Long-term model predictive control of gene expression at the population and single-cell levels

Gene expression plays a central role in the orchestration of cellular processes. The use of inducible promoters to change the expression level of a gene from its physiological level has significantly contributed to the understanding of the functioning of regulatory networks. However, from a quantitative point of view, their use is limited to short-term, population-scale studies to average out cell-to-cell variability and gene expression noise and limit the nonpredictable effects of internal feedback loops that may antagonize the inducer action. Here, we show that, by implementing an external feedback loop, one can tightly control the expression of a gene over many cell generations with quantitative accuracy. To reach this goal, we developed a platform for real-time, closed-loop control of gene expression in yeast that integrates microscopy for monitoring gene expression at the cell level, microfluidics to manipulate the cells' environment, and original software for automated imaging, quantification, and model predictive control. By using an endogenous osmostress responsive promoter and playing with the osmolarity of the cells environment, we show that long-term control can, indeed, be achieved for both time-constant and time-varying target profiles at the population and even the single-cell levels. Importantly, we provide evidence that real-time control can dynamically limit the effects of gene expression stochasticity. We anticipate that our method will be useful to quantitatively probe the dynamic properties of cellular processes and drive complex, synthetically engineered networks.     

Rate of environmental change determines stress response specificity

Cells use general stress response pathways to activate diverse target genes in response to a variety of stresses. However, general stress responses coexist with more specific pathways that are activated by individual stresses, provoking the fundamental question of whether and how cells control the generality or specificity of their response to a particular stress. Here we address this issue using quantitative time-lapse microscopy of the Bacillus subtilis environmental stress response, mediated by σ^B. We analyzed σ^B activation in response to stresses such as salt and ethanol imposed at varying rates of increase. Dynamically, σ^B responded to these stresses with a single adaptive activity pulse, whose amplitude depended on the rate at which the stress increased. This rate-responsive behavior can be understood from mathematical modeling of a key negative feedback loop in the underlying regulatory circuit. Using RNAseq we analyzed the effects of both rapid and gradual increases of ethanol and salt stress across the genome. Because of the rate responsiveness of σ^B activation, salt and ethanol regulons overlap under rapid, but not gradual, increases in stress. Thus, the cell responds specifically to individual stresses that appear gradually, while using σ^B to broaden the cellular response under more rapidly deteriorating conditions. Such dynamic control of specificity could be a critical function of other general stress response pathways.     

Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale

The low-temperature thermal properties of dielectric crystals are governed by acoustic excitations with large wavelengths that are well described by plane waves. This is the Debye model, which rests on the assumption that the medium is an elastic continuum, holds true for acoustic wavelengths large on the microscopic scale fixed by the interatomic spacing, and gradually breaks down on approaching it. Glasses are characterized as well by universal low-temperature thermal properties that are, however, anomalous with respect to those of the corresponding crystalline phases. Related universal anomalies also appear in the low-frequency vibrational density of states and, despite a longstanding debate, remain poorly understood. By using molecular dynamics simulations of a model monatomic glass of extremely large size, we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the acoustic excitations breaks down abruptly on the mesoscopic, medium-range-order length scale of ≈10 interatomic spacings, where it still works well for the corresponding crystalline systems. On this scale, the sound velocity shows a marked reduction with respect to the macroscopic value. This reduction turns out to be closely related to the universal excess over the Debye model prediction found in glasses at frequencies of ≈1 THz in the vibrational density of states or at temperatures of ≈10 K in the specific heat.     

Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism

Gravity profoundly influences plant growth and development. Plants respond to changes in orientation by using gravitropic responses to modify their growth. Cholodny and Went hypothesized over 80 years ago that plants bend in response to a gravity stimulus by generating a lateral gradient of a growth regulator at an organ's apex, later found to be auxin. Auxin regulates root growth by targeting Aux/IAA repressor proteins for degradation. We used an Aux/IAA-based reporter, domain II (DII)-VENUS, in conjunction with a mathematical model to quantify auxin redistribution following a gravity stimulus. Our multidisciplinary approach revealed that auxin is rapidly redistributed to the lower side of the root within minutes of a 90° gravity stimulus. Unexpectedly, auxin asymmetry was rapidly lost as bending root tips reached an angle of 40° to the horizontal. We hypothesize roots use a "tipping point" mechanism that operates to reverse the asymmetric auxin flow at the midpoint of root bending. These mechanistic insights illustrate the scientific value of developing quantitative reporters such as DII-VENUS in conjunction with parameterized mathematical models to provide high-resolution kinetics of hormone redistribution.     

