Optimal strategy for public good production is set by balancing intertemporal trade-off between population growth rate and carrying capacity

Public goods are biomolecules that contribute to the community welfare. Their production can benefit populations in many ways, such as by providing access to previously unutilized resources. However, public good production has often been energetically costly, resulting in a reduction in the cellular growth rate. To reduce this cost, populations have evolved strategies to regulate biosynthesis of public good. Among these cell densities dependent regulation of public goods, as accomplished by quorum sensing, is a widely studied mechanism. Given that the fitness costs and benefits of public good production must be balanced, adoption of quorum sensing as a regulatory pathway by bacterial cells may have parallels with several economic principles that are used to study optimal investment decisions. Here, we explore the regulation of a public good, whose benefit is an increase in the carrying capacity, through experimental measurements of growth for engineered strains of Escherichia coli and analysis of those results using a modified logistic growth model. By varying the cell density at which the production of the public good was activated, we showed sharply-peaked optimum population fitness. Analysis further revealed that cell density associated with maximum public good benefits was determined by the trade-off between the cost of public good production, in terms of reduced growth rate, and benefits received from public good, in the form of increased carrying capacity. Moreover, our model showed that cells with luxRI quorum sensing seem to upregulate public good expression when the benefits from the production was immediate. These results demonstrate a case where a biological system apparently has evolved to optimize the timing of public good production to account for short-term costs and delays in reaping a future benefit.

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Adaptive significance of quorum sensing-dependent regulation of public goods by integration of growth rate: a trade-off between survival and efficiency

10.1101/042739 ◽

2016 ◽

Author(s):

Arvin Nickzad ◽

Eric Deziel

Keyword(s):

Growth Rate ◽

Quorum Sensing ◽

Public Goods ◽

Cell Density ◽

Cooperative Behavior ◽

Adaptive Significance ◽

Nutrient Concentrations ◽

Burkholderia Glumae ◽

Nutritional Conditions ◽

Extracellular Metabolites

Quorum sensing (QS) is a mechanism of communication used by bacteria to monitor cell density and coordinate cooperative behaviors. An emerging framework is that the adaptive significance of QS in regulation of production of costly extracellular metabolites (public goods) is to maintain the homeostasis of cooperation. We investigated the functionality of QS-dependent regulation of rhamnolipids, extracellular surface-active glycolipids promoting the social swarming motility behavior, inBurkholderia glumaeand found that QS is superfluous under rich nutritional conditions. In contrast, decreasing nutrient concentrations to reduce the growth rate amplifies rhamnolipid biosynthesis gene expression, revealing a system where QS-dependent regulation is triggered by the growth rate of the population rather than by its cell density. Our results provide evidence that the adaptive significance of QS in regulation of public goods is to maintain an optimized demand-driven supply of target cooperative behavior, wherein efficiency can be traded off against survival.

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Bacterial Quorum Sensing Stabilizes Cooperation by Optimizing Growth Strategies

Applied and Environmental Microbiology ◽

10.1128/aem.01945-16 ◽

2016 ◽

Vol 82 (22) ◽

pp. 6498-6506 ◽

Cited By ~ 21

Author(s):

Eric L. Bruger ◽

Christopher M. Waters

Keyword(s):

Growth Rate ◽

Quorum Sensing ◽

Experimental Evidence ◽

Fundamental Problem ◽

Growth Yield ◽

Cellular Growth ◽

Growth Strategies ◽

High Cell ◽

Content Type ◽

Cell Densities

ABSTRACTCommunication has been suggested as a mechanism to stabilize cooperation. In bacteria, chemical communication, termed quorum sensing (QS), has been hypothesized to fill this role, and extracellular public goods are often induced by QS at high cell densities. Here we show, with the bacteriumVibrio harveyi, that QS provides strong resistance against invasion of a QS defector strain by maximizing the cellular growth rate at low cell densities while achieving maximum productivity through protease upregulation at high cell densities. In contrast, QS mutants that act as defectors or unconditional cooperators maximize either the growth rate or the growth yield, respectively, and thus are less fit than the wild-type QS strain. Our findings provide experimental evidence that regulation mediated by microbial communication can optimize growth strategies and stabilize cooperative phenotypes by preventing defector invasion, even under well-mixed conditions. This effect is due to a combination of responsiveness to environmental conditions provided by QS, lowering of competitive costs when QS is not induced, and pleiotropic constraints imposed on defectors that do not perform QS.IMPORTANCECooperation is a fundamental problem for evolutionary biology to explain. Conditional participation through phenotypic plasticity driven by communication is a potential solution to this dilemma. Thus, among bacteria, QS has been proposed to be a proximate stabilizing mechanism for cooperative behaviors. Here, we empirically demonstrate that QS inV. harveyiprevents cheating and subsequent invasion by nonproducing defectors by maximizing the growth rate at low cell densities and the growth yield at high cell densities, whereas an unconditional cooperator is rapidly driven to extinction by defectors. Our findings provide experimental evidence that QS regulation prevents the invasion of cooperative populations by QS defectors even under unstructured conditions, and they strongly support the role of communication in bacteria as a mechanism that stabilizes cooperative traits.

