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HYPOTHESIS AND THEORY article
Sec. Systems Microbiology
Why do bacteria regulate public goods by quorum sensing?—How the shapes of cost and benefit functions determine the form of optimal regulation
- 1Computational Biology, Xavier lab, Memorial Sloan Kettering Cancer Center, New York, NY, USA
- 2National Centre for Biological Sciences, Simons Centre for the Study of Living Machines, Bangalore, India
- 3Department of Biology, University of Washington, Seattle, WA, USA
Many bacteria secrete compounds which act as public goods. Such compounds are often under quorum sensing (QS) regulation, yet it is not understood exactly when bacteria may gain from having a public good under QS regulation. Here, we show that the optimal public good production rate per cell as a function of population size (the optimal production curve, OPC) depends crucially on the cost and benefit functions of the public good and that the OPC will fall into one of two categories: Either it is continuous or it jumps from zero discontinuously at a critical population size. If, e.g., the public good has accelerating returns and linear cost, then the OPC is discontinuous and the best strategy thus to ramp up production sharply at a precise population size. By using the example of public goods with accelerating and diminishing returns (and linear cost) we are able to determine how the two different categories of OPSs can best be matched by production regulated through a QS signal feeding back on its own production. We find that the optimal QS parameters are different for the two categories and specifically that public goods which provide accelerating returns, call for stronger positive signal feedback.
Bacterial cells live complex lives, constantly adjusting to the fluctuating presence or absence of nutrients, toxins, competitors and other environmental factors. They do this by regulating the production of different molecules that can perform the functions required to give them a fitness advantage in the current environment. Some of these molecules, like membrane bound nutrient receptors, are “private goods” which provide a benefit only to the individual cell that produced them. Others are molecules that are secreted by the cells and perform their function outside. Once secreted these molecules can diffuse away and potentially benefit other cells making them “public goods.” Microbes which produce extracellular molecules that can be thought of as public goods are ubiquitous. Examples of such products are: extracellular enzymes (Pirhonen et al., 1993), exopolysaccharides (used in biofilms) (Weiner et al., 1995; Vu et al., 2009), surfactants (aiding motility) (Kearns, 2010; Xavier et al., 2011), antimicrobial (for fighting other microbes) (Mazzola et al., 1992; Moons et al., 2005, 2006; An et al., 2006), virulence factors (for fighting a host organism's immune system, or for exploitation of host resources) (Zhu et al., 2002; Sandoz et al., 2007; Köhler et al., 2009), siderophores (for scavenging iron from the environment) (Neilands, 1984; Harrison and Buckling, 2009; Kümmerli and Brown, 2010). Although such cooperation in bacteria has received a lot of attention (Hense and Schuster, 2015), exactly how benefit and cost depends on the extracellular concentration of public good and the production rate of common goods (hereafter referred to as the benefit/cost function of the public good) has in general not been studied in great detail experimentally. Results from a recent theoretical paper (Cornforth et al., 2012), however shows that non-linearity in the benefit and cost curves is expected to radically impact the evolutionary dynamics of a cooperating population and that the shape of the benefit function will influence whether a population may benefit from having a public good under quorum sensing1 (QS) regulation. Bacterial public goods are in fact often under QS regulation. For example in P. aeruginosa secreted compounds are significantly overrepresented in the list of quorum sensing regulated gene products (Schuster and Greenberg, 2006). It is often assumed that public goods provide more benefit at higher population densities (e.g., Waters and Bassler, 2005; Diggle et al., 2007) and this has also recently been shown to be true experimentally for a specific public good produced by P. aeruginosa (Darch et al., 2012). There is however still a lack of general analytical arguments concerning exactly when and why a bacterial population may benefit from having a public good under QS regulation.
Here we use simple mathematical models, to find out how the shape of the cost and benefit function of a public good determines the optimal way to regulate the production of the public good. To illustrate our general point we have determined how the optimal public good production rate depends on the population size, for public goods with either accelerating or diminishing returns when cost is linear. Further we have determined how well a QS system can generate production curves that mimic the analytically determined optimal curves, and we discuss whether there might be evolutionary trade-offs associated with the optimal QS parameters for regulating certain public goods.
2. Models and Results
2.1. Optimal Production of Public Goods in a Well-mixed Population
We consider a well-mixed2 population of isogenic cells that produce a public good, E. Let Δg denote the change in growth rate of such a population due to the act of producing the public good. Δg, which could be negative or positive, can be decomposed into the benefits accrued from having the public good present and the costs of producing it. We make the following assumptions about the cost and benefit functions:
(1) The cost is an increasing function of the rate of production of the public good.
(2) The cost is zero when no public good is being produced.
(3) The benefit is an increasing function of the concentration of the public good.
(4) The benefit does not increase indefinitely as the concentration of the public good increases; it saturates at some finite value.
(5) The benefit is zero when there is no public good present.
For now, we will assume that the cost is a linear function3 of the rate of production, σE, of the public good, and the benefit a sigmoidal function of the concentration, E, of public good:
KE is the concentration of of public good where the benefit is half of the maximum value, β1 + β2 is the maximum benefit possible and κ is the proportionality constant which quantifies how common good production translate to growth rate reduction. We will for now focus in particular on the shape of the first two terms of Equation (1), i.e., the benefit function of the public good, (see Figures 1A,B). The exponent h allows us to modulate the shape of the benefit function. When h ≤ 1, the benefit function is always concave, i.e., its slope is highest at E = 0 and steadily decreases as E increases. In other words, increasing public goods results in diminishing returns. In contrast, when h > 1, increasing public goods initially results in accelerating returns; i.e., the benefit function is initially convex. In Figure 2 we propose a concrete example of a class of public goods that can have differently shaped benefit functions depending on the precise molecular mechanism by which the public good works. Proteases that work by degrading proteins in the environment into smaller metabolizable pieces can work in two different ways: Exoproteases break the polymer peptide bonds starting from the end of the polymer and endoproteases target specific peptide bonds effectively breaking the polymers at random. These two modes of action can cause the benefit function to be either initially convex (endo) or concave (exo) (providing accelerating or diminishing returns, respectively. See supplement for the full length derivation which leads to this conclusion).
Figure 1. Concave/convex benefit function. (A) The benefit is here a sigmoidal function: , plotted for two different values of the exponent h = [1, 2], with x = E. The parameter h can be manipulated so that benefit initially decelerates (h = 1, concave, light green) or accelerates (h > 1, convex, dark green) with increasing concentration of public good. The remaining parameters are β1 = 0.7, β2 = 0.3, KE = 25. (B) When the timescale of public good production and degradation are much faster than the timescale for growth of cells, public good concentration is proportional with production rate and population size, E ∝ σEN. Dark green, the convex benefit curve BN(σE) = b(NσE) is shown as a function of the common good production rate per cell σE for N = [1, 10, 25, 49, 100, 200]. Red, linear cost curve c(σE) = κσE, κ = 1.
Figure 2. Example of public goods with differently shaped benefit functions. Proteases which works extracellularly by degrading polymers that are too large to be transported over the cell membrane can either break the peptide bonds of the polymer starting from the end of the polymer (exoprotease) or target a range of specific types of peptide bond within the chain, effectively breaking bonds at random (endoprotease). In this scenario benefit is proportional to the probability of yielding “edible” pieces of polymer. (A1,A2) Benefit increases approximately linearly with exoprotease concentration resulting in an initially concave benefit function. (B1,B2) The probability of breaking the polymer at a site producing an piece small enough to transport over the cell membrane is low when enzyme concentration is low, but accelerates as endoprotease concentration increases, resulting in a initially convex benefit function.
We now wish to determine how the convexity/concavity of the benefit function influences the optimal production strategy for a public good when the cost function is linear. The rate of change of the concentration of a public good E in a well-mixed system with N cells wil be given by:
where σE is the public good production rate per cell and γE is the degradation rate of the public good. For the sake of simplicity we will for now make the assumption that the timescales of public good production and degradation are much faster than the timescale for growth of cells. This allows us to assume that the public good concentration is always at steady state value E* for a given population size:
and thus we can express E* as a function of σE When this assumption holds we can, by replacing E in Equation (1) with E* from Equation (3) write the effect of the public good on the growth rate Δg(σE, N) in terms of population size N and production rate per cell σE only. In this situation, it is evident that cells which produce public good at a rate, that maximizes Equation (1), for each value of N, will grow fastest. In Figure 3 we have plotted this optimal rate as a function of N. We see that the function has very different properties when the benefit function is always concave (e.g., h = 1), compared to when it is initially convex (h > 1), even though the curves in Figure 1 appear quite similar at first glance. When h = 1, rises smoothly from zero at Ncrit to a maximum and then decreases smoothly to zero as N → ∞. In contrast, when h > 1, i.e., with accelerating returns, for low values of N, jumps discontinuously to a non-zero value at Ncrit. After the jump the production rate may rise further to a maximum before decreasing to zero, or may simply decrease to zero, as N → ∞, depending on the values of other parameters such as h, β1, β2, c. For both a concave and a convex benefit curve (when cost is linear) the optimal behavior can be only to turn on common good production when a critical population size, Ncrit > 1 has been reached4. The take home message is that the difference between the concave and the convex benefit curve cases is that in the convex case the optimal production curve will be discontinuous at the critical population size Ncrit5.
Figure 3. Concave/convex benefit curves result in continuous/discontinuous optimal production curves respectively. (A,B) Green curves show optimal production rate of public good, as a function of population size, N for the concave/convex benefit functions shown in figure 1. The optimal value, , corresponds to the σE which maximizes Δg for N. The magnitude of Δg in the (N, σE)-space is shown by the colorbar. (A) In the case h = 1 the optimal production function is continuous and can be put in closed form: , where β = β1 + β2. The critical population size above which public good production is nonzero, when h = 1 is: . (B) When the benefit curve is convex, h = 2, the optimal production function is discontinuous. (C,D): Light/dark green curves show the effect on growth rate Δg for a population producing common good at exactly the optimal rate when the benefit curve is concave/convex respectively. Black dashed curves show the effect on growth rate Δg for a population producing common good at a constant rate , equal to the average of the non-zero part of the optimal curve, (shown as black dashed lines in (A,B). (E) The cumulative fitness, , where , (def. in Equation fitnessDef) of different constant production strategies for a common good with concave (light green) and convex (dark green) benefit functions respectively. Note that in the case of the “concave common good” there is a range of different constant production rates which allows the population to perform better than a nonproducing population w > 0, however for the “convex common good” any constant production strategy will leed to worse fitness than that of a nonproducing population, w < 0 for all . (In this figure σE is given in units of κ∕γE, which was set to one).
2.2. Regulating public goods using a quorum sensing system
In the previous paragraph we saw that the convexity/concavity of the public good benefit function is important for determining the shape of the optimal public good production curve, i.e., the way the optimal production rate depends on population size. Although the curves are very different it is clear that for both h = 1 and h > 1 the optimal production rate varies with the population size, (see Figures 3A,B) and that in both cases it thus looks like cells would benefit from having production linked to a mechanism which senses the cell density; a property which QS systems possess. We now wish to determine just how closely a QS regulation mechanism realistically could come to generating production curves matching the optimal curves in Figures 3A,B.
2.2.1. A Simple Well-mixed Model of QS Regulated Public Good Production
We formulate a simple ODE model of a well mixed population producing signal and public good with a positive feedback of signal on its own production:
