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![(A) Calculated formula of the growth of the system as a function of its modes (l) and the adimensional variables K, P, M, and W (SI Appendix, Fig. S16). (B) The growth rate λ+ as a function of the mode number l, corresponding to K = 84, M = 1, P = 0.00015, and W = 1; a magnified section of the latter (C) shows that the l = 8 mode becomes unstable. (D) Instability is exquisitely sensitive to W but not to the other variables (SI Appendix, Fig. S17). (E) Density plots of the real parts of various spherical harmonics Y 8m ðθ, φÞ for different values of M. (F) See extended explanation in SI Appendix, Fig. S17. (I) The bacterial membrane (e.g., S. aureus membrane) is a lipid-based surface, under cytoplasm-induced turgor pressure and tethered to the cell wall, which contains protein complexes whose distribution is a 3D phenomenon that can be defined by a mathematical function (SI Appendix, Fig. S16). (II) The latter depends on multiple independent variables that can be grouped into dimensionless variables (P, K, M, and W) for convenience. (III) This enables one to solve the differential equations corresponding to the various components ðF b + F d + F t Þ of the overall free energy of the system (F). The P, K, M, and W variables do not directly correspond to biological variables, but they relate to them in terms of controlling the relative competition between the energy contributions; K relates to F t vs. F b , P and M relate to F d , and W relates to F d vs. F b. (IV and V) The solutions to the equation are two functions λ + and λ − , representing the growth (λ > 0; pattern formation of protein complexes) or decay (λ < 0 and λ = 0; random distribution of protein complexes) in the membrane. A combination of selected values of K, P, M, and W (Fig. 4 B-D) as a function of the characteristic modes of the system (l) results in positive λ+ (SI Appendix, Figs. S16 and S17). Linear analysis (Fig. 4 B-D) reveals W as the key variable determining the distribution of protein complexes. Hence, the presence of a protein complex in the membrane induces a membrane deformation that results in localized membrane curvature (H p ) and will entail a bending cost. If the curvature is larger than a critical threshold (H pc ), it will result in a system that will enable the growth of patterns. If H p < H pc , the resulting system will lead to the decay of patterns. (VI) The separation of variables into spherical coordinates leads to spherical harmonics of the form [Y ℓm ðθ, φÞ] (Fig. 4E) that can be represented as a density plot.](profile/Ramin-Golestanian-2/publication/286376188/figure/fig4/AS:667841019797530@1536237115737/A-Calculated-formula-of-the-growth-of-the-system-as-a-function-of-its-modes-l-and-the.png)
(A) Calculated formula of the growth of the system as a function of its modes (l) and the adimensional variables K, P, M, and W (SI Appendix, Fig. S16). (B) The growth rate λ+ as a function of the mode number l, corresponding to K = 84, M = 1, P = 0.00015, and W = 1; a magnified section of the latter (C) shows that the l = 8 mode becomes unstable. (D) Instability is exquisitely sensitive to W but not to the other variables (SI Appendix, Fig. S17). (E) Density plots of the real parts of various spherical harmonics Y 8m ðθ, φÞ for different values of M. (F) See extended explanation in SI Appendix, Fig. S17. (I) The bacterial membrane (e.g., S. aureus membrane) is a lipid-based surface, under cytoplasm-induced turgor pressure and tethered to the cell wall, which contains protein complexes whose distribution is a 3D phenomenon that can be defined by a mathematical function (SI Appendix, Fig. S16). (II) The latter depends on multiple independent variables that can be grouped into dimensionless variables (P, K, M, and W) for convenience. (III) This enables one to solve the differential equations corresponding to the various components ðF b + F d + F t Þ of the overall free energy of the system (F). The P, K, M, and W variables do not directly correspond to biological variables, but they relate to them in terms of controlling the relative competition between the energy contributions; K relates to F t vs. F b , P and M relate to F d , and W relates to F d vs. F b. (IV and V) The solutions to the equation are two functions λ + and λ − , representing the growth (λ > 0; pattern formation of protein complexes) or decay (λ < 0 and λ = 0; random distribution of protein complexes) in the membrane. A combination of selected values of K, P, M, and W (Fig. 4 B-D) as a function of the characteristic modes of the system (l) results in positive λ+ (SI Appendix, Figs. S16 and S17). Linear analysis (Fig. 4 B-D) reveals W as the key variable determining the distribution of protein complexes. Hence, the presence of a protein complex in the membrane induces a membrane deformation that results in localized membrane curvature (H p ) and will entail a bending cost. If the curvature is larger than a critical threshold (H pc ), it will result in a system that will enable the growth of patterns. If H p < H pc , the resulting system will lead to the decay of patterns. (VI) The separation of variables into spherical coordinates leads to spherical harmonics of the form [Y ℓm ðθ, φÞ] (Fig. 4E) that can be represented as a density plot.
