PATTERNED BIOFILM FORMATION TO INVESTIGATE BACTERIA-SURFACE INTERACTIONS

Bacterial adhesion to surfaces and subsequent formation of microcolonies play important roles in biofilm formation, which is a major cause of chronic infections and persistent biofouling. Despite the significance, mechanistic understanding of biofilm formation is still hindered by the structural heterogeneity in biofilms; and effective control of biofilm formation remains challenging. Biofilm formation is a dynamic process that involves numerous changes in bacterial gene and protein expression. These changes are highly sensitive to environmental factors such as surface chemistry, topography, charge, and hydrophobicity. To better control biofilm morphology and specifically investigate the effects of these factors, a platform was developed in this study to obtain patterned biofilm formation using surfaces with well-defined patterns of chemistry and topography. By modifying surfaces with systematically varied square patterns of self-assembled monolayers (SAMs) of functional alkanthiols, the size of cell clusters and inter-cluster distance were well controlled. By following biofilm formation of Escherichia coli on these surfaces, it was found that multicellular connections were formed between adjacent cell clusters when the clusters were within a threshold distance (10 µm); and such connections were influenced by the size of interacting cell clusters. It was also found that the connections were formed by active interactions of cell clusters, rather than nonspecific binding of planktonic cells on the bioinert background. Interestingly, the mutants of luxS and motB exhibited major defects in interaction between cell clusters. The phenotype of the luxS mutant was successfully restored by both complementing the luxS gene on a plasmid and by adding the precursor of autoinducer-2 (AI-2) signal in the culture. These results suggest that AI-2 mediated quorum sensing and motility are involved in the interaction among cell clusters. Based on these findings, a model was proposed to explain the intrinsic heterogeneity in biofilm structures. Consistently, cells attached between interacting clusters were found to be more sensitive to the antibiotic ampicillin. Besides surfaces with patterns of surface chemistry, poly(dimethylsiloxane) (PDMS) surfaces with microtopographic patterns of different shapes, dimensions and inter-pattern distances were used to understand the effects of surface topography on bacteria-surface interactions and biofilm formation. E. coli was found to preferentially attach and form biofilms in the valleys between square shaped plateaus. In addition, there appeared to be a threshold dimension of a plateau to allow bacterial attachment and biofilm formation on top of the plateaus. The threshold was found to be 40 µm × 40 µm for inverted patterns used in this study. Inspired by this finding, we created PDMS surfaces with hexagon shaped patterns and found that the ones with 15 µm side width and 2 µm inter-pattern distance can reduce biofilm formation by 7-fold compared to flat PDMS surfaces. These results were integrated with additional tests to better understand the resistance of biofilm cells to antibiotics. Specifically, the biofilm formation of fluorescently labeled donors and recipients on PDMS surfaces with square shaped microtopographic patterns was followed to investigate the effects of cell density on bacterial conjugation. PDMS surfaces with microtopogrpahic patterns were found to promote both biofilm formation and bacterial conjugation. This result was found to be due to the aggregation of biofilm cells on the side of plateaus, providing hot spots for bacterial conjugation. Bacterial motility was also found to play an important role in biofilm formation and bacterial conjugation. Collectively, these results are helpful for understanding the mechanism of biofilm formation and associated drug resistance, as well as the design of nonfouling surfaces

External Direct Sum Invariant Subspace and Decomposition of Coupled Differential-Difference Equations

This article discusses the invariant subspaces that are restricted to be external direct sums. Some existence conditions are presented that facilitate finding such invariant subspaces. This problem is related to the decomposition of coupled differential-difference equations, leading to the possibility of lowering the dimensions of coupled differential-difference equations. As has been well documented, lowering the dimension of coupled differential-difference equations can drastically reduce the computational time needed in stability analysis when a complete quadratic Lyapunov-Krasovskii functional is used. Most known ad hoc methods of reducing the order are special cases of this formulation

Zeroth-Order Negative Curvature Finding: Escaping Saddle Points without Gradients

We consider escaping saddle points of nonconvex problems where only the function evaluations can be accessed. Although a variety of works have been proposed, the majority of them require either second or first-order information, and only a few of them have exploited zeroth-order methods, particularly the technique of negative curvature finding with zeroth-order methods which has been proven to be the most efficient method for escaping saddle points. To fill this gap, in this paper, we propose two zeroth-order negative curvature finding frameworks that can replace Hessian-vector product computations without increasing the iteration complexity. We apply the proposed frameworks to ZO-GD, ZO-SGD, ZO-SCSG, ZO-SPIDER and prove that these ZO algorithms can converge to $(\epsilon,\delta)$-approximate second-order stationary points with less query complexity compared with prior zeroth-order works for finding local minima