Here S is the concentration of quorum sensing signal molecule6, E, the concentration of public good and N is the number of cells. The equations are non-dimensionalized by measuring all rates in units of the basal rate of signal production (i.e., the rate of signal production when signal concentration is very low) and by measuring time in units of the mean lifetime of a signal molecule 1∕γS. The rate of signal production when the population is fully induced is and7 is the maximum rate of public good production per cell. The mean lifetime of a public good molecule is 1∕γE and KS is the signal concentration where both signal production and public good production is at half of the maximum rate. The exponent α captures the strength of the positive feedback of the signal on its own production; for example this could be the cooperativity of the DNA binding by the transcription factor which activates production of signal synthase. In this model, signal receptor molecules are not modeled explicitly for the sake of simplicity. The parameter, α, does thus strictly not need to be interpreted just as the cooperativity of the transcription factor DNA binding but could also be influenced by the effect of signal positively feeding back on production of receptor molecules, (as discussed in Haseltine and Arnold, 2008; Rai et al., 2012). Assuming that both signal and public good have the same half-saturation constant KS and feedback exponent α is probably a crude assumption which we will nonetheless make for the sake of simplicity.
Once again we make the assumption that production and decay of quorum sensing molecules and public good molecules happen at a much faster timescale than growth of cells. This means that we can assume that for each population size N, signal concentration, S, will reach steady state, S*. In Figure 4 the steady state concentration of QS signal S* is plotted as function of the population size N for different values of the feedback exponent α. We see that when α goes above a certain critical value αC (see supplement for an analytical expression for αC) the system will have a bistable region with two stable equilibria, and (and one unstable, in between). Such bistability has indeed been observed in Vibrio fischeri: In Williams et al. (2008) they show that the regulation of expression of luxI during the Vibrio fischeri QS response exhibits hysteretic dependency on QS signal molecule (auto inducer) concentration [AI], due to AI-dependent autoregulation of luxR expression. They find that the “memory” of QS induction is maintained in the population due to a high level of LuxR, and thus a relatively high level of LuxR–AI complexes, even when [AI] is gradually decreased.
Figure 4. Increasing the QS signal feedback exponent α causes hysteretic response to population changes. Steady state QS signal concentration, S* as function of the population size N, plotted for four different values of the QS feedback exponent α = [1.0, 1.2, 1.5, 2.0]. When the system will be bistable for a certain range of population sizes. (, concentration of S is here given in units of . is the basal production rate and γS is the degradation/depletion rate of the of signal, which is here set to 1.)
The public good production rate per cell, σE, for a given population size N will be given by the first right hand side term in Equation (E) and thus depend on the steady state concentration of signal, S*(N):
When the system is in the bistable regime this means that there will be two different production curves; one which involves the lower stable equilibria () that the system will follow when going from low to high cell numbers and another curve which involves the the higher stable equilibria () which the system will follow when going from high cell numbers to low. Figures 5A–C (left panels) show examples of such QS production curves (with and without bistability) plotted together with the corresponding optimal curves.
Figure 5. Quorum sensing parameters optimized for different ecological scenarios and different types of public goods. (A–C) Left side panels: Green curves shows optimal production rate, , as a function of population size N. Black full line and dashed line show the production rate as a function of population size, N, when production is regulated by (A): a QS system with parameters such that cumulative fitness, w is optimized for a public good with the concave benefit function shown in Figure 1 (α = 1.1, KS = 2200, ), (B): a system with QS parameters for a public good with a convex benefit function maximizing cumulative fitness w in only “turn on” scenarios, (α = 2, KS = 980, and ), and (C): a QS system with parameters that maximize cumulative fitness w for a public good with a concave benefit function in both “turn on” and “turn off” scenarios, (α = 1.4, KS = 2600, and ). (A–C) Right side panels: Green lines show Δgopt, the increase in growth rate achieved, as a function of N when producing public good using the optimal production curve . Full black line shows Δg as a function of N for the QS regulated production curve marked “Turn on” in the plot to the right. Dashed black line shows Δg as a function of N for the QS regulated production curve marked “Turn off” in the plot to the left. The colored area underneath the Δg curves in the range N = [1, Nmax], (Nmax = 70) is proportional to the cumulative fitness, w (defined in Equations 7 and 8).
2.3. Quantifying the Fitness of a Public Good Regulation Strategy
Different choices of QS parameters α, KS and result in different public good production curves, σE(N) and these curves, may resemble the optimal curves from Figures 3A,B more or less. In order to determine which QS parameters optimize the regulation of a public good with a specific benefit function we need a way to assess the fitness of a population of cells which utilize a specific “production curve” or in other words a specific “common good regulation strategy.” Equation (1) expresses how the impact of production on growth rate, Δg, depend on the production rate, σE. For a given QS regulated production curve σE(N), Equation (1) gives a corresponding function Δg(N, h) ≤ Δgopt(N, h) which shows how growth is affected by public good production as population size, N, varies. In the right panels of Figures 5A–C, the corresponding Δg(N, h) curve of the production curve σE(N) from the left panel is plotted.
The cumulative fitness/performance of a given production curve/production strategy, σE(N), can be quantified by the following expression:
This fitness measure quantifies how growth is affected by public good production over a range of different population sizes (the range set by the limits8 of the integral, [1, Nmax]). The cumulative fitness, w, is normalized with respect to the performance of a population which follows the optimal production strategy. This means that fitness will be one (w = 1) if the QS production curve perfectly mimics the optimal curve and fitness will be zero (w = 0) for a population which does not produce public good at all, (negative fitness corresponds to having a lower fitness than a non-producing population).
2.3.1. “Turn on” and “Turn off” of Public Good Production in the Wild
It has been observed in several experimental studies (e.g., Sandoz et al., 2007) that, often non-producing cheater mutants will arise over time in populations which secrete a public good. Invasion of a faster growing cheater mutant could fragment the producer population and thus lead to an effective dilution of the wild type population. It seems that in this type of situation, having a mechanism which would down regulate production of public good in response to the decreasing producer cell density would be crucial for the wild type cells' ability to avoid population collapse (this scenario is also discussed in Melke et al., 2010). It thus seems there could exists ecological settings where both “turn on” and “turn off” scenarios are important for the fitness of the QS strategy.
Very little is known about actual ecological situations in the wild where bacteria use quorum sensing to regulate gene expression. In most of the quorum sensing literature the emphasis has been on the process of turning on QS regulated genes when population size increases, not off when it decreases. This bias might stem from the fact that “turn off” scenarios are probably not of great importance in the organism where QS was first discovered, Vibrio fischeri. This bacterium lives in symbiosis with the bobtailed squid (McFall-Ngai and Ruby, 2000; Visick et al., 2000; McFall-Ngai et al., 2012), an ecological setting where the bacteria periodically go through stages of population increase and decrease. The bacteria slowly grow to high density inside the light organ of the squid, reach the point where they turn on light production at nightfall only to be quickly diluted and turn off light production when the squid spurts out the majority of the bacteria by morning. In this situation, the dilution of signal and decrease in the population density happen so fast when the squid vents its light organ, that there is probably no need to have an accurate mechanism for down regulating light production as the population density decreases since very little time is spent at intermediate densities.
2.3.2. Quantifying Fitness in both “Turn On” and “Turn Off” Scenarios
As we saw earlier, there exist parameters for which the QS signaling system is bistable and thus where a set of QS parameters, (), correspond to not one production curve but to two: one “turn on” curve which the population will follow when going from low to high numbers and one “turn off” curve which it will follow when going from high to low numbers. For a bacteria population that encounters both situations where they need to regulate public good expression as the population is increasing and when it is decreasing and which has such a bistable set of parameters, we thus need to assess the performance in both situations and include both in the fitness measure. One way of doing this is simply by using a weighted average of the cumulative fitness, w, of the two individual production curves:
[where the weights add up to one (θon + θoff = 1)]. Depending on how often a population encounters “turn on” and “turn off” situations and on the relative importance of these situations the weight would be distributed differently. Since we do not have any information about what exactly these weights are for any actual ecological setting we will here, for the sake of argument, just compare the two extreme cases of (θon = 1, θoff = 0) where strictly “turn on” scenarios are important for fitness (possibly an ecological setting like the case of Vibrio fischeri living in the bobtailed squid where population dilution happens very fast) and the case where “turn on” scenarios and “turn off” scenarios are equally important for fitness (θon = 0.5, θoff = 0.5), (possibly an ecological setting where the population relatively often faces the risk of slow dilution due to the appearance of a cheater mutant).
2.3.3. Fitness as a Function of the QS Feedback Exponent, α
For a public good with a certain benefit/cost function pair there will be a specific set of QS parameters, (α, KS, ), which maximizes the fitness, w (def. in Equations 7 and 8). This is, roughly speaking, the set of parameters that within the range [1, Nmax] manage to best mimic the optimal production curve (e.g., Figure 5A), or in the case where there is bistability and both “turn on” and “turn off” curves are considered to be equally important, it is the set of parameters which allows both curves to best mimic the optimal curve at the same time, (e.g., Figure 5C).
Often a single QS system will regulate the expression of many different secreted products that can be very diverse in nature and potentially have differently shaped benefit and cost functions. Since the parameter KS quantifies the binding strength and the overall promoter strength of the promoter regulating a specific gene product, it seems likely that these two parameters in most cases can be fine tuned by evolution to suit the regulation needs of individual QS products. The parameter α, on the other hand, characterizes the way the QS signal molecule feeds back on its own production and will thus in most cases be a parameter which has to be the same for all the QS regulated products, with the two exceptions that there can be more than one QS system in the cell and that it is possible to have different promoter sequences for signal synthase expression and public good production. For example LasR can bind either cooperatively or noncooperatively depending on the promoter sequence, Schuster et al. (2004). In Figures 5A–C left panels, the black lines show the QS regulated production curves where the choice of parameters , KS and α maximize cumulative fitness, w, in three different situations. Interestingly, we see in Figure 5 that the feedback exponent α which optimizes fitness for a population regulating the “concave good” (h = 1) and the “convex good” (h = 2) are quite different. For h = 1 the optimal fitness of a QS production regulation curve is generally found at lower values of α, where there is no bistability, (in Figure 5A the optimal α value is around α ≈ 1). For h = 2 on the other hand, when fitness is optimized for “turn on” only, fitness increases monotonically with increasing α, approaching the maximal value of one, (note however that beyond α = 2 there is virtually no extra advantage to be had from increasing α further, so in Figure 5B the QS curve plotted simply has α = 2). At α values higher than αc ≈ 1.2 we are in the bistable regime where the production curves will be different when going from “low to high” and “high to low” cell numbers. When h = 2 and fitness is optimized for both “turn on” and “turn off” the optimal feedback exponent is at an intermediate value α ≈ 3∕2. The reason for this is that at low values of α the QS production curve do not ramp up production fast enough while at higher values of α, the system becomes highly bistable and “turn on” and “turn off” curves thus very different which means they cannot both resemble the optimal curve.
2.3.4. Regulating Expression of both Convex and Concave Public Goods with one QS System
The α-values that optimize fitness for public goods with convex and concave benefit functions (when cost is linear) are different. It is thus interesting to think about what a bacteria population which needs to regulate several different types of public good with the same QS system would do. In general it is the case that a broader range of α-values will result in QS production curves with positive fitness for a concave good than for a convex, just as we saw in Figure 3E that a range of different constant production strategies resulted in w > 0 for the concave good, while all constant production startegies gave w < 0 for the convex good. This suggest that the evolutionary pressure which will drive the system towards the optimal α value could be stronger in the case of a convex good than for a concave good.
In Figures 5A–C left panels it is clear that for a concave good and a convex good the topology of the Δg-“landscape” is quite different. Recall that different sets of QS parameters, (α, KS and ), correspond to different production curves: From at Figure 5A it is apparent that for a concave good there are several ways to “draw” suboptimal production curves through the Δg “landscape” without encountering regions where Δg ≪ 0, i.e., many choices of QS parameters which would give a positive cumulative fitness w. For h > 1 on the other hand we see that only curves which keep production relatively low for low N and then ramp up production very rapidly later can avoid passing through regions where Δg ≪ 0. This means that for a convex good the range of QS parameters α, KS and that result in positive fitness is relatively narrow.
3.1. Generalization to all Cases of Nonlinear Cost and Benefit Function Pairs
