The motility-matrix production switch in Bacillus subtilis-a modeling perspective.

Phenotype switching can be triggered by external stimuli and by intrinsic stochasticity. Here, we focus on the motility-matrix production switch in Bacillus subtilis. We use modeling to describe the SinR-SlrR bistable switch and its regulation by SinI and to distinguish different sources of stochasticity. Our simulations indicate that intrinsic fluctuations in the synthesis of SinI are insufficient to drive spontaneous switching and suggest that switching is triggered by upstream noise from the Spo0A phosphorelay. IMPORTANCE The switch from motility to matrix production is the first step toward biofilm formation and, thus, to multicellular behavior in Bacillus subtilis. The transition is governed by a bistable switch based on the interplay of the regulators SinR and SlrR, while SinI transmits upstream signals to that switch. Quantitative modeling can be used to study the switching dynamics. Here, we build such a model step by step to describe the dynamics of the switch and its regulation and to study how spontaneous switching is triggered by upstream noise from the Spo0A phosphorelay.

Growth rate-dependent global effects on gene expression in bacteria.

Bacterial gene expression depends not only on specific regulatory mechanisms, but also on bacterial growth, because important global parameters such as the abundance of RNA polymerases and ribosomes are all growth-rate dependent. Understanding of these global effects is necessary for a quantitative understanding of gene regulation and for the design of synthetic genetic circuits. We find that the observed growth-rate dependence of constitutive gene expression can be explained by a simple model using the measured growth-rate dependence of the relevant cellular parameters. More complex growth dependencies for genetic circuits involving activators, repressors, and feedback control were analyzed and verified experimentally with synthetic circuits. Additional results suggest a feedback mechanism mediated by general growth-dependent effects that does not require explicit gene regulation if the expressed protein affects cell growth. This mechanism can lead to growth bistability and promote the acquisition of important physiological functions such as antibiotic resistance and tolerance (persistence).

Multiscale mechanics and temporal evolution of vimentin intermediate filament networks.

The cytoskeleton, an intricate network of protein filaments, motor proteins, and cross-linkers, largely determines the mechanical properties of cells. Among the three filamentous components, F-actin, microtubules, and intermediate filaments (IFs), the IF network is by far the most extensible and resilient to stress. We present a multiscale approach to disentangle the three main contributions to vimentin IF network mechanics-single-filament mechanics, filament length, and interactions between filaments-including their temporal evolution. Combining particle tracking, quadruple optical trapping, and computational modeling, we derive quantitative information on the strength and kinetics of filament interactions. Specifically, we find that hydrophobic contributions to network mechanics enter mostly via filament-elongation kinetics, whereas electrostatics have a direct influence on filament-filament interactions.

Quasi-essentiality of RNase Y in Bacillus subtilis is caused by its critical role in the control of mRNA homeostasis.

RNA turnover is essential in all domains of life. The endonuclease RNase Y (rny) is one of the key components involved in RNA metabolism of the model organism Bacillus subtilis. Essentiality of RNase Y has been a matter of discussion, since deletion of the rny gene is possible, but leads to severe phenotypic effects. In this work, we demonstrate that the rny mutant strain rapidly evolves suppressor mutations to at least partially alleviate these defects. All suppressor mutants had acquired a duplication of an about 60 kb long genomic region encompassing genes for all three core subunits of the RNA polymerase-α, ß, ß'. When the duplication of the RNA polymerase genes was prevented by relocation of the rpoA gene in the B. subtilis genome, all suppressor mutants carried distinct single point mutations in evolutionary conserved regions of genes coding either for the ß or ß' subunits of the RNA polymerase that were not tolerated by wild type bacteria. In vitro transcription assays with the mutated polymerase variants showed a severe decrease in transcription efficiency. Altogether, our results suggest a tight cooperation between RNase Y and the RNA polymerase to establish an optimal RNA homeostasis in B. subtilis cells.