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Cheater suppression and spite through quorum sensing

10.1101/2021.06.16.448736 ◽

2021 ◽

Author(s):

Alexander S Moffett ◽

Peter J Thomas ◽

Michael Hinczewski ◽

Andrew W Eckford

Keyword(s):

Population Dynamics ◽

Quorum Sensing ◽

Public Good ◽

Bacterial Population ◽

Extinction Time ◽

Population Extinction ◽

Good Production ◽

Alternative Sources ◽

Demographic Noise ◽

The Cost

The evolutionary consequences of quorum sensing in regulating bacterial cooperation are not fully understood. In this study, we reveal unexpected consequences of regulating public good production through quorum sensing on bacterial population dynamics, showing that quorum sensing can be a "spiteful" alternative to unregulated production. We analyze a birth-death model of bacterial population dynamics accounting for public good production and the presence of non-producing cheaters. Our model demonstrates that when demographic noise is a factor, the consequences of controlling public good production according to quorum sensing depend on the cost of public good production and the presence of alternative sources of the fitness benefits provided by public goods. When public good production is inexpensive, quorum sensing is a spiteful alternative to unconditional production, in terms of the mean population extinction time. When costs are higher, quorum sensing becomes a selfish strategy for the producing strain, both stabilizing cooperation and decreasing the risk of population extinction.

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Initial cell density encodes proliferative potential in cancer cell populations

Scientific Reports ◽

10.1038/s41598-021-85406-z ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Chiara Enrico Bena ◽

Marco Del Giudice ◽

Alice Grob ◽

Thomas Gueudré ◽

Mattia Miotto ◽

...

Keyword(s):

Growth Rate ◽

Population Growth ◽

Cancer Cells ◽

Cell Density ◽

Cancer Cell ◽

Initial Density ◽

Logistic Growth ◽

Cell Populations ◽

Initial Cell ◽

Initial Cell Density

AbstractIndividual cells exhibit specific proliferative responses to changes in microenvironmental conditions. Whether such potential is constrained by the cell density throughout the growth process is however unclear. Here, we identify a theoretical framework that captures how the information encoded in the initial density of cancer cell populations impacts their growth profile. By following the growth of hundreds of populations of cancer cells, we found that the time they need to adapt to the environment decreases as the initial cell density increases. Moreover, the population growth rate shows a maximum at intermediate initial densities. With the support of a mathematical model, we show that the observed interdependence of adaptation time and growth rate is significantly at odds both with standard logistic growth models and with the Monod-like function that governs the dependence of the growth rate on nutrient levels. Our results (i) uncover and quantify a previously unnoticed heterogeneity in the growth dynamics of cancer cell populations; (ii) unveil how population growth may be affected by single-cell adaptation times; (iii) contribute to our understanding of the clinically-observed dependence of the primary and metastatic tumor take rates on the initial density of implanted cancer cells.

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Neighborhood size-effects in nonlinear public goods games

10.1101/347401 ◽

2018 ◽

Cited By ~ 2

Author(s):

Gregory J. Kimmel ◽

Philip Gerlee ◽

Joel S. Brown ◽

Philipp M. Altrock

Keyword(s):

Public Goods ◽

Public Good ◽

Size Effects ◽

Evolutionary Dynamics ◽

Logistic Growth ◽

Neighborhood Size ◽

Frequency Dependent ◽

Frequency Dependent Selection ◽

The Public ◽

Public Goods Games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics’ equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.

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Selection of horizontal gene transfer through public good production

10.1101/315960 ◽

2018 ◽

Cited By ~ 2

Author(s):

Tatiana Dimitriu ◽

Dusan Misevic ◽

Julien Benard Capelle ◽

Ariel B Lindner ◽

Sam P Brown ◽

...