For the sake of simplicity we have throughout this paper considered the specific case of a linear cost function and two slightly different sigmoidal benefit functions, one concave and one convex (see Figure 1A). There is however no reason to believe that actual public goods will have costs and benefits which fit these arbitrarily chosen functions exactly. Fortunately it turns out that more general cases of nonlinear cost and benefit function pairs can be mapped onto the results presented. When cost is linear, we saw that the convex and the concave sigmoidal benefit functions fall into two major categories: Either they have continuous or discontinuous optimal production curves. It turns out that general pairs of (monotonically increasing) cost and benefit functions all fall into either of these two classes. We will refer to common goods with cost-benefit functions that cause them to have continuous optimal production curves as belonging to the “continuous class” and common goods with cost and benefit functions which cause them to have discontinuous optimal production curves as belonging to the “discontinuous class.” If the benefit function b(NσE) and the cost function c(σE) for a certain common good are known, it is possible to determine whether the common good belong to the continuous or the discontinuous class. If
for all 0 < y, then the optimal production curve is a continuous function.
While if there exists a value 0 < y* such that
then the optimal production curve has a discontinuity, causing it to jump from zero to a non zero value at N = Ncrit. See Supplementary Materials for the derivations of these criteria. It must be emphasized that as we expect the shape and magnitude of the cost and benefit functions to depend sensitively on specific growth conditions, we thus predict that the optimal production curves, and particularly the critical population size where production needs to be ramped up, to vary in different environmental conditions too. This prediction fits well with the observation by Duan and Surette (2007) that Las and Rhl expression profiles can vary greatly for different growth conditions. Such environmentally sensitive responce could for example be achieved by making QS parameters like KS and , dependent on environmental cues such as nutrient availability and stress factors recently dubbed “pull” factors in the paper on core principles of QS systems by Hense and Schuster (2015).
3.2. Discontinuous Class Public Goods Require Density Dependent Regulation
Overall we can draw the conclusion that when Ncrit > 1 the discontinuous class of public goods (which resemble the case of a convex benefit curve and linear cost) require density dependent regulation more so than the continuous class of public goods, based on the properties of the optimal production curves. To reiterate, these properties are for a discontinuous class good:
1. The optimal production curve has a discontinuous jump from low to high production rate at Ncrit.
2. Even when N > Ncrit production at a rate lower than the optimal one can cause a negative impact on fitness. (see Figure 5).
The optimal production curve of a continuous class good on the other hand have quite different properties:
1. It is possible to impact fitness negatively when N > Ncrit by producing a continuous class good, but only by producing at too high a rate compared to the optimum, never when producing at a rate which is less than the optimum.
2. A group can indeed benefit from letting production of a continuous class good depend of population size but deviating from the optimal curve does not necessarily come at a great fitness cost.
Because of the different properties of the optimal production curves for continuous and discontinuous class goods the QS parameters which would be needed to regulate them differ too. In the case of a discontinuous class good, fitness can be negatively impacted if the QS feedback exponent is not appropriate. Conversely for a continuous class good, fitness can be positive for a broad range of QS feedback exponents and one could thus speculate that constant constitutive expression could be a better choice for regulation of a continuous class good than a potentially costly and elaborate QS regulation mechanism.
Interestingly Schuster et al. (2004) find that LasR can bind either cooperatively or non-cooperatively depending on the promoter sequence. So although the overall signal feedback is characterized by a single exponent αS, the individual public goods, Ei, can have different responses to the signal-receptor complex characterized by different exponents αEi (Schuster et al., 2004). The reason for these differences could perhaps be that the various secreted products have different cost/benefit functions and thus different optimal production curves and consequently different regulation needs.
3.3. QS Signal Feedback
Quorum sensing is a mechanism usually assumed to give individual cells information about the density of the population. It is thus paradoxical that one feature found in many quorum sensing systems, the positive signal feedback, actually makes a system less accurate for sensing population size changes. Roughly speaking a strong positive signal feedback makes a QS system more appropriate for answering the binary question “are we many or few?” than for providing information about the precise population size over a broad range of densities. The reason usually given for why QS signals often feed back positively on their own production, is that this feedback ensures a synchronized response across a population (Hense and Schuster, 2015). Our analysis inspires another explanation for the existence of positive QS signal feedback, which does not however exclude the existing one. Recall that for a discontinuous class public good the optimal production strategy calls for a sudden discontinuous jump in production rate at a critical population size Ncrit. After this critical population size has been reached a substantial growth increase can be gained by producing public good at a specific optimal rate, but there will exist a production rate lower than the optimal one which will result in a growth rate decrease (see Figures 5B,C, for N > Ncrit there exists a local fitness minima below the optimal rate ). When ramping up production from zero to the optimal rate, the population thus necessarily has to pass through a local fitness minimum. A reason for having a strong positive signal feedback could thus be to ensure a sharper turn on of the public good production in order to minimize the time spent at the low production rates where fitness is impacted negatively.
3.4. Potential Trade Offs
When only “turn on” scenarios are important for fitness it is just the production curve that the population follows when going from low to high numbers, which needs to mimic the optimal curve, and bistability does not matter. If however both “turn on” and “turn off” scenarios are important for fitness, this changes. Now both the production curve which the population follows going from low to high numbers and the curve it follows from high to low numbers needs to mimic the optimal one simultaneously. For higher values of the feedback exponent this becomes problematic since the two curves will differ more and more due to the increasing width of the bistable range. This suggests that a bacterial species which needs to accurately regulate the production of a discontinuous class good both in situations where the population increases and decreases, will face an evolutionary trade off between “precision” and “sharpness” of the production curves. Too high a feedback exponent will mean imprecise turn on/off points for either (or both curves) due to the bistability and too low a feedback will mean that the turn on/turn off of the public good does not happen sharply enough. We thus predict that a bacteria living in such an ecological settings will have a feedback exponent bound at intermediate values—relatively close to the point where the QS system starts to display bistability.
3.5. Ideas for Experiments
With few exceptions (Melke et al., 2010; Sappington et al., 2011) there is a general tendency in the QS literature to focus only on the “turn on” of QS genes and only few studies have looked thoroughly at the effect of positive signal feedback (in fact it is disregarded in some theoretical studies, Brown and Johnstone, 2001; Nadell et al., 2008; Pai and You, 2009). To our knowledge no one has attempted to assess the fitness cost of bistability when both “turn on” and “turn off” scenarios are important. Our analysis suggest thats it could be interesting to explore experimental setups which examine how QS regulated genes are turned off in response to a decrease in population density, and setups which probe the effect of signal feedback on bistability. For example our results suggest that two strains engineered to differ in their QS feedback exponents would perform differently when placed in the experimental setup of a turbidostat where controlled slow fluctuations in density was set to occur right around the point of QS turn-on and turn-off. A separate treatment could involve major quick dilution and growth well past the turn-on point. In the first case, both turn-on and turn-off would be relevant, whereas in the second case, turn-on would be more important.
3.5.1. Measuring the Shape of Public Good Cost and Benefit Functions
The benefit function of a public good (e.g., elastase produced by P. aeruginosa Pearson et al., 1997; Beaufort et al., 2013) could be quantified by measuring the growth rates of signal-blind cheats (e.g., the lasRrhlR mutant) in a chemostat, as a function of the concentration of externally added public good (e.g., LasB, which would act as a public good by facilitating the break down of the main source of carbon which would be in the form of casein peptide chains to large for transport across the cell membrane). The cost function could be quantified by measuring the growth rate of an inducible constitutive producer mutant at different expression rates. It would be interesting to automate these types of measurements so that they could be done for a wide range of different molecules thought to be public goods, from different bacterial species. The shape/convexity of the measured benefit and cost functions could then be compared with already known information about whether the molecules are QS regulated or not, to determine whether discontinuous class public goods are overrepresented among QS regulated compounds.
3.5.2. Manipulating the Shape of the Benefit Function Experimentally
The way the specific public good LasB of P. aeruginosa works might provide a way to manipulate the convexity of its benefit function. When provided solely with a diet of casein polymers, P. aeruginosa growth depends on the production of LasB (and similar proteases) that degrade the casein polymers into smaller importable units, which can be transported across the cell membrane and metabolized (Efrat and Mary, 2014). In the Supplementary Materials we show that the benefit function becomes increasingly convex if the maximum length of the polymers in the environment is increased. This suggests that one way of experimentally manipulating the benefit function would be to pre-digest casein polymers to varying degrees before providing them to P. aeruginosa. Media with undigested casein should result in a more convex benefit function than media with pre-digested casein. Growth of constitutive producer mutants could then be compared with growth of wild-type P. aeruginosa in these media to test our predictions regarding the importance of the convexity of the benefit function for QS regulation.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Thanks to Brian Connelly, Josie Chandler, Ajai Dandekar, Katie Dickinson, Pete Greenberg, Sarah Hammarlund, John Mittler, Brook Peterson, Wenying Shou and Joao Xavier for fruitful discussions. This work was supported by the National Science Foundation under Cooperative Agreement Number DBI-0939454 and a NSF CAREER Award Grant (DEB0952825) (BK), by Simons Foundation (SK) and by James S. McDonnell Foundation for studying complex systems (SH).
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/article/10.3389/fmicb.2015.00767
1. ^Quorum sensing (QS) is a bacterial behavior ubiquitously present in the microbial world and most bacteria possess at least one quorum-sensing system, (Fuqua et al., 2001; Miller and Bassler, 2001; Schauder and Bassler, 2001). This term covers all types of behavior where bacteria produce, secrete, and subsequently respond to diffusable signal molecules. Typically, the signal molecules are small and relatively cheap to produce, e.g., an acyl homoserine lactone (Fuqua et al., 2001).
2. ^Using a well-mixed system is a simplification that allows us to treat each cell as identical to all others and to ignore spatial variations in the public good concentration.
3. ^More on general nonlinear cost and benefit functions in the discussion.
4. ^If Ncrit < 1 even a single cell will obviously benefit from production no matter what the benefit curve is shaped like
5. ^See Supplementary Materials for a further discussion on (1) the case of a spatially structured system, (2) situations where the assumption that timescales of production and decay of public good are much faster than the time scale of growth does not hold.
6. ^Actually the feedback acts not on the signal production but on the production of the signal synthase, an enzyme which facilitates the production of signal intracellularly, but since concentration of signal synthase and signal has been found to be approximately proportional (e.g., in the Las system of P. aeruginosa Duan and Surette, 2007), we can model concentration of signal and signal synthase by one symbol S.
7. ^Note that because all rates are given in units of the basal signal production rate (), is in fact the ratio between the basal rate and the maximum rate.
8. ^For this study we examine the behavior of the system in the vicinity of the critical turn on point, Ncrit and not in the limit of high N. As a population approaches stationary state or starvation additional layers of gene regulation will become relevant and cause down regulation of genes which have been activated by QS, (Navarro Llorens et al., 2010; Gopalkrishnan et al., 2014). This type of regulation was not included in our simple QS model which is the reason that we choose to evaluate the QS production curves as a function of population size only on in the range [1; Nmax] where Nmax is not much larger than the critical population size Ncrit above which cooperation become beneficial.
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Keywords: quorum sensing, cooperation, cost and benefit functions, bacteria, public good production and regulation
Citation: Heilmann S, Krishna S and Kerr B (2015) Why do bacteria regulate public goods by quorum sensing?—How the shapes of cost and benefit functions determine the form of optimal regulation. Front. Microbiol. 6:767. doi: 10.3389/fmicb.2015.00767
Received: 24 April 2015; Accepted: 14 July 2015;
Published: 28 July 2015.
Edited by:Jochen Ait Mueller, Helmholtz Centre for Environmental Research - UFZ, Germany
Reviewed by:Migun Shakya, Dartmouth College, USA
Hideaki Koike, National Institute of the Advanced Industrial Science and Technology (AIST), Japan
Copyright © 2015 Heilmann, Krishna and Kerr. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Silja Heilmann, Computational Biology, Xavier lab, Memorial Sloan Kettering Cancer Center, 417 E68th Street, Zuckerman Research Center, 11 Floor, Room 1145, New York, NY 10065, USA, firstname.lastname@example.org