Stokesian dynamics simulations of a magnetotactic bacterium.

The swimming of bacteria provides insight into propulsion and steering under the conditions of low-Reynolds number hydrodynamics. Here we address the magnetically steered swimming of magnetotactic bacteria. We use Stokesian dynamics simulations to study the swimming of single-flagellated magnetotactic bacteria (MTB) in an external magnetic field. Our model MTB consists of a spherical cell body equipped with a magnetic dipole moment and a helical flagellum rotated by a rotary motor. The elasticity of the flagellum as well as magnetic and hydrodynamic interactions is taken into account in this model. We characterized how the swimming velocity is dependent on parameters of the model. We then studied the U-turn motion after a field reversal and found two regimes for weak and strong fields and, correspondingly, two characteristic time scales. In the two regimes, the U-turn time is dominated by the turning of the cell body and its magnetic moment or the turning of the flagellum, respectively. In the regime for weak fields, where turning is dominated by the magnetic relaxation, the U-turn time is approximately in agreement with a theoretical model based on torque balance. In the strong-field regime, strong deformations of the flagellum are observed. We further simulated the swimming of a bacterium with a magnetic moment that is inclined relative to the flagellar axis. This scenario leads to intriguing double helical trajectories that we characterize as functions of the magnetic moment inclination and the magnetic field. For small inclination angles ([Formula: see text]) and typical field strengths, the inclination of the magnetic moment has only a minor effect on the swimming of MTB in an external magnetic field. Large inclination angles result in a strong reduction in the velocity in direction of the magnetic field, consistent with recent observations that bacteria with large inclination angles use a different propulsion mechanism.

Large-scale reduction of the Bacillus subtilis genome: consequences for the transcriptional network, resource allocation, and metabolism.

Understanding cellular life requires a comprehensive knowledge of the essential cellular functions, the components involved, and their interactions. Minimized genomes are an important tool to gain this knowledge. We have constructed strains of the model bacterium, Bacillus subtilis, whose genomes have been reduced by ∼36%. These strains are fully viable, and their growth rates in complex medium are comparable to those of wild type strains. An in-depth multi-omics analysis of the genome reduced strains revealed how the deletions affect the transcription regulatory network of the cell, translation resource allocation, and metabolism. A comparison of gene counts and resource allocation demonstrates drastic differences in the two parameters, with 50% of the genes using as little as 10% of translation capacity, whereas the 6% essential genes require 57% of the translation resources. Taken together, the results are a valuable resource on gene dispensability in B. subtilis, and they suggest the roads to further genome reduction to approach the final aim of a minimal cell in which all functions are understood.

Chemotaxis in external fields: Simulations for active magnetic biological matter.

The movement of microswimmers is often described by active Brownian particle models. Here we introduce a variant of these models with several internal states of the swimmer to describe stochastic strategies for directional swimming such as run and tumble or run and reverse that are used by microorganisms for chemotaxis. The model includes a mechanism to generate a directional bias for chemotaxis and interactions with external fields (e.g., gravity, magnetic field, fluid flow) that impose forces or torques on the swimmer. We show how this modified model can be applied to various scenarios: First, the run and tumble motion of E. coli is used to establish a paradigm for chemotaxis and investigate how it is affected by external forces. Then, we study magneto-aerotaxis in magnetotactic bacteria, which is biased not only by an oxygen gradient towards a preferred concentration, but also by magnetic fields, which exert a torque on an intracellular chain of magnets. We study the competition of magnetic alignment with active reorientation and show that the magnetic orientation can improve chemotaxis and thereby provide an advantage to the bacteria, even at rather large inclination angles of the magnetic field relative to the oxygen gradient, a case reminiscent of what is expected for the bacteria at or close to the equator. The highest gain in chemotactic velocity is obtained for run and tumble with a magnetic field parallel to the gradient, but in general a mechanism for reverse motion is necessary to swim against the magnetic field and a run and reverse strategy is more advantageous in the presence of a magnetic torque. This finding is consistent with observations that the dominant mode of directional changes in magnetotactic bacteria is reversal rather than tumbles. Moreover, it provides guidance for the design of future magnetic biohybrid swimmers.

