DNA surface exploration and operator bypassing during target search.

Many proteins that bind specific DNA sequences search the genome by combining three-dimensional diffusion with one-dimensional sliding on nonspecific DNA1-5. Here we combine resonance energy transfer and fluorescence correlation measurements to characterize how individual lac repressor (LacI) molecules explore the DNA surface during the one-dimensional phase of target search. To track the rotation of sliding LacI molecules on the microsecond timescale, we use real-time single-molecule confocal laser tracking combined with fluorescence correlation spectroscopy (SMCT-FCS). The fluctuations in fluorescence signal are accurately described by rotation-coupled sliding, in which LacI traverses about 40 base pairs (bp) per revolution. This distance substantially exceeds the 10.5-bp helical pitch of DNA; this suggests that the sliding protein frequently hops out of the DNA groove, which would result in the frequent bypassing of target sequences. We directly observe such bypassing using single-molecule fluorescence resonance energy transfer (smFRET). A combined analysis of the smFRET and SMCT-FCS data shows that LacI hops one or two grooves (10-20 bp) every 200-700 µs. Our data suggest a trade-off between speed and accuracy during sliding: the weak nature of nonspecific protein-DNA interactions underlies operator bypassing, but also speeds up sliding. We anticipate that SMCT-FCS, which monitors rotational diffusion on the microsecond timescale while tracking individual molecules with millisecond resolution, will be applicable to the real-time investigation of many other biological interactions and will effectively extend the accessible time regime for observing these interactions by two orders of magnitude.

Evolution of high-level resistance during low-level antibiotic exposure.

It has become increasingly clear that low levels of antibiotics present in many environments can select for resistant bacteria, yet the evolutionary pathways for resistance development during exposure to low amounts of antibiotics remain poorly defined. Here we show that Salmonella enterica exposed to sub-MIC levels of streptomycin evolved high-level resistance via novel mechanisms that are different from those observed during lethal selections. During lethal selection only rpsL mutations are found, whereas at sub-MIC selection resistance is generated by several small-effect resistance mutations that combined confer high-level resistance via three different mechanisms: (i) alteration of the ribosomal RNA target (gidB mutations), (ii) reduction in aminoglycoside uptake (cyoB, nuoG, and trkH mutations), and (iii) induction of the aminoglycoside-modifying enzyme AadA (znuA mutations). These results demonstrate how the strength of the selective pressure influences evolutionary trajectories and that even weak selective pressures can cause evolution of high-level resistance.

Variation in Mutational Robustness between Different Proteins and the Predictability of Fitness Effects.

Random mutations in genes from disparate protein classes may have different distributions of fitness effects (DFEs) depending on different structural, functional, and evolutionary constraints. We measured the fitness effects of 156 single mutations in the genes encoding AraC (transcription factor), AraD (enzyme), and AraE (transporter) used for bacterial growth on l-arabinose. Despite their different molecular functions these genes all had bimodal DFEs with most mutations either being neutral or strongly deleterious, providing a general expectation for the DFE. This contrasts with the unimodal DFEs previously obtained for ribosomal protein genes where most mutations were slightly deleterious. Based on theoretical considerations, we suggest that the 33-fold higher average mutational robustness of ribosomal proteins is due to stronger selection for reduced costs of translational and transcriptional errors. Whereas the large majority of synonymous mutations were deleterious for ribosomal proteins genes, no fitness effects could be detected for the AraCDE genes. Four mutations in AraC and AraE increased fitness, suggesting that slightly advantageous mutations make up a significant fraction of the DFE, but that they often escape detection due to the limited sensitivity of commonly used fitness assays. We show that the fitness effects of amino acid substitutions can be predicted based on evolutionary conservation, but those weakly deleterious mutations are less reliably detected. This suggests that large-effect mutations and the fraction of highly deleterious mutations can be computationally predicted, but that experiments are required to characterize the DFE close to neutrality, where many mutations ultimately fixed in a population will occur.

Quantification of transcription factor-DNA binding affinity in a living cell.

The apparent dissociation constant (Kd) for specific binding of glucocorticoid receptor (GR) and androgen receptor (AR) to DNA was determined in vivo in Xenopus oocytes. The total nuclear receptor concentration was quantified as specifically retained [(3)H]-hormone in manually isolated oocyte nuclei. DNA was introduced by nuclear microinjection of single stranded phagemid DNA, chromatin is then formed during second strand synthesis. The fraction of DNA sites occupied by the expressed receptor was determined by dimethylsulphate in vivo footprinting and used for calculation of the receptor-DNA binding affinity. The forkhead transcription factor FoxA1 enhanced the DNA binding by GR with an apparent Kd of ∼1 µM and dramatically stimulated DNA binding by AR with an apparent Kd of ∼0.13 µM at a composite androgen responsive DNA element containing one FoxA1 binding site and one palindromic hormone receptor binding site known to bind one receptor homodimer. FoxA1 exerted a weak constitutive- and strongly cooperative DNA binding together with AR but had a less prominent effect with GR, the difference reflecting the licensing function of FoxA1 at this androgen responsive DNA element.

What matters for lac repressor search in vivo--sliding, hopping, intersegment transfer, crowding on DNA or recognition?