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In Post-Surgery Lung Cancer Surveillance, More Is Not Better
An annual CT screening is better than frequent follow-up scans, a new study reports.
Shutterstock/Image Point Fr
For people who have had cancer surgery, post-surgical surveillance -- usually at intervals of three, six and 12 months -- is standard care. But the reasoning behind such monitoring, including decisions on the best methods to use and their frequency, has been based on expert opinion and limited empirical data such as small retrospective studies. The Institute of Medicine lists establishing the efficacy of post-surgical surveillance among its most urgent goals.
A five-year study published in the October 2018 Annals of Surgery tackles that goal with a look at lung cancer. The study reveals that frequent surveillance does not improve lung cancer patient survival. Researchers from some of the United States’ largest public health and cancer treatment centers, along with medical societies including the American College of Surgeons, evaluated surveillance among non-small-cell lung cancer (NSCLC) patients. The researchers chose NSCLC because, they wrote, it is the “fourth leading diagnosis among cancer survivors ... that affects 450,000 Americans and is expected to grow 20 percent by 2022.” A database of 4,463 NSCLC survivors representative of the national patient population was abstracted from the National Cancer Database. These patients had been followed for five years and undergone routine follow-up CT scans.
Although a higher number of scans was not associated with better survival, the authors find reason for optimism. NSCLC patients have historically had a poor chance of surviving a recurrence, but the National Lung Screening Trial has shown that annual low-dose CT scans found smaller NSCLC tumors at earlier stages, reducing lung cancer mortality by 20 percent. The authors of the current study believe this finding justifies annual CT screening even as it also creates many more patients needing post-surgery surveillance. But their own findings indicate a more frequent schedule is not warranted, and absent the presence of other serious conditions, patient care would not be compromised by reducing the frequency of ineffective and expensive scans.