Simulations of structure formation by confined dipolar active particles.

Dipolar active particles describe a class of self-propelled, biological or artificial particles equipped with an internal (typically magnetic) dipole moment. Because of the interplay between self-propulsion and dipole-dipole interactions, complex collective behavior is expected to emerge in systems of such particles. Here, we use Brownian dynamics simulations to explore this collective behavior. We focus on the structures that form in small systems in spatial confinement. We quantify the type of structures that emerge and how they depend on the self-propulsion speed and the dipolar (magnetic) strength of the particles. We observe that the dipolar active particles self-assemble into chains and rings. The dominant configuration is quantified with an order parameter for chain and ring formation and shown to depend on the self-propulsion speed and the dipolar magnetic strength of the particles. In addition, we show that the structural configurations are also affected by the confining walls. To that end, we compare different confining geometries and study the impact of a reorienting 'wall torque' upon collisions of a particle with a wall. Our results indicate that dipolar interactions can further enhance the already rich variety of collective behaviors of active particles.

Is F1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip.

We present a chemomechanical network model of the rotary molecular motor F1-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F1-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque.

Force-Dependent Unbinding Rate of Molecular Motors from Stationary Optical Trap Data.

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show how this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1.

Decoding Biomineralization: Interaction of a Mad10-Derived Peptide with Magnetite Thin Films.

Protein-surface interactions play a pivotal role in processes as diverse as biomineralization, biofouling, and the cellular response to medical implants. In biomineralization processes, biomacromolecules control mineral deposition and architecture via complex and often unknown mechanisms. For studying these mechanisms, the formation of magnetite nanoparticles in magnetotactic bacteria has become an excellent model system. Most interestingly, nanoparticle morphologies have been discovered that defy crystallographic rules (e.g., in the species Desulfamplus magnetovallimortis strain BW-1). In certain conditions, this strain mineralizes bullet-shaped magnetite nanoparticles, which exhibit defined (111) crystal faces and are elongated along the [100] direction. We hypothesize that surface-specific protein interactions break the nanoparticle symmetry, inhibiting the growth of certain crystal faces and thereby favoring the growth of others. Screening the genome of BW-1, we identified Mad10 (Magnetosome-associated deep-branching) as a potential magnetite-binding protein. Using atomic force microscope (AFM)-based single-molecule force spectroscopy, we show that a Mad10-derived peptide, which represents the most conserved region of Mad10, binds strongly to (100)- and (111)-oriented single-crystalline magnetite thin films. The peptide-magnetite interaction is thus material- but not crystal-face-specific. It is characterized by broad rupture force distributions that do not depend on the retraction speed of the AFM cantilever. To account for these experimental findings, we introduce a three-state model that incorporates fast rebinding. The model suggests that the peptide-surface interaction is strong in the absence of load, which is a direct result of this fast rebinding process. Overall, our study sheds light on the kinetic nature of peptide-surface interactions and introduces a new magnetite-binding peptide with potential use as a functional coating for magnetite nanoparticles in biotechnological and biomedical applications.

Lateral Subunit Coupling Determines Intermediate Filament Mechanics.

The cytoskeleton is a composite network of three types of protein filaments, among which intermediate filaments (IFs) are the most extensible ones. Two very important IFs are keratin and vimentin, which have similar molecular architectures but different mechanical behaviors. Here we compare the mechanical response of single keratin and vimentin filaments using optical tweezers. We show that the mechanics of vimentin strongly depends on the ionic strength of the buffer and that its force-strain curve suggests a high degree of cooperativity between subunits. Indeed, a computational model indicates that in contrast to keratin, vimentin is characterized by strong lateral subunit coupling of its charged monomers during unfolding of α helices. We conclude that cells can tune their mechanics by differential use of keratin versus vimentin.