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The fundamental processes of life are organized and based on common basic principles. Molecular organizers, often interacting with the membrane, capitalize on cellular polarity to precisely orientate essential processes. The study of organisms lacking apparent polarity or known cellular organizers (e.g., the bacterium Staphylococcus au...
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... expansion in spherical harmonics Y ℓm ðθ, φÞ for both fields, a linear stability analysis can be performed to find the growth rates of the char- acteristic modes of the system. It is convenient to group the many parameters in the system into the dimensionless variables K = kR 4 =κ, M = L ψ =ðκL u χÞ, P = ξ 2 =R 2 , and W = κχρ 2 0 a 2 0 H 2 p . Fig. 4B shows the relevant growth rate λ + in units of κL u =R 2 as a function of the mode number ℓ, at selected values of K, M, and P for W = 1. It shows that λ + acquires a positive value (Fig. 4C) for the ℓ = 8 mode, which means that this mode becomes unstable. The instability in the intermediate ℓ = 8 mode de- velops as the parameter W is ...
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... to group the many parameters in the system into the dimensionless variables K = kR 4 =κ, M = L ψ =ðκL u χÞ, P = ξ 2 =R 2 , and W = κχρ 2 0 a 2 0 H 2 p . Fig. 4B shows the relevant growth rate λ + in units of κL u =R 2 as a function of the mode number ℓ, at selected values of K, M, and P for W = 1. It shows that λ + acquires a positive value (Fig. 4C) for the ℓ = 8 mode, which means that this mode becomes unstable. The instability in the intermediate ℓ = 8 mode de- velops as the parameter W is changed from 0.8 to 1 (Fig. 4D), leading to the development of slowly growing patterns that are linear combinations of the Y 8m ðθ, φÞ for different values of m, which could lead to eight foci ...
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... relevant growth rate λ + in units of κL u =R 2 as a function of the mode number ℓ, at selected values of K, M, and P for W = 1. It shows that λ + acquires a positive value (Fig. 4C) for the ℓ = 8 mode, which means that this mode becomes unstable. The instability in the intermediate ℓ = 8 mode de- velops as the parameter W is changed from 0.8 to 1 (Fig. 4D), leading to the development of slowly growing patterns that are linear combinations of the Y 8m ðθ, φÞ for different values of m, which could lead to eight foci in a cross-section of the sphere (Fig. 4E). This example demonstrates that patterns such as those observed (Figs. 2 B-E ...
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... means that this mode becomes unstable. The instability in the intermediate ℓ = 8 mode de- velops as the parameter W is changed from 0.8 to 1 (Fig. 4D), leading to the development of slowly growing patterns that are linear combinations of the Y 8m ðθ, φÞ for different values of m, which could lead to eight foci in a cross-section of the sphere (Fig. 4E). This example demonstrates that patterns such as those observed (Figs. 2 B-E ...
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... will entail a bending cost. If the curvature is larger than a critical threshold (H pc ), it will result in a system that will enable the growth of patterns. If H p < H pc , the resulting system will lead to the decay of patterns. (VI) The separation of variables into spherical coordinates leads to spherical harmonics of the form [Y ℓm ðθ, φÞ] (Fig. 4E) that can be represented as a density ...
