Understanding the evolution of novel physiological traits is highly relevant for expanding the ch... more Understanding the evolution of novel physiological traits is highly relevant for expanding the characterization and manipulation of biological systems. Acquisition of new traits can be achieved through horizontal gene transfer (HGT). Here, we investigate drivers that promote or deter the maintenance of HGT-driven degeneracy, occurring when processes accomplish identical functions through nonidentical components. Subsequent evolution can optimize newly acquired functions; for example, beneficial alleles identified in an engineered Methylorubrum extorquens strain allowed it to utilize a “Foreign” formaldehyde oxidation pathway substituted for its Native pathway for methylotrophic growth. We examined the fitness consequences of interactions between these alleles when they were combined with the Native pathway or both (Dual) pathways. Unlike the Foreign pathway context where they evolved, these alleles were often neutral or deleterious when moved into these alternative genetic backgroun...
ABSTRACTThe potency and indiscriminate nature of formaldehyde reactivity upon biological molecule... more ABSTRACTThe potency and indiscriminate nature of formaldehyde reactivity upon biological molecules make it a universal stressor. However, some organisms such as Methylorubrum extorquens possess means to rapidly and effectively mitigate formaldehyde-induced damage. EfgA is a recently identified formaldehyde sensor predicted to halt translation in response to elevated formaldehyde as a means to protect cells. Herein, we investigate growth and changes in gene expression to understand how M. extorquens responds to formaldehyde with and without the EfgA-formaldehyde-mediated translational response, and how this mechanism compares to antibiotic-mediated translation inhibition. These distinct mechanisms of translation inhibition have notable differences: they each involve different specific players and in addition, formaldehyde also acts as a general, multi-target stressor and a potential carbon source. We present findings demonstrating that in addition to its characterized impact on trans...
ABSTRACTFor bacteria to thrive they must be well-adapted to their environmental niche, which may ... more ABSTRACTFor bacteria to thrive they must be well-adapted to their environmental niche, which may involve specialized metabolism, timely adaptation to shifting environments, and/or the ability to mitigate numerous stressors. These attributes are highly dependent on cellular machinery that can sense both the external and intracellular environment. Methylorubrum extorquens is an extensively studied facultative methylotroph, an organism that can use single-carbon compounds as their sole source of carbon and energy. In methylotrophic metabolism, carbon flows through formaldehyde as a central metabolite; thus, formaldehyde is both an obligate metabolite and a metabolic stressor. Via the one-carbon dissimilation pathway, free formaldehyde is rapidly incorporated by formaldehyde activating enzyme (Fae), which is constitutively expressed at high levels. In the presence of elevated formaldehyde levels, a recently identified formaldehyde-sensing protein, EfgA, induces growth arrest. Herein, we...
As selection frequently favors non-cooperating defectors in mixed populations with cooperators, m... more As selection frequently favors non-cooperating defectors in mixed populations with cooperators, mechanisms that promote cooperation stability clearly exist. One potential mechanism is bacterial cell-to-cell communication, quorum sensing (QS), which can allow cooperators to prevent invasion by defectors. However, the impact of QS on widespread maintenance of cooperation in well-mixed conditions has not been experimentally demonstrated over extended evolutionary timescales. Here, we use wild-type (‘WT’) Vibrio harveyi that regulates cooperation with QS and an unconditionally cooperating (‘UC’) mutant to examine the evolutionary origins and subsequent dynamics of novel defectors during a long-term evolution experiment. We found that UC lineages were completely outcompeted by defectors, whereas functioning QS enabled the maintenance of cooperative variants in most WT populations. Sequencing of evolved populations revealed multiple luxR mutations that swept the UC lineages. However, the ...
Applied and environmental microbiology, Jan 15, 2018
Quorum sensing (QS) is a form of bacterial chemical communication that regulates cellular phenoty... more Quorum sensing (QS) is a form of bacterial chemical communication that regulates cellular phenotypes, including certain cooperative behaviors, in response to environmental and demographic changes. Despite the existence of proposed mechanisms that stabilize QS against defector exploitation, it is unclear if or how QS cooperators can proliferate in some model systems in populations mostly consisting of defectors. We predicted that growth in fragmented subpopulations could allow QS cooperators to invade a QS defector population. This could occur despite cooperators having lower relative fitnesses than defectors due to favored weighting of genotypes that produce larger populations of bacteria. Mixed metapopulations of QS-proficient or unconditional cooperators and QS defectors were diluted and fragmented into isolated subpopulations in an environment that requires QS-regulated public good production to achieve larger population yields. Under these conditions, we observed global invasion...