Simulating Genetic Circuits in Bacterial Populations with Growth Heterogeneity.

We computationally study genetic circuits in bacterial populations with heterogeneities in the growth rate. To that end, we present a stochastic simulation method for gene circuits in populations of cells and propose an efficient implementation that we call the "Next Family Method". Within this approach, we implement different population setups, specifically Chemostat-type growth and growth in an ideal Mother Machine and show that the population structure and its statistics are different for the different setups whenever there is growth heterogeneity. Such dependence on the population setup is demonstrated, in the case of bistable systems with different growth rates in the stable states, to have distinctive signatures on quantities including the distributions of protein concentration and growth rates, and hysteresis curves. Applying this method to a bistable antibiotic resistance circuit, we find that as a result of the different statistics in different population setups, the estimated minimal inhibitory concentration of the antibiotic becomes dependent on the population setup in which it is measured.

Magnetosome Organization in Magnetotactic Bacteria Unraveled by Ferromagnetic Resonance Spectroscopy.

Magnetotactic bacteria form assemblies of magnetic nanoparticles called magnetosomes. These magnetosomes are typically arranged in chains, but other forms of assemblies such as clusters can be observed in some species and genetic mutants. As such, the bacteria have developed as a model for the understanding of how organization of particles can influence the magnetic properties. Here, we use ferromagnetic resonance spectroscopy to measure the magnetic anisotropies in different strains of Magnetosprillum gryphiswaldense MSR-1, a bacterial species that is amendable to genetic mutations. We combine our experimental results with a model describing the spectra. The model includes chain imperfections and misalignments following a Fisher distribution function, in addition to the intrinsic magnetic properties of the magnetosomes. Therefore, by applying the model to analyze the ferromagnetic resonance data, the distribution of orientations in the bulk sample can be retrieved in addition to the average magnetosome arrangement. In this way, we quantitatively characterize the magnetosome arrangement in both wild-type cells and ΔmamJ mutants, which exhibit differing magnetosome organization.

Buckling of elastic filaments by discrete magnetic moments.

We study the buckling of an idealized, semiflexible filament along whose contour magnetic moments are placed. We give analytic expressions for the critical stiffness of the filament below which it buckles due to the magnetic compression. For this, we consider various scenarios of the attachment of the magnetic particles to the filament. One possible application for this model are the magnetosome chains of magnetotactic bacteria. An estimate of the critical bending stiffness indicates that buckling may occur within the range of biologically relevant parameters and suggests a role for the bending stiffness of the filament to stabilize the filament against buckling, which would compromise the functional relevance of the bending stiffness of the used filament.

Segregation of prokaryotic magnetosomes organelles is driven by treadmilling of a dynamic actin-like MamK filament.

BACKGROUND: The navigation of magnetotactic bacteria relies on specific intracellular organelles, the magnetosomes, which are membrane-enclosed crystals of magnetite aligned into a linear chain. The magnetosome chain acts as a cellular compass, aligning the cells in the geomagnetic field in order to search for suitable environmental conditions in chemically stratified water columns and sediments. During cytokinesis, magnetosome chains have to be properly positioned, cleaved and separated in order to be evenly passed into daughter cells. In Magnetospirillum gryphiswaldense, the assembly of the magnetosome chain is controlled by the actin-like MamK, which polymerizes into cytoskeletal filaments that are connected to magnetosomes through the acidic MamJ protein. MamK filaments were speculated to recruit the magnetosome chain to cellular division sites, thus ensuring equal organelle inheritance. However, the underlying mechanism of magnetic organelle segregation has remained largely unknown. RESULTS: Here, we performed in vivo time-lapse fluorescence imaging to directly track the intracellular movement and dynamics of magnetosome chains as well as photokinetic and ultrastructural analyses of the actin-like cytoskeletal MamK filament. We show that magnetosome chains undergo rapid intracellular repositioning from the new poles towards midcell into the newborn daughter cells, and the driving force for magnetosomes movement is likely provided by the pole-to-midcell treadmilling growth of MamK filaments. We further discovered that splitting and equipartitioning of magnetosome chains occurs with unexpectedly high accuracy, which depends directly on the dynamics of MamK filaments. CONCLUSION: We propose a novel mechanism for prokaryotic organelle segregation that, similar to the type-II bacterial partitioning system of plasmids, relies on the action of cytomotive actin-like filaments together with specific connectors, which transport the magnetosome cargo in a fashion reminiscent of eukaryotic actin-organelle transport and segregation mechanisms.