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... Therefore, only normal equilibrium equations should be solved with one variable u n ; while the in-plane equilibrium equations are not strictly satisfied. In this way, we do not need to assume that the chemical concentrations are near the stationary state like (25), or the chemical regulations in Eq. 3 leave only the modulation on curvature while the modulation on stretching vanishes ( (c A ) = 1) in previous curvaturesensible models (29,31,71). After obtaining the displacement fields u n i at t i , we can solve the nondimensional chemical dynamic Eq. 10 in the deforming configuration through a fourth-order, six-stage, linearly semi-implicit Runge-Kutta method (63). ...
Morphogenesis of active shells such as cells is a fundamental chemomechanical process that often exhibits three-dimensional (3D) large deformations and chemical pattern dynamics simultaneously. Here, we establish a chemomechanical active shell theory accounting for mechanical feedback and biochemical regulation to investigate the symmetry-breaking and 3D chiral morphodynamics emerging in the cell cortex. The active bending and stretching of the elastic shells are regulated by biochemical signals like actomyosin and RhoA, which, in turn, exert mechanical feedback on the biochemical events via deformation-dependent diffusion and inhibition. We show that active deformations can trigger chemomechanical bifurcations, yielding pulse spiral waves and global oscillations, which, with increasing mechanical feedback, give way to traveling or standing waves subsequently. Mechanical feedback is also found to contribute to stabilizing the polarity of emerging patterns, thus ensuring robust morphogenesis. Our results reproduce and unravel the experimentally observed solitary and multiple spiral patterns, which initiate asymmetric cleavage in Xenopus and starfish embryogenesis. This study underscores the crucial roles of mechanical feedback in cell development and also suggests a chemomechanical framework allowing for 3D large deformation and chemical signaling to explore complex morphogenesis in living shell-like structures.
... This lack of activity could be related to the structure and composition of the cell wall, which differs between strains. 22,23 In fact, the composition and organization of the membrane determines the efficacy and extent of several phenomena, such as signaling, polarity and stability. The formation of biofilm is dependent on this as well, and an explanation for the lack of activity in the ATCC strain tested could lie in the diversity of the membrane structure, which differs between species, as was observed previously. ...
Antimicrobial resistance arises due to several adaptation mechanisms, being the overexpression of efflux pumps (EPs) one of the most worrisome. In bacteria, EPs can also play important roles in virulence, quorum-sensing (QS) and biofilm formation. To identify new potential antimicrobial adjuvants, a library of diarylpentanoids and chalcones was synthesized and tested. These compounds presented encouraging results in potentiating the activity of antimicrobials, being diarylpentanoid 13 the most promising. Compounds 9, 13, 16, 19, 22, and 23 displayed EP inhibitory effect, mainly in Staphylococcus aureus 272123. Compounds 13, 19, 22, and 23 exhibited inhibitory effect on biofilm formation in S. aureus 272123 while 13 and 22 inhibited QS in the pair Sphingomonas paucimobilis Ezf 10-17 and Chromobacterium violaceum CV026. The overall results, demonstrated that diarylpentanoid 13 and chalcone 22 were active against all the resistance mechanisms tested, suggesting their potential as antimicrobial adjuvants.
... Phospholipid-biosynthetic proteins have been found to form large multicomponent complexes in 96 bacteria such as S. aureus [17,18]. To analyze a role of PplT in such complexes, its potential interaction 97 with several phospholipid-biosynthetic proteins was studied in the bacterial two-hybrid system [8, 19, 98 20]. ...
... Likewise, MprF proteins have been found to interact with larger phospholipid-biosynthetic protein 147 complexes in S. aureus [17,18]. 148 ...