domain: literature


CLAY, MACycle and Mac Farmstand rescinded
Photo C/O Mac Farmstand via Twitter
On March 8, the Student Representative Assembly passed motions to cut the Creating Leadership Amongst Youth Conference, MACycle and Mac Farmstand. These MSU services will no longer be operational for the upcoming 2020-2021 academic year.
On Feb. 27, the McMaster Student Union’s Executive Board recommended that the operating policy for these services be rescinded because they were running over-budget and had low student engagement.
According to a memo presented to the Executive Board on Feb. 27 by Vice President (Finance) Alex Johnston and Vice President (Administration) Sarah Figueiredo, the decision to rescind these MSU services is a result of the Student Choice Initiative and a large operating fund deficit of $598,950 in the 2018-2019 academic year.
“Though the Student Choice Initiative is currently deemed unlawful, it is important to continue this work in light of ongoing deficits, financial ability, and whether or not they continue to fill a gap in the McMaster Undergraduate Community,” the memo reads.
Creating Leadership Amongst Youth Conference
CLAY is an annual three-day long conference held in May at Camp Trillium that aims to develop high school students’ leadership skills across Hamilton and the Greater Toronto Area.
According to a memo presented to the Executive Board on Feb. 27 by Figueiredo and Associate Vice-President (Services) Martino Salciccioli, CLAY has low student engagement. While delegates enjoy CLAY, only around 70 MSU members, or approximately 0.3 per cent of students, attend the conference consistently each year.
Moreover, the memo states that CLAY has run over-budget by a total of $57,021 between 2011 and 2019. At the SRA meeting on March 8, Salciccioli added that attempts to reduce CLAY’s operating budget have already been taken in previous years. These efforts included reducing the conference’s length from four days to three days and changing the conference location from Camp Muskoka to McMaster University to Camp Trillium.
“All of the options have been exhausted with what to do with rebranding of the service. We’ve looked at shortening dates, we’ve looked at cutting costs, we’ve looked at moving [locations]. We’re currently at the cheapest place to hold three days and two nights, we figured if we shortened the days and nights it wouldn’t be CLAY as it is. It would be a totally different service and a totally different mission,” said Salciccioli at the March 8 SRA meeting.
In their Feb. 27 memo, Figueiredo and Salciccioli suggested other opportunities for students to develop their leadership skills in the community, such as the Central Ontario Leadership Seminar. The memo also references Empowerment Squares, Pathways, the Boys & Girls Club, the Space and the YMCA as additional organizations that offer similar opportunities.
“While these opportunities may not be CLAY, it is clear that there are similar initiatives in our community that function in a similar way to the conference,” the memo reads.
The fee MSU members currently pay towards CLAY will be replaced by a fee $5,000 bursary divided between several high school students pursuing youth leadership opportunities in and around Hamilton. It is currently unclear which leadership programs the bursary is eligible towards.
MACycle aims to educate the McMaster community about cycling as a mode of transportation and to provide student and community cyclists with tools, parts and volunteer assistance for bicycle repair and maintenance. MACycle also sells refurbished and used bicycles.
According to a memo presented to the Executive Board on Feb. 27 by Johnston and Figueiredo, student and volunteer engagement with MACycle is low, with four new and two returning volunteer applications in the 2019-2020 academic year. The memo also includes data from the 2019-2020 MSU Feedback Survey available from Nov. 19, 2019 to Dec. 18, 2020. In the survey, 790 students ranked their participation in MaCycle. Thirty two students responded that they often or heavily used services offered by MacCyle. Six hundred and sixty seven students responded that they had never used services offered by MACycle or knew what MACycle was.
MaCycle 2019-2020 MSU Feedback Survey Results
Additionally, Johnston and Figueiredo state in the memo that MACycle has run a total of $13,270.28 over budget from 2015 to 2020. Upon consultation with the previous MACycle director, there were few options for reducing the cost of the service. The memo adds that previous recommendations made in 2017 to increase service use such as extending service operations, creating a larger volunteer team, increasing the price of parts and creating a paid assistant coordinator position have been unsuccessful.
Johnston added that there are additional resources for bike repairs available to members of the McMaster community.
“There is a bike store right in Westdale, and if you want to get broader into the Hamilton community [. . .] there are a lot of different options for students if they need to repair their bike. And there are also some bike repair stations just outside BSB station, and that was a project funded through the Student Life Enhancement Fund two years ago,” said Johnston at the SRA meeting on March 8.
The Feb. 27 memo states that the MSU Maroons will take over MaCycle’s annual bike auction and proceeds will be donated to an undisclosed Hamilton charity. Johnston explained that the reason the MSU Maroons were recommended to take on the annual bike auction is because of the team’s large number of volunteers.
“That’s a team that we’re looking to rebuild and give a different purpose too . . . It's also a team with a very large amount of volunteers that can facilitate an auction like this without adding additional work onto another service,” said Johnston at the SRA meeting on March 8.
The memo also states MACycle will be replaced by additional advocacy and partnership efforts between the MSU and the Office of Sustainability.
Mac Farmstand is a student-run farmers market that sells local produce on campus weekly between June and October, and aims to raise awareness of the importance of purchasing local food items.
According to another memo presented to the Executive Board on Feb. 27 by Johnston and Figueiredo, student engagement with Mac Farmstand has declined. There were only seven volunteer applications for executive positions in the 2019-2020 academic year. Out of 790 that ranked their engagement with MacFarmstand in the 2019-2020 MSU Feedback Survey, 45 students responded that they often or heavily participated in Mac Farmstand and 535 students responded that they never participated in Mac Farmstand or knew what Mac Farmstand was. Moreover, the memo states that since Mac Farmstand operates in the summer, the service predominantly caters to faculty and staff as opposed to undergraduate students.
Mac Farmstand 2019-2020 MSU Feedback Survey Results
The memo states that Mac Farmstand has also exceeded its budget by $17,421.56 total since 2015 due to low sales revenues. Johnston and Figueiredo state that reducing expenses would require increasing the costs of products.
“While it is expected to pay a premium for locally sourced goods, it is also important that prices remain reasonable. To generate an increased revenue, prices would need to increase further than they did this year, which is simply not possible and would lead to fewer students/patrons purchasing from the stand,” the memo states.
Concerns that other efforts to provide affordable food to McMaster students, faculty and staff would not be sourced locally were raised in the Silhouette. According to Johnston, she and the future Vice President (Finance) will work with the MSU’s food and beverage department to explore selling local seasonal goods elsewhere on campus.
“I can work with the and the future VP the Food and Beverage Manager to work with our existing supplier to provide those at Union Market . . . and even the Grind,” said Johnston at the SRA meeting on March 8.
The Feb. 27 memo states that local produce may be sold at Union Market in the upcoming 2020-2021 academic year and the grocery store within the Student Activity Building in DBAC when it becomes operational in 2021.