The narrow escape problem for diffusion in cellular microdomains

The study of the diffusive motion of ions or molecules in confined biological microdomains requires the derivation of the explicit dependence of quantities, such as the decay rate of the population or the forward chemical reaction rate constant on the geometry of the domain. Here, we obtain this explicit dependence for a model of a Brownian particle (ion, molecule, or protein) confined to a bounded domain (a compartment or a cell) by a reflecting boundary, except for a small window through which it can escape. We call the calculation of the mean escape time the narrow escape problem. This time diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. Here, we present asymptotic formulas for the mean escape time in several cases, including regular domains in two and three dimensions and in some singular domains in two dimensions. The mean escape time comes up in many applications, because it represents the mean time it takes for a molecule to hit a target binding site. We present several applications in cellular biology: calcium decay in dendritic spines, a Markov model of multicomponent chemical reactions in microdomains, dynamics of receptor diffusion on the surface of neurons, and vesicle trafficking inside a cell.     

Molecular structure of the lecithin ripple phase

Molecular dynamics simulations of lecithin lipid bilayers in water as they are cooled from the liquid crystalline phase show the spontaneous formation of rippled bilayers. The ripple consists of two domains of different length and orientation, connected by a kink. The organization of the lipids in one domain of the ripple is found to be that of a splayed gel; in the other domain the lipids are gel-like and fully interdigitated. In the concave part of the kink region between the domains the lipids are disordered. The results are consistent with the experimental information available and provide an atomic-level model that may be tested by further experiments.     

Caulobacter chromosome segregation is an ordered multistep process

Despite its fundamental nature, bacterial chromosome segregation remains poorly understood. Viewing segregation as a single process caused multiple proposed mechanisms to appear in conflict and failed to explain how asymmetrically dividing bacteria break symmetry to move only one of their chromosomes. Here, we demonstrate that the ParA ATPase extends from one cell pole and pulls the chromosome by retracting upon association with the ParB DNA-binding protein. Surprisingly, ParA disruption has a specific effect on chromosome segregation that only perturbs the latter stages of this process. Using quantitative high-resolution imaging, we demonstrate that this specificity results from the multistep nature of chromosome translocation. We propose that Caulobacter chromosome segregation follows an ordered pathway of events with distinct functions and mechanisms. Initiation releases polar tethering of the origin of replication, distinction spatially differentiates the two chromosomes, and commitment irreversibly translocates the distal centromeric locus. Thus, much as eukaryotic mitosis involves a sequence of distinct subprocesses, Caulobacter cells also segregate their chromosomes through an orchestrated series of steps. We discuss how the multistep view of bacterial chromosome segregation can help to explain and reconcile outstanding puzzles and frame future investigation.     

Gate-controlled proton diffusion and protonation-induced ratchet motion in the stator of the bacterial flagellar motor