Second messengers are intracellular molecules regulated by external stimuli known as first messen... more Second messengers are intracellular molecules regulated by external stimuli known as first messengers that are used for rapid organismal responses to dynamic environmental changes. Cyclic di-AMP (c-di-AMP) is a relatively newly discovered second messenger implicated in cell wall homeostasis in many pathogenic bacteria. C-di-AMP is synthesized from ATP by diadenylyl cyclases (DAC) and degraded by specific c-di-AMP phosphodiesterases (PDE). C-di-AMP DACs and PDEs are present in all sequenced cyanobacteria, suggesting roles for c-di-AMP in the physiology and/or development of these organisms. Despite conservation of these genes across numerous cyanobacteria, the functional roles of c-di-AMP in cyanobacteria have not been well-investigated. In a unique feature of cyanobacteria, phylogenetic analysis indicated that the broadly conserved DAC, related to CdaA/DacA, is always co-associated in an operon with genes critical for controlling cell wall synthesis. To investigate phenotypes regula...
A core phosphorelay pathway that directs developmental transitions and cellular asymmetries in Ag... more A core phosphorelay pathway that directs developmental transitions and cellular asymmetries in Agrobacterium tumefaciens putatively includes two overlapping, integrated phosphorelays. One of these phosphorelays putatively includes at least four histidine sensor kinase homologues, DivJ, PleC, PdhS1, and PdhS2, and at least two response regulators, DivK and PleD. Previously we demonstrated that PdhS2 reciprocally regulates biofilm formation and swimming motility. In the current study we further dissect the role and regulatory impact of PdhS2 in A. tumefaciens revealing that PdhS2-dependent effects on attachment and motility require the response regulator, DivK, but do not require PdhS2 autokinase or phosphotransfer activities. We also demonstrate that PdhS2 regulation of biofilm formation is dependent upon multiple diguanylate cyclases, including PleD, DgcA, and DgcB, implying that PdhS2 regulation of this process intersects with pathways regulating levels of the second messenger cycl...
Vibrio vulnificus is an estuarine bacterium and potent opportunistic human pathogen. It enters th... more Vibrio vulnificus is an estuarine bacterium and potent opportunistic human pathogen. It enters the food chain by asymptomatically colonizing a variety of marine organisms, most notably oysters. Expression of the brp -encoded extracellular polysaccharide, which enhances cell-surface adherence, is regulated by cyclic di-GMP (c-di-GMP) and the activator BrpT. The Vibrio cholerae and Vibrio parahaemolyticus homologs VpsT and CpsQ, directly bind c-di-GMP via a novel W[F/L/M][T/S]R motif, and c-di-GMP binding is absolutely required for activity. Notably, BrpT belongs to a distinct subclass of VpsT-like regulators that harbor a proline in the third position of the c-di-GMP binding motif (WLPR), and the impact of this change on activity is unknown. We show that the brp locus is organized as two linked operons with BrpT specifically binding to promoters upstream of brpA and brpH . Expression data and structural modeling suggested that BrpT might be less dependent on c-di-GMP binding for acti...
The aquatic bacterium and human intestinal pathogen, Vibrio cholerae, senses and responds to a va... more The aquatic bacterium and human intestinal pathogen, Vibrio cholerae, senses and responds to a variety of environment-specific cues to regulate biofilm formation. Specifically, the polyamines norspermidine and spermidine enhance and repress V. cholerae biofilm formation, respectively. These effects are relevant for understanding V. cholerae pathogenicity and are mediated through the periplasmic binding protein, NspS, and the transmembrane c-di-GMP phosphodiesterase MbaA. However, the levels of spermidine required to inhibit biofilm formation through this pathway are unlikely to be encountered by V. cholerae in aquatic reservoirs or within the human host during infection. We therefore hypothesized that other polyamines in the gastrointestinal tract may control V. cholerae biofilm formation at physiological levels. The tetramine spermine has been reported to be present at nearly 50 micromolar concentrations in the intestinal lumen. Here, we report that spermine acts as an exogenous cu...
