctly identify the binding face for two control sequences, A15 and U6, using the E. coli, S. aureus and L. monocytogenes Hfq homologues. Using fluorescence anisotropy and crystallography it is observed that Trp mutants necessary for TFQ may affect binding to some degree but do not affect the overall structure or RNA binding function of Hfq. TFQ is then used to examine the distal face binding motifs for both Gram-negative (E. coli) and Gram-positive (S. aureus/L. monocytogenes) Hfq, (A-R-N)n and (R-L)n respectively. Using sequences that either fulfilled just (A-R-N)n or both (A-R-N)n and (A-A-N)n motifs it is shown that the distal face motif for Gram-negative Hfq is the more specific (A-A-N)n motif. Using sequences that either fulfilled just (R-L)n or both (R-L)n and (A-L)n motifs it is shown that the Gram-positive distal face motif can be redefined to the (A-L)n motif. Finally TFQ is used to explore autoregulation of E. coli hfq. Two identified binding sites located in the 5'UTR of hfq mRNA, site A and site B, were used for TFQ, along with a longer RNA sequence that contains both sites and their native linker, 5' UTR. TFQ illustrates that the individual sites and the 5' UTR are capable of binding both faces. Each site appears to prefer binding to one face over the other, suggesting a model for hfq 5' UTR mRNA binding to Hfq where either one or two hfq mRNA bind a single Hfq hexamer. In conclusion, TFQ is a straightforward method for analyzing how RNA sequences interact with Hfq that can be utilized to study how longer, physiologically relevant RNA sequences bind Hfq.