The proton permeation process of the stator complex MotA/B in the flagellar motor of Escherichia coli was investigated. The atomic model structure of the transmembrane part of MotA/B was constructed based on the previously published disulfide cross-linking and tryptophan scanning mutations. The dynamic permeation of hydronium/sodium ions and water molecule through the channel formed in MotA/B was observed using a steered molecular dynamics simulation. During the simulation, Leu46 of MotB acts as the gate for hydronium ion permeation, which induced the formation of water wire that may mediate the proton transfer to Asp32 on MotB. Free energy profiles for permeation were calculated by umbrella sampling. The free energy barrier for H₃O⁺ permeation was consistent with the proton transfer rate deduced from the flagellar rotational speed and number of protons per rotation, which suggests that the gating is the rate-limiting step. Structure and dynamics of the MotA/B with nonprotonated and protonated Asp32, Val43Met, and Val43Leu mutants in MotB were investigated using molecular dynamics simulation. A narrowing of the channel was observed in the mutants, which is consistent with the size-dependent ion selectivity. In MotA/B with the nonprotonated Asp32, the A3 segment in MotA maintained a kink whereas the protonation induced a straighter shape. Assuming that the cytoplasmic domain not included in the atomic model moves as a rigid body, the protonation/deprotonation of Asp32 is inferred to induce a ratchet motion of the cytoplasmic domain, which may be correlated to the motion of the flagellar rotor.Bacterial flagella are multifuel engines that convert ion motive force to molecular motor rotation. Escherichia coli has a few proton-driven flagellar motors with stators (protein MotA/B complex) in the inner membrane that act as proton channels (1–5). In addition, Vibrio alginolyticus has a polar flagellum powered by sodium ions (6). Bacillus alcalophilus has motors driven by rubidium (Rb⁺), potassium (K⁺), and sodium ions (Na⁺) that can be converted to Na⁺-driven motors by a single mutation (7).The proton transfer mechanism in membrane proteins is associated with water wire and/or a hydrogen bond chain (HBC) (8, 9). The water wire comprises water molecules aligned in a protein channel, where protons are transferred by hopping along the wire. Protons are conducted through the hydrogen bonds formed by the polar amino acid residues and water molecules along the proton transfer pathway in the HBC. Protons can also be transferred by diffusion of hydronium ions (H₃O⁺). The diffusion distance in a hydrophilic environment is short in a liquid (the lifetime in water is ca. 1 ps) (10, 11), but it should be longer in a more hydrophobic environment. H₃O⁺ forms a hydrogen bond (H bond) with the nearest neighbor water molecules and the carbonyl groups, and proton hopping along the H bonds is faster than diffusion of Na⁺ and K⁺ in the ion channel of Gramicidin A (12, 13).These flagellar motors can rotate in both clockwise (CW) and counterclockwise (CCW) directions (viewed from the outside of the cell), and the swimming pattern of the bacteria is controlled by reversal of the motor rotation (14). In E. coli, the FliG, FliM, FliN, MotA, and MotB proteins are involved with torque generation (Fig. 1A) (14, 15). FliG, FliM, and FliN constitute the flagellar rotor and are also involved with the CW/CCW switching. Each rotor is typically surrounded by 10 stators that consist of two membrane proteins, MotA and MotB (PomA and PomB in V. alginolyticus). Each stator is composed of four MotA and two MotB proteins, and can independently produce torque for flagellar rotation.Open in a separate windowFig. 1.Overall structure of MotA/B. (A) Schematic views of the flagellar motors of E. coli (Left) and V. alginolyticus (Right), (B) TM regions modeled, and (C) TM helix arrangement in the initial modeling of MotA/B in E. coli. The obtained atomic model structure viewed parallel to the membrane (D) and from the periplasmic side (E). Spheres denote P atoms in the lipid head groups. MotA/B cross sections of the area enclosed by magenta in E around a channel at the levels of Leu46 (F) and Asp32 (G). x, y, and z axes are defined as in D and E.Systematic Cys and Trp mutagenesis (16–20) has provided essential information on the structure and function of the flagellar motor. Each MotA (295 residues) contains four transmembrane (TM) alpha helical segments (A1–A4), two short loops in the periplasm, and two long segments (residues 61–160 and 228–295) in the cytoplasm (Fig. 1B) (3, 21). Arg90 and Glu98 on the MotA cytoplasmic domain interact with the polar residues on the rotor protein, FliG, during the rotation of the motor (22, 23). It has been suggested that Pro173 and Pro222 at the cytoplasmic sides of A3 and A4 regulate the conformational changes required for torque generation (24). MotB (308 residues) is composed of a short N-terminal cytoplasimic segment, one TM helix (B), and a large C-terminal periplasmic domain (Fig. 1B) (4, 5). Asp32, which is situated near the cytoplasmic end of the B segment, is conserved across the species and considered to be the most plausible proton binding site (25). The B segment is expected to form a proton channel together with A3 and A4 (Fig. 1C) (17). Only a few polar residues have been identified in the predicted TM segments of MotA/B (19, 20), which implies that the channel surface should be relatively hydrophobic. The periplasmic region of MotB has a peptidoglycan binding motif, which anchors the stator complex to the peptidoglycan layer around the rotor (5, 26). Deletion of residues 52–65 just after the B segment causes proton leakage and cell growth arrest, which suggests that this fragment acts as a plug to suppress proton leakage (27). The generation of torque is hypothesized to originate from the conformational changes of the MotA cytoplasmic domain upon proton association/dissociation at the carboxyl group of Asp32 on MotB and by the interaction with FliG in the rotor (28–31).In the present study, the mechanism for proton permeation in MotA/B was investigated (Fig. S1). The atomic structure of MotA/B was constructed based on the disulfide cross-linking (16–18) and tryptophan scanning mutations (19, 20). The dynamic permeation of hydronium ions, sodium ions, and water molecules was observed using a steered molecular dynamics (SMD) simulation (32–34), and free energy profiles for ion/water permeation were calculated by umbrella sampling. The effects of amino acid substitutions related to ion selectivity was investigated, and the possible ratchet motion of the cytoplasmic domain induced by protonation/deprotonation cycle of Asp32 was examined.Open in a separate windowFig. S1.Overall scheme of this study.     