Genome sequencing has revolutionized studies using experimental evolution of microbes because it ... more Genome sequencing has revolutionized studies using experimental evolution of microbes because it readily provides comprehensive insight into the genetic bases of adaptation. In this perspective we discuss applications of sequencing-based technologies used to study evolution in microbes, including genomic sequencing of isolated evolved clones and mixed evolved populations, and also the use of sequencing methods to follow the fate of introduced variations, whether neutral barcodes or variants introduced by genome editing. Collectively, these sequencing-based approaches have vastly advanced the examination of evolution in the lab, as well as begun to synthesize this work with examination of the genetic bases of adaptation and evolutionary dynamics within natural populations.
The motile-to-sessile transition is an important lifestyle switch in diverse bacteria and is ofte... more The motile-to-sessile transition is an important lifestyle switch in diverse bacteria and is often regulated by the intracellular second messenger cyclic diguanylate monophosphate (c-di-GMP). In general, high c-di-GMP concentrations promote attachment to surfaces, whereas cells with low levels of signal remain motile. In the plant pathogen Agrobacterium tumefaciens, c-di-GMP controls attachment and biofilm formation via regulation of a unipolar polysaccharide (UPP) adhesin. The levels of c-di-GMP in A. tumefaciens are controlled in part by the dual-function diguanylate cyclase-phosphodiesterase (DGC-PDE) protein DcpA. In this study, we report that DcpA possesses both c-di-GMP synthesizing and degrading activities in heterologous and native genetic backgrounds, a binary capability that is unusual among GGDEF-EAL domain-containing proteins. DcpA activity is modulated by a pteridine reductase called PruA, with DcpA acting as a PDE in the presence of PruA and a DGC in its absence. PruA ...
The second messenger nucleotide cyclic diadenylate monophosphate (c-di-AMP) has been identified i... more The second messenger nucleotide cyclic diadenylate monophosphate (c-di-AMP) has been identified in several species of Gram positive bacteria and Chlamydia trachomatis. This molecule has been associated with bacterial cell division, cell wall biosynthesis and phosphate metabolism, and with induction of type I interferon responses by host cells. We demonstrate that B. burgdorferi produces a c-di-AMP synthase, which we designated CdaA. Both CdaA and c-di-AMP levels are very low in cultured B. burgdorferi, and no conditions were identified under which cdaA mRNA was differentially expressed. A mutant B. burgdorferi was produced that expresses high levels of CdaA, yet steady state borrelial c-di-AMP levels did not change, apparently due to degradation by the native DhhP phosphodiesterase. The function(s) of c-di-AMP in the Lyme disease spirochete remains enigmatic.
IEEE Transactions on Visualization and Computer Graphics, 2000
Chromium Renderserver (CRRS) is software infrastructure that provides the ability for one or more... more Chromium Renderserver (CRRS) is software infrastructure that provides the ability for one or more users to run and view image output from unmodified, interactive OpenGL and X11 applications on a remote, parallel computational platform equipped with graphics hardware accelerators via industry-standard Layer 7 network protocols and client viewers. The new contributions of this work include a solution to the problem of synchronizing X11 and OpenGL command streams, remote delivery of parallel hardware-accelerated rendering, and a performance analysis of several different optimizations that are generally applicable to a variety of rendering architectures. CRRS is fully operational, Open Source software.
Traditional models of ecosystems often assume that the species composing an unperturbed ecosystem... more Traditional models of ecosystems often assume that the species composing an unperturbed ecosystem become fixed so that only the relative abundances of the species change over time. Such ecosystems are said to have reached an optimal fixed point. However, recent work has suggested that neutral evolutionary processes can significantly alter the species composition of an ecosystem, allowing the ecosystem to exist in a dynamic steady state. Here, we investigate the stability of ecosystems and the nature of the equilibrium that forms using the digital evolution platform Avida, tracking evolving ecosystems over thousands of generations. We find that the communities that form are remarkably stable, and do not experience a significant loss of diversity in the long run even in experimental treatments where the communities suffer catastrophic population bottlenecks. When diversity rebounds, ecological communities are reconstituted in a different form than the one that was destroyed, but this difference is comparable to the difference the system would have accumulated if it had been left untouched. Thus, digital ecological communities exist in a dynamic steady state, which ultimately eliminates the effect of historical disturbances.