Keyword(s):

Public Goods ◽

Public Good ◽

Horizontal Transfer ◽

Good Genes ◽

Selective Pressures ◽

Good Production ◽

Genes Encoding ◽

Selection For ◽

Benefits And Costs ◽

Selection Of

AbstractIn bacteria, cooperative genes encoding public good molecules are preferentially located on mobile genetic elements (MGEs), and horizontal transfer of MGEs favours the maintenance of public good cooperation. The rate of horizontal transfer itself can evolve in response to selective pressures acting on both MGEs and bacterial hosts: benefits and costs of infectious spread, but also indirect effects of MGE genes to the host. We show here that carriage of public good genes on MGEs can generate another indirect selection for MGE transfer. Transfer increases public good production and, when relatedness is sufficiently high, public goods benefit preferentially genotypes with high transfer ability. Both our simulations and experiments indicate that transfer is not required to occur among kin, provided that public goods still benefit kin. Public good gene mobility thus aligns the interests of chromosomes and MGEs concerning transfer, promoting gene exchange among bacteria.

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Quorum Sensing Protects Pseudomonas aeruginosa against Cheating by Other Species in a Laboratory Coculture Model

Journal of Bacteriology ◽

10.1128/jb.00482-15 ◽

2015 ◽

Vol 197 (19) ◽

pp. 3154-3159 ◽

Cited By ~ 28

Author(s):

Nicole E. Smalley ◽

Dingding An ◽

Matthew R. Parsek ◽

Josephine R. Chandler ◽

Ajai A. Dandekar

Keyword(s):

Pseudomonas Aeruginosa ◽

Quorum Sensing ◽

Public Goods ◽

Public Good ◽

Hydrogen Cyanide ◽

Cooperative Behavior ◽

Bacterial Species ◽

Cell Communication ◽

Content Type ◽

Burkholderia Multivorans

ABSTRACTMany species of bacteria use a cell-cell communication system called quorum sensing (QS) to coordinate group activities. QS systems frequently regulate the production of exoproducts. Some of these products, such as proteases, are “public goods” that are shared among the population and vulnerable to cheating by nonproducing members of the population. Because the QS system of the opportunistic pathogenPseudomonas aeruginosaregulates several public goods, it can serve as a model for studying cooperation. Bacteria also commonly regulate antimicrobial production through QS. In this study, we focused on the hypothesis that QS-regulated antimicrobials may be important forP. aeruginosato protect against cheating by another bacterial species,Burkholderia multivorans.We assessed laboratory cocultures ofP. aeruginosaandB. multivoransand investigated the importance of threeP. aeruginosaQS-regulated antimicrobials, hydrogen cyanide, rhamnolipids, and phenazines, for competition. We found thatP. aeruginosadominates cocultures withB. multivoransand that the three antimicrobials together promoteP. aeruginosacompetitiveness, with hydrogen cyanide contributing the greatest effect. We show that these QS-regulated antimicrobials are also critical forP. aeruginosato preventB. multivoransfrom cheating under nutrient conditions where both species require aP. aeruginosaquorum-regulated protease for growth. Together our results highlight the importance of antimicrobials in protecting cooperating populations from exploitation by other species that can act as cheaters.IMPORTANCECooperative behaviors are threatened by social cheating, wherein individuals do not produce but nonetheless benefit from shared public goods. Bacteria have been shown to use several genetic mechanisms to restrain the emergence of cheaters from within the population, but public goods might also be used by other bacterial species in the vicinity. We demonstrate that a public good produced byPseudomonas aeruginosacan be used by another species,Burkholderia multivorans, to obtain carbon and energy. We also show thatP. aeruginosaantimicrobials that are coregulated with the public good prevent invasion by the cheating species. Our results demonstrate that cross-species cheating can occur and that coregulation of public goods with antimicrobials may stabilize cooperative behavior in mixed microbial communities.

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Penerapan Persamaan Diferensial Verhulst dalam Menentukan Proyeksi Penduduk di Kabupaten Tulungagung

Jurnal Fourier ◽

10.14421/fourier.2018.72.87-102 ◽

2018 ◽

Vol 7 (2) ◽

pp. 87-102

Author(s):

Dewi Anggreini

Keyword(s):