The use of oscillatory signals in the study of genetic networks

The structure of a genetic network is uncovered by studying its response to external stimuli (input signals). We present a theory of propagation of an input signal through a linear stochastic genetic network. We found that there are important advantages in using oscillatory signals over step or impulse signals and that the system may enter into a pure fluctuation resonance for a specific input frequency.     

Lateral acquisition of genes is affected by the friendliness of their products

A major factor in the evolution of microbial genomes is the lateral acquisition of genes that evolved under the functional constraints of other species. Integration of foreign genes into a genome that has different components and circuits poses an evolutionary challenge. Moreover, genes belonging to complex modules in the pretransfer species are unlikely to maintain their functionality when transferred alone to new species. Thus, it is widely accepted that lateral gene transfer favors proteins with only a few protein-protein interactions. The propensity of proteins to participate in protein-protein interactions can be assessed using computational methods that identify putative interaction sites on the protein. Here we report that laterally acquired proteins contain significantly more putative interaction sites than native proteins. Thus, genes encoding proteins with multiple protein-protein interactions may in fact be more prone to transfer than genes with fewer interactions. We suggest that these proteins have a greater chance of forming new interactions in new species, thus integrating into existing modules. These results reveal basic principles for the incorporation of novel genes into existing systems.     

Arp2/3 complex is bound and activated by two WASP proteins

Actin related protein 2/actin related protein 3 (Arp2/3) complex nucleates new actin filaments in eukaryotic cells in response to signals from proteins in the Wiskott-Aldrich syndrome protein (WASP) family. The conserved VCA domain of WASP proteins activates Arp2/3 complex by inducing conformational changes and delivering the first actin monomer of the daughter filament. Previous models of activation have invoked a single VCA acting at a single site on Arp2/3 complex. Here we show that activation most likely involves engagement of two distinct sites on Arp2/3 complex by two VCA molecules, each delivering an actin monomer. One site is on Arp3 and the second is on ARPC1 and Arp2. The VCAs at these sites have distinct roles in activation. Our findings reconcile apparently conflicting literature on VCA activation of Arp2/3 complex and lead to a new model for this process.     

Structure of the yeast F1Fo-ATP synthase dimer and its role in shaping the mitochondrial cristae

We used electron cryotomography of mitochondrial membranes from wild-type and mutant Saccharomyces cerevisiae to investigate the structure and organization of ATP synthase dimers in situ. Subtomogram averaging of the dimers to 3.7 nm resolution revealed a V-shaped structure of twofold symmetry, with an angle of 86° between monomers. The central and peripheral stalks are well resolved. The monomers interact within the membrane at the base of the peripheral stalks. In wild-type mitochondria ATP synthase dimers are found in rows along the highly curved cristae ridges, and appear to be crucial for membrane morphology. Strains deficient in the dimer-specific subunits e and g or the first transmembrane helix of subunit 4 lack both dimers and lamellar cristae. Instead, cristae are either absent or balloon-shaped, with ATP synthase monomers distributed randomly in the membrane. Computer simulations indicate that isolated dimers induce a plastic deformation in the lipid bilayer, which is partially relieved by their side-by-side association. We propose that the assembly of ATP synthase dimer rows is driven by the reduction in the membrane elastic energy, rather than by direct protein contacts, and that the dimer rows enable the formation of highly curved ridges in mitochondrial cristae.