Understanding the evolution of novel physiological traits is highly relevant for expanding the ch... more Understanding the evolution of novel physiological traits is highly relevant for expanding the characterization and manipulation of biological systems. Acquisition of new traits can be achieved through horizontal gene transfer (HGT). Here, we investigate drivers that promote or deter the maintenance of HGT-driven degeneracy, occurring when processes accomplish identical functions through nonidentical components. Subsequent evolution can optimize newly acquired functions; for example, beneficial alleles identified in an engineered Methylorubrum extorquens strain allowed it to utilize a “Foreign” formaldehyde oxidation pathway substituted for its Native pathway for methylotrophic growth. We examined the fitness consequences of interactions between these alleles when they were combined with the Native pathway or both (Dual) pathways. Unlike the Foreign pathway context where they evolved, these alleles were often neutral or deleterious when moved into these alternative genetic backgroun...
ABSTRACTThe potency and indiscriminate nature of formaldehyde reactivity upon biological molecule... more ABSTRACTThe potency and indiscriminate nature of formaldehyde reactivity upon biological molecules make it a universal stressor. However, some organisms such as Methylorubrum extorquens possess means to rapidly and effectively mitigate formaldehyde-induced damage. EfgA is a recently identified formaldehyde sensor predicted to halt translation in response to elevated formaldehyde as a means to protect cells. Herein, we investigate growth and changes in gene expression to understand how M. extorquens responds to formaldehyde with and without the EfgA-formaldehyde-mediated translational response, and how this mechanism compares to antibiotic-mediated translation inhibition. These distinct mechanisms of translation inhibition have notable differences: they each involve different specific players and in addition, formaldehyde also acts as a general, multi-target stressor and a potential carbon source. We present findings demonstrating that in addition to its characterized impact on trans...
ABSTRACTFor bacteria to thrive they must be well-adapted to their environmental niche, which may ... more ABSTRACTFor bacteria to thrive they must be well-adapted to their environmental niche, which may involve specialized metabolism, timely adaptation to shifting environments, and/or the ability to mitigate numerous stressors. These attributes are highly dependent on cellular machinery that can sense both the external and intracellular environment. Methylorubrum extorquens is an extensively studied facultative methylotroph, an organism that can use single-carbon compounds as their sole source of carbon and energy. In methylotrophic metabolism, carbon flows through formaldehyde as a central metabolite; thus, formaldehyde is both an obligate metabolite and a metabolic stressor. Via the one-carbon dissimilation pathway, free formaldehyde is rapidly incorporated by formaldehyde activating enzyme (Fae), which is constitutively expressed at high levels. In the presence of elevated formaldehyde levels, a recently identified formaldehyde-sensing protein, EfgA, induces growth arrest. Herein, we...
As selection frequently favors non-cooperating defectors in mixed populations with cooperators, m... more As selection frequently favors non-cooperating defectors in mixed populations with cooperators, mechanisms that promote cooperation stability clearly exist. One potential mechanism is bacterial cell-to-cell communication, quorum sensing (QS), which can allow cooperators to prevent invasion by defectors. However, the impact of QS on widespread maintenance of cooperation in well-mixed conditions has not been experimentally demonstrated over extended evolutionary timescales. Here, we use wild-type (‘WT’) Vibrio harveyi that regulates cooperation with QS and an unconditionally cooperating (‘UC’) mutant to examine the evolutionary origins and subsequent dynamics of novel defectors during a long-term evolution experiment. We found that UC lineages were completely outcompeted by defectors, whereas functioning QS enabled the maintenance of cooperative variants in most WT populations. Sequencing of evolved populations revealed multiple luxR mutations that swept the UC lineages. However, the ...
Applied and environmental microbiology, Jan 15, 2018
Quorum sensing (QS) is a form of bacterial chemical communication that regulates cellular phenoty... more Quorum sensing (QS) is a form of bacterial chemical communication that regulates cellular phenotypes, including certain cooperative behaviors, in response to environmental and demographic changes. Despite the existence of proposed mechanisms that stabilize QS against defector exploitation, it is unclear if or how QS cooperators can proliferate in some model systems in populations mostly consisting of defectors. We predicted that growth in fragmented subpopulations could allow QS cooperators to invade a QS defector population. This could occur despite cooperators having lower relative fitnesses than defectors due to favored weighting of genotypes that produce larger populations of bacteria. Mixed metapopulations of QS-proficient or unconditional cooperators and QS defectors were diluted and fragmented into isolated subpopulations in an environment that requires QS-regulated public good production to achieve larger population yields. Under these conditions, we observed global invasion...
