A biophysical limit for quorum sensing in biofilms

Bacteria grow on surfaces in complex immobile communities known as biofilms, which are composed of cells embedded in an extracellular matrix. Within biofilms, bacteria often interact with members of their own species and cooperate or compete with members of other species via quorum sensing (QS). QS is a process by which microbes produce, secrete, and subsequently detect small molecules called autoinducers (AIs) to assess their local population density. We explore the competitive advantage of QS through agent-based simulations of a spatial model in which colony expansion via extracellular matrix production provides greater access to a limiting diffusible nutrient. We note a significant difference in results based on whether AI production is constitutive or limited by nutrient availability: If AI production is constitutive, simple QS-based matrix-production strategies can be far superior to any fixed strategy. However, if AI production is limited by nutrient availability, QS-based strategies fail to provide a significant advantage over fixed strategies. To explain this dichotomy, we derive a biophysical limit for the dynamic range of nutrient-limited AI concentrations in biofilms. This range is remarkably small (less than 10-fold) for the realistic case in which a growth-limiting diffusible nutrient is taken up within a narrow active growth layer. This biophysical limit implies that for QS to be most effective in biofilms AI production should be a protected function not directly tied to metabolism.

Bacteria are capable of communicating with their neighbors through a process known as quorum sensing (QS). QS depends on the secretion and detection of small, diffusible molecules known as autoinducers (AIs), whose concentration increases with increasing cell density (1, 2). QS allows bacteria to control processes that are unproductive when undertaken by an individual but effective when undertaken by all members of the group and thus leads to a competitive advantage for bacterial communities that employ QS (1–6).QS is known to promote and regulate bacterial biofilms: immobile communities of cells densely packed in an extracellular matrix (7). QS has been demonstrated to be critical to proper biofilm formation (8–13). For example, Pseudomonas aeruginosa mutants that do not synthesize AIs terminate biofilm formation at an early stage (14). Given that the interior of biofilms is known to be nutrient-deficient (15), it is an open question to what extent these interior cells participate in AI production. Indeed, in many cases AI production relies on central metabolic compounds. For example, a substrate for synthesis of the ubiquitous acyl-HSL AIs is produced by one-carbon metabolism, which is highly dependent on nutrient availability (16–18). Thus, we sought to understand whether QS can be advantageous to cells in a biofilm if AI production depends on access to nutrients.One context in which QS has been found to afford a competitive advantage in biofilms is via regulation of production of the extracellular matrix, which is composed of biopolymers, including polysaccharides, proteins, nucleic acids, and lipids. Advantages provided by the matrix include adhering cells to each other and to a substrate, creating a protective barrier against chemicals and predators, and facilitating horizontal gene transfer.In simple models of biofilms that incorporate realistic reaction-diffusion effects, Xavier and Foster (19) found that matrix production allows cells to push descendants outward from a surface into a more O2-rich environment. Consequently, they found that matrix production provides a strong competitive advantage to cell lineages by suffocating neighboring nonproducing cells (19). Building upon this work, Nadell et al. (20) showed that strategies that employ QS to deactivate matrix production in mature biofilms can yield a further advantage by redirecting resources into reproduction, and this scenario has been replicated and further developed (21–23). Notably, all these models assume constitutive AI production with no dependence on nutrient availability (20–23). We were therefore inspired to ask whether QS still provide an advantage in regulating matrix production if AI production is limited by nutrient availability.To this end, we simulated competitions among biofilm-forming cells, comparing matrix-production strategies that employ QS with strategies that do not. While QS cells that constitutively produce AI could outcompete all fixed strategies, we found, surprisingly, that QS cells which produce AI in a nutrient-dependent manner have essentially no advantage over non-QS cells. We trace this result to a novel biophysical limit on the dynamic range (DR) of AI concentrations if AI production is nutrient-limited. This biophysical limit applies to all bacterial systems that employ QS. These results suggest that for QS to be effective in biofilms and other conditions where nutrients are limiting, cells must privilege AI production despite the metabolic cost. From this perspective, autoinduction itself, i.e., positive feedback on AI production from AI sensing, can be viewed as one way that cells decouple AI production from metabolism.     

Autophagy and its neuroprotection in neurodegenerative diseases

It has been suggested that protein misfolding and aggregation contribute significantly to the development of neurodegenerative diseases.Misfolded and aggregated proteins are cleared by ubiquitin proteasomal system (UPS) and by both Micro and Macro autophagy lysosomal pathway (ALP).Autophagosomal dysfunction has been implicated in an increasing number of diseases including neurodegenerative diseases.Autophagy is a cellular self-eating process that plays an important role in neuroprotection as well as neuronal injury and death.While a decrease in autophagic activity interferes with protein degradation and possibly organelle turnover,increased autophagy has been shown to facilitate the clearance of aggregation-prone proteins and promote neuronal survival in a number of disease models.On the other hand,too much autophagic activity can be detrimental,suggesting the regulation of autophagy is critical in dictating cell fate.In this review paper,we will discuss various aspects of ALP biology and its dual functions in neuronal cell death and survival.We will also evaluate the role of autophagy in neurodegenerative diseases including Alzheimer’s disease,Parkinson’s disease,Huntington’s disease,amyotrophic lateral sclerosis.Finally,we will explore the therapeutic potential of autophagy modifiers in several neurodegenerative diseases.     