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Did you recently complete our January-March 2023 clear aligner training, “Orthodontic Mini Residency in Clear Aligner Technique”? If so, you might be wondering what’s next. In addition to the knowledge you’ve gained to confidently offer Invisalign clear aligner treatment at your practice, completing the course opens up alumni perks that will continually benefit your Invisalign service. Here are 5 ideas for taking advantage of the alumni resources available to you.
It’s easy to focus only on your patients and team while you’re building or growing your dental practice. After all, a robust dental practice takes up a lot of time and energy, and you still want to have time for family, friends, and yourself. But when you’re ready, having access to other dental professionals can help your professional practice. When you complete our online orthodontic course, you can join other dentists who have also taken the course in a private and exclusive Facebook group.
This Facebook group is comprised of those who have taken any of Aligner Resources’ online clear aligner courses. So it’s a great forum for connecting with dentists who have added Invisalign to their services. The group is useful for asking questions as you set up your own clear aligner offering — for example, questions about using ClinCheck®, the many digital tools available, or treatment practicalities or issues you encounter. Network and learn from Invisalign practitioners and experts from around the world who can offer experienced insight. And it’s a group and you can contribute advice to in return.
Of course, the online course you took with Aligner Resources included clear aligner treatment sessions that will help equip you for more complex cases. But afterwards, having other dentists weigh in on your real-life, real-time cases can only benefit your patient care and your own professional growth. Within the Facebook group, members can bring up challenging cases as they arise, ask for assistance, and collaborate. As mentioned, the group is made up of online course alumni, so there’s a depth and breadth of fellow dental professionals to turn to for advice.
In almost 25 years of experience as a certified Invisalign orthodontist, Dr. Sandra Khong Tai has treated over 4,000 cases and is a Diamond+ Invisalign Provider. She is a recognized global expert on Invisalign clear aligner treatment, speaking at various industry conferences and events about the intricacies of clear aligner technique. As the creator of Aligner Resources’ orthodontic courses for general dentists and the author of the textbook, Clear Aligner Technique, Dr. Tai serves as a valuable mentor to course alumni.
Reaching out to Dr. Tai through the Facebook group, you can get one-on-one help on a particularly unique Invisalign case in addition to the advice of other dentists in the group. Dr. Tai is happy to answer questions and offer suggestions to help you improve your clear aligner treatment techniques.
Another alumni perk from taking the Aligner Resources’ Invisalign course online is forever-access to a library of review sessions. With these resources in your back pocket, you can troubleshoot challenging cases, as well as refresh your Invisalign knowledge as an Invisalign provider.
Participating in the private, alumni Facebook group can also help you stay abreast of new clear aligner treatment techniques and news. As a global Facebook group, you have the opportunity to stay in-the-know about clear aligners locally — in your own city and country — but also have direct insight into what Invisalign practitioners abroad are doing and achieving.
“Orthodontic Mini Residency in Clear Aligner Technique” is an invaluable online orthodontic course for raising your dental practice to the next level, adding to your professional development, and increasing your bottom line. But it goes beyond that — Aligner Resources clear aligner courses come with alumni perks that will support your Invisalign treatments and techniques long after the course you take is over.
This module-based course is flexible and can be started and completed at your own pace, a perfect fit for busy dentists. And bonus? Completion of this accessible clear aligner continuing education counts as 30 CE credits.
Dr. Tai is based in Vancouver, BC, Canada and has almost 25 years of orthodontic expertise as a certified Invisalign® orthodontist. A Diamond+ Invisalign Provider, Dr. Tai has treated over 4,000 cases with Invisalign.
She is a member of the Editorial Board of the Journal of Aligner Orthodontics, a Diplomat of the American Board of Orthodontics, a Fellow of the College of Dental Surgeons of British Columbia, and a Fellow of the Royal College of Dentists, Canada. Professional affiliations include memberships in the Canadian Association of Orthodontists, American Association of Orthodontists and Edward H. Angle Society of Orthodontists.
As an educator and expert, Dr. Tai is a Clinical Assistant Professor at the University of British Columbia Faculty of Dentistry and an Adjunct Clinical Assistant Professor at the University of the Pacific, San Francisco teaching and mentoring the next generation of dentists and orthodontic specialists.
If you haven’t taken our clear aligner training, don’t worry, you can start the course whenever it works for you. Our previous seasonally-based schedule was so in-demand that we now offer an open start for even better flexibility: you can now begin these online orthodontic courses as soon as you register and attend any ClinCheck review session over Zoom that fits your schedule.
Sign up for what our alumni consider the best online Invisalign courses for busy, practicing dentists and get exclusive access to a global network of fellow Invisalign dentists.
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domain: health


text:
It was a heartbreaking moment for Naga Chaitanya and Samantha Prabhu’s followers when the couple announced separation last year in October. They wanted to know what went wrong and if the couple would ever get back together. Fingers were also raised and netizens kept inundating the actors’ social media accounts with endless comments, queries and allegations. The frenzy was wild and we thought it would never stop. You can only imagine how it might have impacted Naga and Samantha who were both experiencing all of this first-hand. Well, it’s been months since the divorce announcement and if you go and check the actors’ social media accounts, you’ll still find fans leaving broken heart emojis on their posts. However, looks like they have found a way to drown all the noise and move on in life. Samantha is doing exceptionally well in her professional life and has become one of the most talked-about actors in the country today. Meanwhile, Naga seems to be doing well in his personal life and rumours suggest that he has found love again.
Earlier today a popular entertainment media platform quoted a source that made claims about Naga’s rumoured lady-love. According to the source, Naga is now dating the Made in Heaven star Sobhita Dhulipala.
“Chay and Sobhita seemed very comfortable in each other’s company as they spent time at the actor’s new house. Naga Chaitanya was giving her a tour of his massive home. After a few hours, they left together in the same car,” they said. The source further added, “Chay was spotted multiple times at the same hotel as Sobhita Dhulipala where she was staying for the promotions of her last film Major. In fact, she also spent her birthday recently in Hyderabad with her ‘close buddies.'”
That said, we are yet to hear any official word on all these claims but we will love it for both Chay and Sobhita if they have found love in each other. The two will make a beautiful couple and we’d definitely love to see this relationship bloom. Rest assured, we will keep you updated. Here’s to moving on and finding love again!
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domain: news


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Protective and Vulnerability Factors Predicting New-Onset Depressive Episode in a Representative of U.S. Adolescents
- Van Voorhees Benjamin W, Paunesku David, Kuwabara Sachiko A, Basu Anirban, Gollan Jackie, Hankin Benjamin L, Melkonian Stephanie, Reinecke Mark
- The Journal of adolescent health : official publication of the Society for Adolescent Medicine SCI(E) SCOPUS SSCI
- Society for Adolescent Medicine in 2007
- Cited Count
Depressive episodes cause considerable morbidity and mortality in adolescents. We sought to identify factors predicting new onset depressive episode in a representative sample of U.S. adolescents.
1.Epidemiology of DSM-III-R Major Depression and Minor Depression Among Adolescents and Young Adults in the National Comorbidity Survey(1998) Kessler, R. C. et al. Depression and AnxietyMental Health and Medicine cited 159 times
2.Uncovering an epidemic—screening for mental illness in teens. N Engl J Med. Vol. 355. 27172719(2006) Friedman R.A.
3.The Loss of Sadness: How Psychiatry Transformed Normal Sorrow into Depressive Disorder.(2007) Allan V. et al.
4.The construct of resilience: a critical evaluation and guidelines for future work. Child Dev. Vol. 71. 543562(2000) Luthar S.S. et al.
5.Adolescent depression: description, causes, and interventions. Epilepsy Behav. Vol. 8. 102114(2006) Hankin B.L.
6.Vulnerability to depressionamong adolescents: implications for cogntive treatment. Cognit Behav Pract. Vol. 12. 166176(2005)
7.Continuities in depression from adolescence to young adulthood: contrasting ecological influences. Dev Psychopathol. Vol. 16. 967984(2004) Gutman L.M. et al.
8.Adolescent Psychopathology: I. Prevalence and Incidence of Depression and Other DSM-III-R Disorders in High School Students(1993) Lewinsohn, P. M. et al. Journal of Abnormal PsychologyPsychology cited 426 times
9.Representativeness of Clinical Samples of Youths With Mental Disorders: A Preliminary Population-Based Study(1997) Goodman, S. H. et al. Journal of Abnormal PsychologyPsychology cited 34 times
10.Major Depression in the Transition to Adulthood: Risks and Impairments(1999) Reinherz, H. Z. et al. Journal of Abnormal PsychologyPsychology cited 40 times