Second messengers are intracellular molecules regulated by external stimuli known as first messen... more Second messengers are intracellular molecules regulated by external stimuli known as first messengers that are used for rapid organismal responses to dynamic environmental changes. Cyclic di-AMP (c-di-AMP) is a relatively newly discovered second messenger implicated in cell wall homeostasis in many pathogenic bacteria. C-di-AMP is synthesized from ATP by diadenylyl cyclases (DAC) and degraded by specific c-di-AMP phosphodiesterases (PDE). C-di-AMP DACs and PDEs are present in all sequenced cyanobacteria, suggesting roles for c-di-AMP in the physiology and/or development of these organisms. Despite conservation of these genes across numerous cyanobacteria, the functional roles of c-di-AMP in cyanobacteria have not been well-investigated. In a unique feature of cyanobacteria, phylogenetic analysis indicated that the broadly conserved DAC, related to CdaA/DacA, is always co-associated in an operon with genes critical for controlling cell wall synthesis. To investigate phenotypes regula...
A core phosphorelay pathway that directs developmental transitions and cellular asymmetries in Ag... more A core phosphorelay pathway that directs developmental transitions and cellular asymmetries in Agrobacterium tumefaciens putatively includes two overlapping, integrated phosphorelays. One of these phosphorelays putatively includes at least four histidine sensor kinase homologues, DivJ, PleC, PdhS1, and PdhS2, and at least two response regulators, DivK and PleD. Previously we demonstrated that PdhS2 reciprocally regulates biofilm formation and swimming motility. In the current study we further dissect the role and regulatory impact of PdhS2 in A. tumefaciens revealing that PdhS2-dependent effects on attachment and motility require the response regulator, DivK, but do not require PdhS2 autokinase or phosphotransfer activities. We also demonstrate that PdhS2 regulation of biofilm formation is dependent upon multiple diguanylate cyclases, including PleD, DgcA, and DgcB, implying that PdhS2 regulation of this process intersects with pathways regulating levels of the second messenger cycl...
Vibrio vulnificus is an estuarine bacterium and potent opportunistic human pathogen. It enters th... more Vibrio vulnificus is an estuarine bacterium and potent opportunistic human pathogen. It enters the food chain by asymptomatically colonizing a variety of marine organisms, most notably oysters. Expression of the brp -encoded extracellular polysaccharide, which enhances cell-surface adherence, is regulated by cyclic di-GMP (c-di-GMP) and the activator BrpT. The Vibrio cholerae and Vibrio parahaemolyticus homologs VpsT and CpsQ, directly bind c-di-GMP via a novel W[F/L/M][T/S]R motif, and c-di-GMP binding is absolutely required for activity. Notably, BrpT belongs to a distinct subclass of VpsT-like regulators that harbor a proline in the third position of the c-di-GMP binding motif (WLPR), and the impact of this change on activity is unknown. We show that the brp locus is organized as two linked operons with BrpT specifically binding to promoters upstream of brpA and brpH . Expression data and structural modeling suggested that BrpT might be less dependent on c-di-GMP binding for acti...
The aquatic bacterium and human intestinal pathogen, Vibrio cholerae, senses and responds to a va... more The aquatic bacterium and human intestinal pathogen, Vibrio cholerae, senses and responds to a variety of environment-specific cues to regulate biofilm formation. Specifically, the polyamines norspermidine and spermidine enhance and repress V. cholerae biofilm formation, respectively. These effects are relevant for understanding V. cholerae pathogenicity and are mediated through the periplasmic binding protein, NspS, and the transmembrane c-di-GMP phosphodiesterase MbaA. However, the levels of spermidine required to inhibit biofilm formation through this pathway are unlikely to be encountered by V. cholerae in aquatic reservoirs or within the human host during infection. We therefore hypothesized that other polyamines in the gastrointestinal tract may control V. cholerae biofilm formation at physiological levels. The tetramine spermine has been reported to be present at nearly 50 micromolar concentrations in the intestinal lumen. Here, we report that spermine acts as an exogenous cu...