A traveling-wave solution for bacterial chemotaxis with growth

Bacterial cells navigate their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. Analytical understanding of such complex spatiotemporal dynamic processes is rare. Our analytical results and the methods employed to attain them provide a mathematical framework for investigations of the roles of taxis in diverse ecological contexts across broad parameter regimes.

As a fundamental part of their life cycle, bacteria spread by dispersing into and colonizing new habitats. Many species of bacteria navigate in these new habitats by sensing gradients of certain chemicals and biasing their flagellum-based swimming to move themselves along these gradients (1, 2). This process, known as chemotaxis, is among the most extensively investigated topics in molecular biology (1, 3–7) and was observed in diverse microbial habitats such as the gut (8); the soil (9); leaves (10, 11); and marine environments such as the phycosphere, sinking marine particles, and coral reefs (2, 12–14). Further, chemotaxis is employed by many eukaryotic cells such as the free-living Dictyostelium (15) and is an important element of many tissue-forming processes involved in embryogenesis (16), neuronal patterning (17), wound healing (18), and tumor metastasis (19).Beyond promoting the movements by individual cells, chemotaxis also drives the collective movement of cells leading to emergent patterns and behaviors at the population level (20, 21). Such collective dynamics have been best studied with bacteria in culture plates and microfluidic devices. For example, when Escherichia coli cells are inoculated at the center of a soft agar plate replete with nutrients, consumption of preferred chemicals (referred to as attractants) results in collective cell movement up self-generated attractant gradients (22), leading to the emergence of striking migrating bands that propagate radially outward from the inoculation site (23–25). These migrating bands typically comprise one or two peaks in population density, which stand in contrast to the predictions of canonical models of front propagation and population expansion (26–28); they also expand at much faster speeds than predicted by canonical models. These population-level changes can strongly shape fitness and ecological interactions as recent laboratory studies have shown (29–32).The first attempt to understand these migrating bands mathematically was made by Keller and Segel, who recovered a traveling-wave solution using a pair of reaction–diffusion–convection equations to describe the density of bacterial populations and the concentration of the attractant they consume (33). While being highly influential, the Keller–Segel (KS) model neglected cell growth, a substantial factor in the expansion process. It further required unrealistic assumptions on attractant sensing without which the migrating bands lose stability (34). Subsequent modeling efforts including cell growth managed to recover the stability of the bands, but their predictions did not match major experimental observations such as the sharply peaked density profiles and their rapid migration speeds (31, 35–38).Recent work by Cremer et al. (39) demonstrated that the major features of the migrating bands for E. coli in soft agar can be accurately captured using a model in which bacterial growth is independent of the attractant. Numerical solutions to their growth-expansion (GE) model quantitatively described not only the boosted speed of the migrating band but also the signature spatial profile of the bands and their dependence on molecular parameters (39). Their results established the role of attractants as an environmental cue exploited by bacteria independent of possible nutritional values to promote rapid expansion.The success of the GE model in describing E. coli in soft agar raises the possibility that the phenotype of rapid expansion and distinct density bands might also occur for chemotactic systems in the wild, in situations where growth, diffusion, and chemotaxis dominate. However, from the numerical work of Cremer et al. (39), it is not clear what aspects of their results are generalizable given that both bacterial and environmental characteristics can be vastly different in the wild. For example, bacteria living near sulphidic sediments move more than 30 times faster than E. coli (39, 40), while bacterial motility is significantly reduced by high viscosity in the gut (41, 42). Addressing the generalizability of the GE model requires a detailed mathematical analysis of the interplay of 1) growth, 2) diffusion, and 3) chemotaxis, preferably with analytical solutions. While growth and diffusion have been studied together in the canonical models of front propagation (26–28), as have diffusion and chemotaxis in the KS model (33, 36, 43–45), a sufficient understanding of the interplay of all three is still lacking.Toward obtaining such an understanding, we describe here a detailed analytical study of the GE model. Through a heuristic analysis, we derive analytic relations that describe the dependence of the expansion speed and density profile on important molecular, cellular, and environmental parameters, including the rate of cell growth, the diffusivity and availability of the attractants, the motility and sensitivity of the bacteria, carrying capacity, and the limit of attractant sensing. Our analysis reveals the key condition for the population to attain rapid expansion speed and suggests a very broad parameter regime for which rapid expansion can be expected.