Infiltration of Matrix-Non-producers Weakens the Salmonella Biofilm and Impairs Its Antimicrobial Tolerance and Pathogenicity

Bacterial biofilms display a collective lifestyle, wherein the cells secrete extracellular polymeric substances (EPS) that helps in adhesion, aggregation, stability, and to protect the bacteria from antimicrobials. We asked whether the BPS could act as a public good for the biofilm and observed that infiltration of cells that do not produce matrix components weakened the biofilm of Salmonella enterica serovar Typhimurium. PS production was costly for the producing cells, as indicated by a significant reduction in the fitness of wild type (WT) cells during competitive planktonic growth relative to the non-producers. Infiltration frequency of non-producers in the biofilm showed a concomitant decrease in overall productivity. It was apparent in the confocal images that the non producing cells benefit from the BPS produced by the Wild Type (WT) to stay in the biofilm. The biofilm containing non-producing cells were more significantly susceptible to sodium hypochlorite and ciprofloxacin treatment than the WT biofilm. Biofilm infiltrated with non-producers delayed the pathogenesis, as tested in a murine model. The cell types were spatially assorted, with non producers being edged out in the biofilm. However, cellulose was found to act as a barrier to keep the non-producers away from the WT microcolony. Our results show that the infiltration of non-cooperating cell types can substantially weaken the biofilm making it vulnerable to antibacterials and delay their pathogenesis. Cellulose, a component of BPS, was shown to play a pivotal role of acting as the main public good, and to edge-out the non-producers away from the cooperating microcolony.

A Convex Optimization Framework for Almost Budget Balanced Allocation of a Divisible Good

We address the problem of allocating a single divisible good to a number of agents. The agents have concave valuation functions parameterized by a scalar type. The agents report only the type. The goal is to find allocatively efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria are of interest: the maximum ratio of budget surplus to efficient surplus, and the expected budget surplus, within the class of linear rebate functions. The goal is to minimize them. Assuming that the valuation functions are known, we show that both problems reduce to convex optimization problems, where the convex constraint sets are characterized by a continuum of half-plane constraints parameterized by the vector of reported types. We then propose a randomized relaxation of these problems by sampling constraints. The relaxed problem is a linear programming problem (LP). We then identify the number of samples needed for ``near-feasibility'' of the relaxed constraint set. Under some conditions on the valuation function, we show that value of the approximate LP is close to the optimal value. Simulation results show significant improvements of our proposed method over the Vickrey-Clarke-Groves (VCG) mechanism without rebates. In the special case of indivisible goods, the mechanisms in this paper fall back to those proposed by Moulin, by Guo and Conitzer, and by Gujar and Narahari, without any need for randomization. Extension of the proposed mechanisms to situations when the valuation functions are not known to the central planner are also discussed. Note to Practitioners-Our results will be useful in all resource allocation problems that involve gathering of information privately held by strategic users, where the utilities are any concave function of the allocations, and where the resource planner is not interested in maximizing revenue, but in efficient sharing of the resource. Such situations arise quite often in fair sharing of internet resources, fair sharing of funds across departments within the same parent organization, auctioning of public goods, etc. We study methods to achieve near budget balance by first collecting payments according to the celebrated VCG mechanism, and then returning as much of the collected money as rebates. Our focus on linear rebate functions allows for easy implementation. The resulting convex optimization problem is solved via relaxation to a randomized linear programming problem, for which several efficient solvers exist. This relaxation is enabled by constraint sampling. Keeping practitioners in mind, we identify the number of samples that assures a desired level of ``near-feasibility'' with the desired confidence level. Our methodology will occasionally require subsidy from outside the system. We however demonstrate via simulation that, if the mechanism is repeated several times over independent instances, then past surplus can support the subsidy requirements. We also extend our results to situations where the strategic users' utility functions are not known to the allocating entity, a common situation in the context of internet users and other problems.