Genome sequencing has revolutionized studies using experimental evolution of microbes because it ... more Genome sequencing has revolutionized studies using experimental evolution of microbes because it readily provides comprehensive insight into the genetic bases of adaptation. In this perspective we discuss applications of sequencing-based technologies used to study evolution in microbes, including genomic sequencing of isolated evolved clones and mixed evolved populations, and also the use of sequencing methods to follow the fate of introduced variations, whether neutral barcodes or variants introduced by genome editing. Collectively, these sequencing-based approaches have vastly advanced the examination of evolution in the lab, as well as begun to synthesize this work with examination of the genetic bases of adaptation and evolutionary dynamics within natural populations.
The motile-to-sessile transition is an important lifestyle switch in diverse bacteria and is ofte... more The motile-to-sessile transition is an important lifestyle switch in diverse bacteria and is often regulated by the intracellular second messenger cyclic diguanylate monophosphate (c-di-GMP). In general, high c-di-GMP concentrations promote attachment to surfaces, whereas cells with low levels of signal remain motile. In the plant pathogen Agrobacterium tumefaciens, c-di-GMP controls attachment and biofilm formation via regulation of a unipolar polysaccharide (UPP) adhesin. The levels of c-di-GMP in A. tumefaciens are controlled in part by the dual-function diguanylate cyclase-phosphodiesterase (DGC-PDE) protein DcpA. In this study, we report that DcpA possesses both c-di-GMP synthesizing and degrading activities in heterologous and native genetic backgrounds, a binary capability that is unusual among GGDEF-EAL domain-containing proteins. DcpA activity is modulated by a pteridine reductase called PruA, with DcpA acting as a PDE in the presence of PruA and a DGC in its absence. PruA ...
The second messenger nucleotide cyclic diadenylate monophosphate (c-di-AMP) has been identified i... more The second messenger nucleotide cyclic diadenylate monophosphate (c-di-AMP) has been identified in several species of Gram positive bacteria and Chlamydia trachomatis. This molecule has been associated with bacterial cell division, cell wall biosynthesis and phosphate metabolism, and with induction of type I interferon responses by host cells. We demonstrate that B. burgdorferi produces a c-di-AMP synthase, which we designated CdaA. Both CdaA and c-di-AMP levels are very low in cultured B. burgdorferi, and no conditions were identified under which cdaA mRNA was differentially expressed. A mutant B. burgdorferi was produced that expresses high levels of CdaA, yet steady state borrelial c-di-AMP levels did not change, apparently due to degradation by the native DhhP phosphodiesterase. The function(s) of c-di-AMP in the Lyme disease spirochete remains enigmatic.
IEEE Transactions on Visualization and Computer Graphics, 2000
Chromium Renderserver (CRRS) is software infrastructure that provides the ability for one or more... more Chromium Renderserver (CRRS) is software infrastructure that provides the ability for one or more users to run and view image output from unmodified, interactive OpenGL and X11 applications on a remote, parallel computational platform equipped with graphics hardware accelerators via industry-standard Layer 7 network protocols and client viewers. The new contributions of this work include a solution to the problem of synchronizing X11 and OpenGL command streams, remote delivery of parallel hardware-accelerated rendering, and a performance analysis of several different optimizations that are generally applicable to a variety of rendering architectures. CRRS is fully operational, Open Source software.
Traditional models of ecosystems often assume that the species composing an unperturbed ecosystem... more Traditional models of ecosystems often assume that the species composing an unperturbed ecosystem become fixed so that only the relative abundances of the species change over time. Such ecosystems are said to have reached an optimal fixed point. However, recent work has suggested that neutral evolutionary processes can significantly alter the species composition of an ecosystem, allowing the ecosystem to exist in a dynamic steady state. Here, we investigate the stability of ecosystems and the nature of the equilibrium that forms using the digital evolution platform Avida, tracking evolving ecosystems over thousands of generations. We find that the communities that form are remarkably stable, and do not experience a significant loss of diversity in the long run even in experimental treatments where the communities suffer catastrophic population bottlenecks. When diversity rebounds, ecological communities are reconstituted in a different form than the one that was destroyed, but this difference is comparable to the difference the system would have accumulated if it had been left untouched. Thus, digital ecological communities exist in a dynamic steady state, which ultimately eliminates the effect of historical disturbances.
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Papers by Eric Bruger