Flippase proteins exchanging phospholipids between the cytoplasmic membrane leaflets have been identified in Eukaryotes but remained largely unknown in Prokaryotes. Only MprF proteins that synthesize aminoacyl phospholipids in some bacteria have been found to contain a domain that translocates the produced lipids. We show here that this domain, which we named 'prokaryotic phospholipid translocator' (PplT), is widespread in Bacteria and Archaea, encoded as a separate protein or fused to different types of enzymes. We also demonstrate that the Escherichia coli PplT protein interacts with many phospholipid-synthetic enzymes and deletion of pplT impaired bacterial growth and membrane fluidity. Thus, PplT domain proteins appear to be general prokaryotic lipid flippases with critical roles in cellular homeostasis.
... Labeling Bsu with short, sequential pulses of two colors of FDAAs or an FDAA followed The mechanism that causes the regular nodal distribution of PBPs and their TP activity in predivisional cells of Spn remains to be determined (Figure 9b). Recent notable studies have demonstrated heterogeneous supramolecular localization of membrane proteins generally and at septa of Sau cells, including interacting enzymes that catalyze phospholipid biosynthesis and the MreD regulator of PG synthesis (Garcia-Lara et al., 2015;Weihs et al., 2018). This heterogenous localization results in punctate patterns of these proteins at division septa, resembling the localization of Spn PBPs reported here (Figures 2 and S2). ...
Bacterial peptidoglycan (PG) synthesis requires strict spatiotemporal organization to reproduce specific cell shapes. In ovoid‐shaped Streptococcus pneumoniae (Spn), septal and peripheral (elongation) PG synthesis occur simultaneously at midcell. To uncover the organization of proteins and activities that carry out these two modes of PG synthesis, we examined Spn cells vertically oriented onto their poles to image the division plane at the high lateral resolution of 3D‐SIM (structured‐illumination microscopy). Labelling with fluorescent D‐amino acids (FDAA) showed that areas of new transpeptidase (TP) activity catalyzed by penicillin‐binding proteins (PBPs) separate into a pair of concentric rings early in division, representing peripheral PG (pPG) synthesis (outer ring) and the leading‐edge (inner ring) of septal PG (sPG) synthesis. Fluorescently tagged PBP2x or FtsZ locate primarily to the inner FDAA‐marked ring, whereas PBP2b and FtsX remain in the outer ring, suggesting roles in sPG or pPG synthesis, respectively. Pulses of FDAA labeling revealed an arrangement of separate regularly spaced “nodes” of TP activity around the division site of predivisional cells. Tagged PBP2x, PBP2b, and FtsX proteins also exhibited nodal patterns with spacing comparable to that of FDAA labeling. Together, these results reveal new aspects of spatially ordered PG synthesis in ovococcal bacteria during cell division.
... Evidence for a phospholipid synthesis enzyme complex. Recently, we showed the interaction of PlsY with CdsA and MreD using a protein-protein interaction system based on Förster Resonance Energy Transfer (FRET) facilitating lower donor photobleaching rates of GFP in the presence of mCherry 14 . This FRET method is simple in terms of image acquisition using a standard widefield microscope. ...
... Overall, these interaction analyses suggest the formation of a phospholipid synthesis enzyme complex consisting of at least of PlsY, CdsA and PgsA which would allow possible metabolic channelling of intermediates. MreD might act as a spatial organiser to stabilise the complex formation as we showed previously 14 . The involvement of CydB in this complex suggests a higher level of complex formation linking several cellular aspects. ...
... Theoretically, membrane protein patterns such as the ones observed here can be generated by the intrinsic properties of the molecules themselves 14 . If integral membrane protein complexes impose a sufficiently large local curvature on the membrane, protein complexes can themselves spontaneously form the observed patterns. ...
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... Very recently, [12] a system was identified in which cell polarisation appears to be controlled by a relatively simple pattern-formation mechanism. In the coccal bacterium Staphylococcus aureus, essential proteins involved in lipid metabolism were seen to distribute in inhomogeneous spatial patterns, that could be explained by a model that considers the dynamics of curvature-inducing proteins on a spherical membrane. ...