Growth Rate ◽

Population Growth ◽

Growth Model ◽

Carrying Capacity ◽

Applied Mathematics ◽

Logistic Growth ◽

Second Stage ◽

The Subject ◽

Logistic Growth Model ◽

To Come

Penelitian ini bertujuan menentukan proyeksi pertumbuhan penduduk di Kabupaten Tulungagung provinsi Jawa Timur dengan model persamaan diferensial Verhulst berdasarkan laju pertumbuhan dan daya tampung (carrying capacity). Target khusus dari hasil penelitian ini adalah model pertumbuhan logistik bisa digunakan sebagai alat untuk mengetahui proyeksi pertumbuhan penduduk berdasarkan laju pertumbuhan dan daya tampung dibeberapa daerah di Indonesia. Metode riset yang digunakan pada tahap pertama adalah menentukan subjek penelitian dan tahap Kedua adalah (1) mengumpulkan data penelitian (2) analisis data dan terakhir menarik kesimpulan. Data penelitian ini diperoleh dari BPS Kabupaten Tulungagung yaitu jumlah penduduk dari tahun 2010-2016. Hasil Penelitian menunjukkan bahwa: 1) Besarnya nilai carrying capacity yang membatasi penduduk di Kabupaten Tulungagung adalah sebesar 1.089.103,3. 2) Laju pertumbuhan intrinsik penduduk di kabupaten Tulungagung dengan menggunakan Model pertumbuhan logistik adalah sebesar r = 0,07480. 3) Jumlah penduduk di Kabupaten Tulungagung pada tahun 2025 dari hasil estimasi menggunakan model pertumbuhan logistik adalah sebesar 1.055.578 jiwa. 4) Proyeksi jumlah penduduk di Kabupaten Tulungagung lebih tepat menggunakan model logistik I dengan persamaannya . Penelitian ini diharapkan dapat bermanfaat bagi semua pihak khususnya pada bidang matematika terapan serta metode dalam menghitung pertumbuhan populasi di suatu daerah pada periode yang akan datang. [This study aims to determine the projected population growth in Tulungagung Regency of East Java province with a model of Verhulst differential equations based on growth rate and carrying capacity. The specific target of this research is logistic growth model can be used as a tool to know the projection of population growth based on growth rate and capacity in some regions in Indonesia. Research methods used in the first stage is to determine the subject of research and the second stage is (1) collect research data (2) data analysis and last draw conclusions. The data of this research is obtained from BPS of Tulungagung Regency that is population from 2010-2016. The results showed that: 1) The amount of carrying capacity that limits the population in Tulungagung Regency is equal 1.089.103,3. 2) The intrinsic growth rate of the population in Tulungagung district using the logistic growth model is r = 0,07480 3) The population in Tulungagung District in 2025 from the estimation using the logistic growth model is 1.055.578 soul, 4) The projection of population in Tulungagung is more appropriate using the logistic model I with the equation . This study is expected to be useful for all parties, especially in the field of applied mathematics and methods in calculating population growth in an area in the period to come.]

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Extinction times in diffusive public good population dynamics

10.1101/424580 ◽

2018 ◽

Author(s):

Gregory J. Kimmel ◽

Philip Gerlee ◽

Philipp M. Altrock

Keyword(s):

Growth Rate ◽

Public Goods ◽

Public Good ◽

Evolutionary Dynamics ◽

Tragedy Of The Commons ◽

Free Rider ◽

Extinction Time ◽

Free Riders ◽

Time To Extinction ◽

The Commons

AbstractThe co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and population structure in space. As co-evolving populations grow into a spatial domain, their initial spatial arrangement, as well as their growth rate differences determine the dynamics. Here, we are interested in the dynamics of producers and free-rider co-evolution in the context of an ecological public good that is produced by a sub-population but evokes growth benefits to all individuals. We consider the spatial growth dynamics in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by birth, death and diffusion. Typically, one population goes extinct. We find that uncorrelated initial spatial structures do not influence the time to extinction in comparison to the well-mixed system. We derive a slow manifold solution in order to estimate the time to extinction of either free-riders or producers. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated to improve the extinction time estimate by a simple superposition of the two times. Our results show that local effects of spatial dynamics evolve independently of the dynamics of the mean populations. Our considerations provide quantitative predictions for the transient dynamics of cooperative traits under pressure of extinction, and a potential experiment to derive elusive details of the fitness function of an ecological public goods game through extinction time observations.Author SummaryEcological public goods (PG) relationships emerge in growing cellular populations, for example between bacteria and cancer cells. We study the eco-evolutionary dynamics of a PG in populations that grow in space. In our model, public good-producer cells and free-rider cells can grow according to their own birth and death rates. Co-evolution occurs due to public good-driven surplus in the intrinsic growth rates and a cost to producers. A net growth rate benefit to free-riders leads to the well-known tragedy of the commons in which producers go extinct. What is often omitted from discussions is the time scale on which this extinction can occur, especially in spatial populations. We derive analytical estimates of the time to extinction in different spatial settings, and identify spatial scenarios in which extinction takes long enough such that the tragedy of the commons never occurs within the lifetime of the populations. Using numerical simulations we analyze the deviations from analytical predictions. Our results have direct implications for inferring ecological public good game properties from in vitro and in vivo experimental observations.

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