Facilitated diffusion in the presence of obstacles on the DNA.

Biological functions of DNA depend on the sequence-specific binding of DNA-binding proteins to their corresponding binding sites. Binding of these proteins to their binding sites occurs through a facilitated diffusion process that combines three-dimensional diffusion in the cytoplasm with one-dimensional diffusion (sliding) along the DNA. In this work, we use a lattice model of facilitated diffusion to study how the dynamics of binding of a protein to a specific site (e.g., binding of an RNA polymerase to a promoter or of a transcription factor to its operator site) is affected by the presence of other proteins bound to the DNA, which act as 'obstacles' in the sliding process. Different types of these obstacles with different dynamics are implemented. While all types impair facilitated diffusion, the extent of the hindrance depends on the type of obstacle. As a consequence of hindrance by obstacles, more excursions into the cytoplasm are required for optimal target binding compared to the case without obstacles.

Differences between cotranscriptional and free riboswitch folding.

Riboswitches are part of noncoding regions of messenger RNA (mRNA) that act as RNA sensors regulating gene expression of the downstream gene. Typically, one out of two distinct conformations is formed depending on ligand binding when the transcript leaves RNA polymerase (RNAP). Elongation of the RNA chain by RNAP, folding and binding all occurs simultaneously and interdependently on the seconds' timescale. To investigate the effect of transcript elongation velocity on folding for the S-adenosylmethionine (SAM)-I and adenine riboswitches we employ two complementary coarse-grained in silico techniques. Native structure-based molecular dynamics simulations provide a 3D, atomically resolved model of folding with homogenous energetics. Energetically more detailed kinetic Monte Carlo simulations give access to longer timescale by describing folding on the secondary structure level and feature the incorporation of competing aptamer conformations and a ligand-binding model. Depending on the extrusion scenarios, we observe and quantify different pathways in structure formation with robust agreements between the two techniques. In these scenarios, free-folding riboswitches exhibit different folding characteristics compared with transcription-rate limited folding. The critical transcription rate distinguishing these cases is higher than physiologically relevant rates. This result suggests that in vivo folding of the analyzed SAM-I and adenine riboswitches is transcription-rate limited.

Control of transcription elongation by GreA determines rate of gene expression in Streptococcus pneumoniae.

Transcription by RNA polymerase may be interrupted by pauses caused by backtracking or misincorporation that can be resolved by the conserved bacterial Gre-factors. However, the consequences of such pausing in the living cell remain obscure. Here, we developed molecular biology and transcriptome sequencing tools in the human pathogen Streptococcus pneumoniae and provide evidence that transcription elongation is rate-limiting on highly expressed genes. Our results suggest that transcription elongation may be a highly regulated step of gene expression in S. pneumoniae. Regulation is accomplished via long-living elongation pauses and their resolution by elongation factor GreA. Interestingly, mathematical modeling indicates that long-living pauses cause queuing of RNA polymerases, which results in 'transcription traffic jams' on the gene and thus blocks its expression. Together, our results suggest that long-living pauses and RNA polymerase queues caused by them are a major problem on highly expressed genes and are detrimental for cell viability. The major and possibly sole function of GreA in S. pneumoniae is to prevent formation of backtracked elongation complexes.