... In the coccal bacterium Staphylococcus aureus, essential proteins involved in lipid metabolism were seen to distribute in inhomogeneous spatial patterns, that could be explained by a model that considers the dynamics of curvature-inducing proteins on a spherical membrane. However, the model first introduced in Ref. 12 is very general, and we expect that it might be able to describe the formation of protein patterns on the surface of other types of cells, as well as in model systems consisting of lipid vesicles and proteins. In this work, we will explore in full generality and detail the predictions of such a model. ...
... This is shown in figure 3, for P = 0.00015, which would correspond to a correlation length of about ξ 12 nm for a spherical membrane of radius R = 1 µm. [12] Using (25), in figure 3(a) we have plotted the lines W = W (K) for modes = 2, ..., 50. As W is increased from low values, the system will hit the instability of the most unstable mode, with a given value of which will depend on the value of K. ...
Spatial organisation is a hallmark of all living cells, and recreating it in model systems is a necessary step in the creation of synthetic cells. It is therefore of both fundamental and practical interest to better understand the basic mechanisms underlying spatial organisation in cells. In this work, we use a continuum model of membrane and protein dynamics to study the behaviour of curvature-inducing proteins on membranes of spherical shape, such as living cells or lipid vesicles. We show that the interplay between curvature energy, entropic forces, and the geometric constraints on the membrane can result in the formation of patterns of highly-curved/protein-rich and weakly-curved/protein-poor domains on the membrane. The spontaneous formation of such patterns can be triggered either by an increase in the average density of curvature-inducing proteins, or by a relaxation of the geometric constraints on the membrane imposed by the membrane tension or by the tethering of the membrane to a rigid cell wall or cortex. These parameters can also be tuned to select the size and number of the protein-rich domains that arise upon pattern formation. The very general mechanism presented here could be related to protein self-organisation in many biological processes, ranging from (proto)cell division to the formation of membrane rafts.
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... Hence, it might be that a polar effect on MreD expression is the reason they identified MreC as essential in their D39 strain. In a recent paper, Garc ıa-Lara et al. (2015) reports that a Staphylococcus aureus DmreC mutant grows identically to the parental strain, while lack of MreD leads to growth defects and abnormal cell morphology. This is very similar to the phenotypes we observe for the pneumococcal mreC and mreD mutants. ...
The oval shape of pneumococci results from a combination of septal and lateral peptidoglycan synthesis. The septal cross-wall is synthesized by the divisome, while the elongasome drives cell elongation by inserting new peptidoglycan into the lateral cell wall. Each of these molecular machines contains penicillin-binding proteins (PBPs), which catalyze the final stages of peptidoglycan synthesis, plus a number of accessory proteins. Much effort has been made to identify these accessory proteins and determine their function. In the present paper we have used a novel approach to identify members of the pneumococcal elongasome that are functionally closely linked to PBP2b. We discovered that cells depleted in PBP2b, a key component of the elongasome, display several distinct phenotypic traits. We searched for proteins that, when depleted or deleted, display the same phenotypic changes. Four proteins, RodA, MreD, DivIVA and Spr0777, were identified by this approach. Together with PBP2b these proteins are essential for the normal function of the elongasome. Furthermore, our findings suggest that DivIVA, which was previously assigned as a divisomal protein, is required to correctly localize the elongasome at the negatively curved membrane region between the septal and lateral cell wall. This article is protected by copyright. All rights reserved.
The droplet interface has adjustable curvature, surface tension and spherical topology, which provide unique experimental conditions for crystallization studies. In recent years, novel experimental phenomena of crystallization behaviors at the droplet interfaces have attracted a lot of attention from researchers, such as spherical crystals with multiple optical centers, shape transformation driven by intermediate rotator phases, self-driven active droplets. This review focuses on these novel experimental phenomena, which are very different from crystallization on flat substrates. We investigate the formation mechanisms behind the complex phenomena and point out the implications of soft matter crystallization and ordered self-organization at the droplet interface for fundamental research in chemistry, physics, biology, and other related fields.