domain: medical


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Under the new sanctions project, assets in the United States may be frozen and a ban on opening correspondent accounts for “a number of Russian banks” may be introduced. Most likely, we are talking about such “pillars” of the domestic financial system as Vnesheconombank, Gazprombank, Sberbank, Russian Agricultural Bank, VTB. It should be understood that the main purpose of these restrictions is nothing more than the complete destruction of the system of currency correspondent accounts operating within Russia. How? We will try to explain: for the enormous influence that Washington has today on our financial system (as well as on the banking sector of most other countries of the world), a big "thank you" should be said to the FATCA extraterritorial law adopted in the USA in 2010. According to him, information about any persons and companies that are US taxpayers is provided to this country without fail by banks of any state in the world. The slightest violations, as they say, are "very fraught" and "strictly subject." Having seen in the activities of any financial institution an attempt to circumvent or ignore the FATCA, US supervisory authorities can give him a luxurious "bouquet" of troubles - up to the complete blocking of all accounts and operations.
About the same thing, only in an even tougher form provides for a new bill. In theory, having seen in the activities of any Russian bank “financing the intervention in the American elections” or, which is simpler, declaring them “under the control of the Russian government” and, moreover, in its ownership, Washington will begin to block any of their transactions through the US financial the system. In the case, it’s already going to the financial war “to annihilation”, the US’s favorite repressive instrument for such cases will be used - SWIFT, and we will focus on the suspension of all operations that our banks are forced to conduct through it so far. Well, the arrests already mentioned above, or at least the freezing of the “wrong” Russian financial institutions and companies wherever Americans can reach them.
Prospects arising from such opportunities? Let's face it - joyless. And if we talk about the further development of events ... An extremely unpleasant feature of the new sanctions is that for the first time, albeit not directly, they are threatening the Central Bank of Russia. All over the world, these organizations are considered to be “untouchable” and not subject to restrictions, even if they are introduced against a particular country. The only exceptions are the Central banks of those states that are declared by the United States "rogue countries", "sponsors of international terrorism" and so on. North Korea, Libya, Iran, Syria ... By the way, which is very characteristic - one of the main “sins” of these banks that raised them to the top of Washington’s blacklist is not only that they belong to the state sector of countries with “dictatorial” regimes, ”and also the fact that in all these countries at one time or another, attempts were made (or are being done now) to get rid of the dollar dictatorship to the maximum.
With him, however, everything is not so bad as with the ones mentioned above - they are not disconnecting from SWIFT, assets are not blocking. However, the fact that the package of impending restrictions for the first time provides for measures specifically affecting it cannot but alarm. We are talking about a ban on the purchase of not only government bonds of Russia, but also any debt securities of its Central Bank, which it will no longer be possible to place on the global financial markets. The funny thing is that such a placement has never, in fact, been practiced - apparently, Washington simply "insures for the future." But the second measure, which makes it impossible for our Central Bank to attract short-term loans for so-called swap operations to Russia from abroad, is already much more serious. Russian state financiers also do not abuse this tool, however, they periodically use it: this was the case in 2009, and in 2017. The main question that arises as a result is - to what limits will they reach in their desire to annoy our "sworn friends" from across the ocean with the tougher Russian financial system? It’s not an hour, and the disconnection of the Central Bank of Russia from international payment systems, and the freezing of its currency assets may become a reality.
Here is the time to mention that the financial system of any country is vulnerable to attacks from Washington, first of all, by using the US currency in it. All dollar transactions conducted in the world are somehow controlled by the United States. There are no "green" in mutual settlements - there is no American control over them. That is why the process of maximally ridding our economy of the participation and influence of the “enemy” currency is not just the right decision, but the arch-correct one, as the “leader of the world proletariat” would say on this occasion. Alas, he started with a fair delay - but here it is certainly better later than never. One of the main tools of dedollarization is, of course, the rejection of American money as a component of Russia's foreign exchange reserves. Last year alone, their dollar share fell by almost half - from 43,7% to about 22%. According to official figures, this year (as of February) the dollar-denominated assets of Russian banks have decreased by almost 5%. Nevertheless, in the total volume of their assets, the American currency is still about 305 billion dollars, so that in the chosen direction still move and move.
At one time, vicious critics and self-proclaimed experts addressed the Russian authorities, and specifically the Central Bank, a lot of taunts were expressed about “unsuccessful attempts at dedollarization”. Like, they throw money away, investing "in the wrong currencies." Well, if the “experiments” of the Central Bank with the Chinese yuan can be considered quite controversial (although the one who does nothing is right), then there can be no doubt about the main instrument of the “anti-dollar struggle” chosen by our country. The bet on the noble metal made in the replacement of the state’s dangerous components of the gold and foreign exchange reserves turned out to be the only right and possible solution. This becomes especially obvious after, without exaggeration, the fateful event - the entry into force on March 29 of a decision adopted in 2011 by the Banking Supervision Committee of the Bank for International Settlements. This financial institution with headquarters in Switzerland, in fact, is the authority that approves the standards and norms of activity for all financiers of the world - first of all, for the central banks of various countries.
On his decision, which has the unofficial name of "Basel III," by golly, it is worthwhile to dwell in detail. Indeed, in accordance with it, from now on, the share of capital of all banks, stored in gold, is estimated in the volume of the full, and not half, market value of this precious metal, as it was before! This, of course, is not a return to the gold currency standard. But, definitely - the first step to it. And the leap is seven-foot. The United States system unilaterally broken in 1971, the gold standard system was one of the most important milestones in Washington’s dismantling of the entire system of world relations that developed after the Second World War. This was done, of course, in order to establish the world hegemony of the United States, and the imposition of the dollar on the world as the only, in fact, universal currency, played a huge role in achieving this goal. Recall: according to the results of the Bretton Woods conference held in 1944, after the war, dollar and gold were to become world money. However, having refused in 1971 the free exchange of US treasury bills for “hard currency” or bank bullions, the Americans finally turned gold into a noble, precious - but still, ordinary metal.
The icy wind of another global financial crisis approaching the world, the clear realization that all the shocks of world financial markets have their source in the United States, or rather, the overwhelming dominance of their currency - all this makes financiers think about the need to take the most drastic measures to protect their capital. No one is interested in the fact that a sinking dollar would “drag to the bottom” for itself and the entire world economy. And although it is unlikely that a large minting of gold coins is expected in the near future, however, the ice has broken, as they say - gold triumphantly returns slowly to the financial markets of the planet, where it reigned for millennia. Proof of this is more than 650 tons of this metal, purchased by central banks of various countries during 2018. This figure is a record for the entire period, taking a reference point in the memorable 1971.
The good news is that 42% of the above-mentioned volume of purchased precious metal are just purchases made by the Central Bank of Russia - almost 275 tons. This is the largest indicator in the world. Following us in the list of "wealthy" countries are Turkey and Kazakhstan. China and India are actively building up their gold reserves. Today, Russia is the country with the fourth gold reserve in the world. And it inspires hope. Of course, you can’t get out on one “yellow metal” - Washington is too serious for us. Therefore, the domestic SPFS - the Financial Message Transfer System should be developed and expanded as much as possible now - while there is no talk of disconnecting Russia from SWIFT yet. Then it may be too late. As of last year, this system had about 500 users, including giants such as Rosneft and Gazprom. However, the problem is different - SPFS desperately needs to go beyond Russia, while foreign users are only timidly trying to connect to it. Old and tested options, the same SWIFT and more familiar and reliable.
This is where Moscow needs to make the most of all the opportunities that the United States itself, in fact, provides it with. It is necessary to “play” on American sanctions against Iran, Venezuela, and even against the DPRK! And consider the situation not from the perspective of “no matter what happens” (it has already happened, but it will be even worse!), But exclusively from the point of view of “just to be in time”! Do not be afraid to “anger” or “provoke” Washington to new sanctions, but to act in advance of its decisions, calculating the development of events according to the worst-case scenario. If the Kremlin fails to correctly use the totality of the US economic contradictions and conflicts existing in the world today, not only with the aforementioned states, but, above all, with China, the countries of Europe, Turkey, they will not put together an “anti-dollar”, but, in fact, anti-American bloc - alone we have to be bad. The economic Third World War is already on and no one will fight in a knightly way.

