Abstract:SignificanceMany fundamental cellular processes are spatially regulated by self-organized protein patterns, which are often based on nucleotide-binding proteins that switch their nucleotide state upon interaction with a second, activating protein. For reliable function, these protein patterns must be robust against parameter changes, although the basis for such robustness is generally elusive. Here we take a combined theoretical and experimental approach to the Escherichia coli Min system, a paradigmatic syste… Show more
“…Diffusion in the cytosol is a simple means of protein transport that accounts for many self-organization processes [1]. To analyze how the interplay of diffusive protein transport and protein-protein interactions on a nanometer scale influences the protein patterns on the cellular scale, mass-conserving reaction-diffusion models have proven useful [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The study of reactiondiffusion systems in general goes back to Turing [19], who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities.…”
The formation of protein patterns inside cells is generically described by reaction-diffusion models.The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g. membranebound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud-site in budding yeast, and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can 'sense' the edge of the template. A mechanism for how this edge sensing may work remains elusive.Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a twocomponent mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems, and for the design of synthetic pattern forming systems. * These three authors contributed equally † frey@lmu.de 1 GTPases are hydrolase enzymes that can bind and hydrolyze guanosine triphosphate (GTP). Ras is a subfamily of small GTPases.
“…Diffusion in the cytosol is a simple means of protein transport that accounts for many self-organization processes [1]. To analyze how the interplay of diffusive protein transport and protein-protein interactions on a nanometer scale influences the protein patterns on the cellular scale, mass-conserving reaction-diffusion models have proven useful [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The study of reactiondiffusion systems in general goes back to Turing [19], who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities.…”
The formation of protein patterns inside cells is generically described by reaction-diffusion models.The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive components have different diffusivities (e.g. membranebound and cytosolic states). However, in nature, systems typically develop in a heterogeneous environment, where upstream protein patterns affect the formation of protein patterns downstream. Examples for this are the polarization of Cdc42 adjacent to the previous bud-site in budding yeast, and the formation of an actin-recruiter ring that forms around a PIP3 domain in macropinocytosis. This suggests that previously established protein patterns can serve as a template for downstream proteins and that these downstream proteins can 'sense' the edge of the template. A mechanism for how this edge sensing may work remains elusive.Here we demonstrate and analyze a generic and robust edge-sensing mechanism, based on a twocomponent mass-conserving reaction-diffusion (McRD) model. Our analysis is rooted in a recently developed theoretical framework for McRD systems, termed local equilibria theory. We extend this framework to capture the spatially heterogeneous reaction kinetics due to the template. This enables us to graphically construct the stationary patterns in the phase space of the reaction kinetics. Furthermore, we show that the protein template can trigger a regional mass-redistribution instability near the template edge, leading to the accumulation of protein mass, which eventually results in a stationary peak at the template edge. We show that simple geometric criteria on the reactive nullcline's shape predict when this edge-sensing mechanism is operational. Thus, our results provide guidance for future studies of biological systems, and for the design of synthetic pattern forming systems. * These three authors contributed equally † frey@lmu.de 1 GTPases are hydrolase enzymes that can bind and hydrolyze guanosine triphosphate (GTP). Ras is a subfamily of small GTPases.
“…Here, on the basis of previous theoretical studies of intracellular protein dynamics [30, 32, 34, 79], we propose a minimal reaction-diffusion system to model Min localization in B. subtilis . Building on the idea of geometry sensing put forward in Ref.…”
Section: Resultsmentioning
confidence: 99%
“…S1 and Tab. S2 ) and the values for the rate constants were estimated from previous work on protein pattern formation [30, 32, 34, 78]. The action on DivIVA and MinJ is accounted for effectively through space-dependent recruitment and detachment rates of MinD at membrane areas with a negative curvature; for details please refer to the Methods section ( Fig.…”
SummaryDivision site selection is a vital process to ensure generation of viable offspring. In many rod-shaped bacteria a dynamic protein system, termed the Min system, acts as a central regulator of division site placement. The Min system is best studied in Escherichia coli where it shows a remarkable oscillation from pole to pole with a time-averaged density minimum at midcell. Several components of the Min system are conserved in the Gram-positive model organism Bacillus subtilis. However, in B. subtilis it is believed that the system forms a stationary bipolar gradient from the cell poles to midcell. Here, we show that the Min system of B. subtilis localizes dynamically to active sites of division, often organized in clusters. We provide physical modelling using measured diffusion constants that describe the observed enrichment of the Min system at the septum. Modelling suggests that the observed localization pattern of Min proteins corresponds to a dynamic equilibrium state. Our data provide evidence for the importance of ongoing septation for the Min dynamics, consistent with a major role of the Min system to control active division sites, but not cell pole areas.
“…MinD kann seinerseits auch bei MinE eine Konformationsänderung auslösen, welche diesem Protein eine stärkere Membranaffinität verleiht. Erst vor kurzem konnte Schwilles Arbeitsgruppe nachweisen, dass auch diese Wechselwirkung eine wichtige Rolle bei der Selbstorganisation und Musterbildung des Systems spielt .…”
Section: Wechselspiel Der Proteine Führt Zur Oszillierenden Reaktionunclassified
Wie das Leben auf der Erde entstanden ist, wird vielleicht nie zweifelsfrei zu klären sein. Aber wie Lebensfunktionen entstehen können – mit oder ohne Beteiligung von Biomolekülen – das ist eine fruchtbare Fragestellung, die auch zu ästhetisch ansprechenden Ergebnissen führt.
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