domain: economics


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"I was starting to go blind," said Mary T. A diabetic, she was being held by US immigration authorities when her vision began to fail. I could only see shades of people," she said, "I couldn't see numbers or letters." She repeatedly complained to her jailers, but received no medical care for 15 days as her condition worsened. When a nurse was finally summoned, Mary T. recalled, the nurse asked her, "Why didn't you tell us?"
For Mary T., who regained her sight, and the thousands of other women detained each year by the US Immigration and Customs Enforcement (ICE), speaking up about health problems is not enough. Two new reports, one from Human Rights Watch and the other from the Florida Immigrant Advocacy Center (FIAC), document dozens of cases in which the immigration agency's medical staff either failed to respond to health problems of women in detention or responded only after considerable delays.
"Women in detention described violations such as shackling pregnant detainees or failing to follow up on signs of breast and cervical cancer, as well as basic affronts to their dignity," said Meghan Rhoad, researcher in the women's rights division at Human Rights Watch. "Because immigration detention is the fastest-growing form of incarceration in the United States, these abuses are especially dangerous. They remain largely hidden from public scrutiny or effective oversight."
Human Rights Watch researchers visited nine detention centers in Florida, Texas, and Arizona, and interviewed 48 women detained or recently released from immigration detention, as well as detention facility staff and health care providers, immigration officials, immigration attorneys and advocates. The FIAC report is based on interviews, phone conversations and correspondence with detainees and jail and immigration officials. It also includes information from US government materials, newspaper articles and other data.
Women described struggling to obtain potentially life-saving services such as Pap smears to detect cervical cancer, mammograms to check for breast cancer, pre-natal care, counseling for survivors of violence, and even basic supplies such as sanitary pads or breast pumps for nursing mothers. The obstacles to health services included inadequate communication about available services, unexplained delays in treatment, unwarranted denial of services, breaches of confidentiality, and failure to transfer medical records. When women were denied services, complaint mechanisms were ineffective, according to the two reports.
More than 300,000 people were in immigration custody in 2008; women accounted for about 10 percent of the total. Immigration law violations are civil infractions, and detainees are held in administrative - not punitive - custody. The average stay is 38 days, but some detainees are held for months and even for years.
Under international standards, detainees are entitled to the same level of medical care as individuals in the community at large. Still, the researchers found a disturbing pattern of neglect. Before her detention, Lucia C., was told by her doctor to have semi-annual Pap smears because the results of her most recent procedure showed abnormalities. When she was detained at a county jail in New Jersey, authorities rebuffed her request for the procedure. "I was supposed to be checked every six months," she told Human Rights Watch. "I asked my daughter to send the records. I got it and I brought it to medical so they could see I'm not lying. I have asked a lot of times." Despite her efforts, Lucia C. did not receive a Pap smear over the 16 months spent in detention. "It's terrible because you feel like you have something you can die for ... and you don't have no assistance."
ICE health-care policy focuses on emergency care. Most of the difficulties arise when detainees require non-emergency care. ICE policy governing off-site medical visits permits non-emergency care only when lack of treatment would "cause deterioration of the detainee's health or uncontrolled suffering affecting his/her deportation status." This policy exists alongside a set of detention standards that were recently revised to upgrade medical care requirements for facilities, but that are not to take effect until 2010. For some of the women currently in custody, they may come too late.
ICE detains individuals at more than 500 facilities nationwide; Division of Immigration Health Services (DIHS) personnel provide on-site medical services at 21 of these. At other facilities, medical care is contracted out along with other detention functions.
Women constitute 10 percent of the immigration detention population, currently a total of about 30,000 on any given day.
Women detainees are held in more than 300 facilities.
Half of the women Human Rights Watch interviewed said they had experienced delays in receiving requested medical care and nearly as many were forced to make repeated appeals to obtain an appropriate response to their medical concerns.
- Ensure that those currently detained are fairly and quickly considered for release and alternatives to detention;
- Issue federal regulations so that ICE detention standards have the force of law, and detained individuals and their advocates have recourse to courts to redress shortfalls in health care;
- Revamp and improve policies limiting access to non-emergency services;
--Stop detaining women who are suffering the effects of persecution or abuse, or who are pregnant or nursing infants;
- Adopt specific standards addressing women's health services, including reproductive health services; and
- Prohibit the shackling of pregnant women.


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The Directorate of State Service (DSS) in Edo has denied invading the residence or arresting anyone associated with Chief Taiwo Akerele, former Chief of Staff (CoS) to Gov. Godwin Obaseki of Edo.
Mr Sheikh Waziri, DSS Director in Edo, told the News Agency of Nigeria (NAN) in Benin on Monday, that no operative of the service invaded the residence of Akerele on Sunday.
There were reports in Benin that the operatives had arrested one Jaspa Olowojoba, Personal Assistant to Akerele, when the operative could not find him.
“I have verified and confirmed that the DSS Edo has not invaded the residence nor arrested anyone associated with the former CoS,” Waziri said.
The former CoS on Saturday resigned his appointment, while Obaseki had replaced him with Mr Osaze Uzamure.


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feeding lasts over a long period of time. Works great
21-0-0. A fast release, quick acting source of nitrogen
4-10-6. Provides the proper nutrients necessary to promote
vigorous growth, abundant vegetable harvest and juicy
tomatoes. 4 lb bag.
TOMATO FERTILIZER PACK Grow great tasting & good looking tomatoes.
Foliar spray: 1 tablespoon per gallon of water
Soil application: 1-16 ounces per gallon depending on size of tree or shrub (see label).
When the term is encountered in an agricultural context, it usually refers to agricultural lime, which is crushed limestone.
Flowers, shrubs and trees: 3-1/2 tablespoons per gallon of water. Mix 1-8 pints per plant transplanted.
House plants: 1/2 cup per quart of soil (a 6-inch pot holds approximately 1 quart of soil).

domain: agronomy


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Sterling Silver Chain Hoops
These little hoop earrings are handmade from the same chain as the necklaces in The Collection of Cells. Made for every day wearing, on thier own, layered together or mixed with other earrings.
Made from recycled silver. The diameter of the Tiny Hoop is 8mm and the Bigger Hoop is 11mm.
Please allow 14 days from order date to be notified about postage. Do get in touch if you need something quickly and I shall try and accomodate.

domain: design


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- Binance Australia’s places of work are being raided by Australian regulators as a part of a derivatives investigation.
- Binance is working with authorities to satisfy native regulatory requirements in Australia.
- The information comes after ASIC revoked the trade’s Australian derivatives license.
Binance Australia’s places of work have been raided by the Australian securities regulator as a part of an investigation into the lately discontinued native derivatives enterprise, Bloomberg reported on Wednesday. The Australian Securities and Investments Fee (ASIC), the regulator that oversees the nation’s company and securities affairs, performed the raid on Tuesday, in accordance with an nameless supply.
A Binance spokesperson informed Reuters:
We work with native governments and Binance is concentrated on assembly native regulatory requirements to serve Australian customers in a totally compliant method.
The information comes after ASIC revoked the license of Binance Australia Derivatives in April after conducting an intensive investigation into Binance’s actions within the nation, significantly the classification of retail and wholesale clients on the platform. rice discipline. In response to ASIC’s revocation of its license, Binance has determined to droop its derivatives buying and selling operations in Australia and as an alternative undertake a extra focused technique.
Binance CEO Changpeng Chao mentioned in a tweet on April 6 that there are solely 104 customers on Binance Australia. Nonetheless, Binance spot cryptocurrency trade in Australia has confirmed that it’ll proceed to function.
Australian regulators have launched an investigation into Binance after the abrupt closure of some derivatives positions in February. Binance cited the investigation as a result of the authorized standing of some customers didn’t meet the factors for being categorized as an Australian wholesale investor.
The world’s largest cryptocurrency trade is at present dealing with regulatory lawsuits and investigations spanning a number of jurisdictions. In March, the U.S. Commodity Futures Buying and selling Fee (CFTC) filed a lawsuit towards Binance and its founder, Zhao Changpeng, for working an trade deemed “unlawful” by regulators.


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UtahCARE Advocating Medical Cannibis
It’s bound to happen, right? With more states every year seeming to jump on the medical marijuana bandwagon, many believe it is only a matter of time before the was bound to happen. The movement for medical marijuana is gaining more traction in the state. A group called UtahCARE (Utah Cannibis Awareness Respect and Education) has become the first grass roots organization in the state to actively pursue and be dedicated to the legalization of medical cannibis.
The group is meeting at events such as farmer’s markets to educate farmers, individuals, and businesses on the benefits of medical marijuana. They are also obtaining signatures, presumably to present to elected officials in hopes of persuading them to change their stances on marijuana.
Reflections on Prohibition
Medical marijuana is akin to the medical alcohol that doctors could prescribe during prohibition. More and more science is showing that cannibis can be used to relieve pain and otherwise benefit individuals sick with cancer and other painful diseases. An exception for the use of marijuana as a medical drug would be in line with our country’s making exceptions for prohibited drugs in the medical sense. Current pharmaceutical drugs can only be used with a prescription. Presumably, the use of cannibis would need a prescription as well as is the case in California and Colorado currently.
No respect for Other State’s Marijuana Law
At Salcido Law Firm our marijuana defense lawyers help clients who have medical marijuana licenses from other states who have been charged with possession of a controlled substance in Utah. Utah does not recognize the medical marijuana licenses of other states and so having marijuana in Utah, even though it is perfectly legal in the other state, is a crime here. Some prosecutors are a little more lenient when they see the defendant has a medical marijuana license from another state, but other prosecutors believe that marijuana is Satan’s tool of crime and so they will prosecute the case to the utmost degree.
Who knows? In the near future, Utah may adopt medical cannibis and pot smokers can rest a little more sound knowing they can smoke in their basement without having to worry about going to jail for getting a little buzzed on weed.