We have investigated which aspects of transcription factor DNA interactions are most important to account for the recent in vivo search time measurements for the dimeric lac repressor. We find the best agreement for a sliding model where non-specific binding to DNA is improbable at first contact and the sliding LacI protein binds at high probability when reaching the specific Osym operator. We also find that the contribution of hopping to the overall search speed is negligible although physically unavoidable. The parameters that give the best fit reveal sliding distances, including hopping, close to what has been proposed in the past, i.e. ∼40 bp, but with an unexpectedly high 1D diffusion constant on non-specific DNA sequences. Including a mechanism of inter-segment transfer between distant DNA segments does not bring down the 1D diffusion to the expected fraction of the in vitro value. This suggests a mechanism where transcription factors can slide less hindered in vivo than what is given by a simple viscosity scaling argument or that a modification of the model is needed. For example, the estimated diffusion rate constant would be consistent with the expectation if parts of the chromosome, away from the operator site, were inaccessible for searching.

High fitness costs and instability of gene duplications reduce rates of evolution of new genes by duplication-divergence mechanisms.

An important mechanism for generation of new genes is by duplication-divergence of existing genes. Duplication-divergence includes several different submodels, such as subfunctionalization where after accumulation of neutral mutations the original function is distributed between two partially functional and complementary genes, and neofunctionalization where a new function evolves in one of the duplicated copies while the old function is maintained in another copy. The likelihood of these mechanisms depends on the longevity of the duplicated state, which in turn depends on the fitness cost and genetic stability of the duplications. Here, we determined the fitness cost and stability of defined gene duplications/amplifications on a low copy number plasmid. Our experimental results show that the costs of carrying extra gene copies are substantial and that each additional kilo base pairs of DNA reduces fitness by approximately 0.15%. Furthermore, gene amplifications are highly unstable and rapidly segregate to lower copy numbers in absence of selection. Mathematical modeling shows that the fitness costs and instability strongly reduces the likelihood of both sub- and neofunctionalization, but that these effects can be offset by positive selection for novel beneficial functions.

Transcription-factor binding and sliding on DNA studied using micro- and macroscopic models.

Transcription factors search for specific operator sequences by alternating rounds of 3D diffusion with rounds of 1D diffusion (sliding) along the DNA. The details of such sliding have largely been beyond direct experimental observation. For this purpose we devised an analytical formulation of umbrella sampling along a helical coordinate, and from extensive and fully atomistic simulations we quantified the free-energy landscapes that underlie the sliding dynamics and dissociation kinetics for the LacI dimer. The resulting potential of mean force distributions show a fine structure with an amplitude of 1 k(B)T for sliding and 12 k(B)T for dissociation. Based on the free-energy calculations the repressor slides in close contact with DNA for 8 bp on average before making a microscopic dissociation. By combining the microscopic molecular-dynamics calculations with Brownian simulation including rotational diffusion from the microscopically dissociated state we estimate a macroscopic residence time of 48 ms at the same DNA segment and an in vitro sliding distance of 240 bp. The sliding distance is in agreement with previous in vitro sliding-length estimates. The in vitro prediction for the macroscopic residence time also compares favorably to what we measure by single-molecule imaging of nonspecifically bound fluorescently labeled LacI in living cells. The investigation adds to our understanding of transcription-factor search kinetics and connects the macro-/mesoscopic rate constants to the microscopic dynamics.

Lost in presumption: stochastic reactions in spatial models.

Physical modeling is increasingly important for generating insights into intracellular processes. We describe situations in which combined spatial and stochastic aspects of chemical reactions are needed to capture the relevant dynamics of biochemical systems.

Selection-driven gene loss in bacteria.

Gene loss by deletion is a common evolutionary process in bacteria, as exemplified by bacteria with small genomes that have evolved from bacteria with larger genomes by reductive processes. The driving force(s) for genome reduction remains unclear, and here we examined the hypothesis that gene loss is selected because carriage of superfluous genes confers a fitness cost to the bacterium. In the bacterium Salmonella enterica, we measured deletion rates at 11 chromosomal positions and the fitness effects of several spontaneous deletions. Deletion rates varied over 200-fold between different regions with the replication terminus region showing the highest rates. Approximately 25% of the examined deletions caused an increase in fitness under one or several growth conditions, and after serial passage of wild-type bacteria in rich medium for 1,000 generations we observed fixation of deletions that substantially increased bacterial fitness when reconstructed in a non-evolved bacterium. These results suggest that selection could be a significant driver of gene loss and reductive genome evolution.

The lac repressor displays facilitated diffusion in living cells.

Transcription factors (TFs) are proteins that regulate the expression of genes by binding sequence-specific sites on the chromosome. It has been proposed that to find these sites fast and accurately, TFs combine one-dimensional (1D) sliding on DNA with 3D diffusion in the cytoplasm. This facilitated diffusion mechanism has been demonstrated in vitro, but it has not been shown experimentally to be exploited in living cells. We have developed a single-molecule assay that allows us to investigate the sliding process in living bacteria. Here we show that the lac repressor slides 45 ± 10 base pairs on chromosomal DNA and that sliding can be obstructed by other DNA-bound proteins near the operator. Furthermore, the repressor frequently (>90%) slides over its natural lacO(1) operator several times before binding. This suggests a trade-off between rapid search on nonspecific sequences and fast binding at the specific sequence.

Selection of resistant bacteria at very low antibiotic concentrations.

The widespread use of antibiotics is selecting for a variety of resistance mechanisms that seriously challenge our ability to treat bacterial infections. Resistant bacteria can be selected at the high concentrations of antibiotics used therapeutically, but what role the much lower antibiotic concentrations present in many environments plays in selection remains largely unclear. Here we show using highly sensitive competition experiments that selection of resistant bacteria occurs at extremely low antibiotic concentrations. Thus, for three clinically important antibiotics, drug concentrations up to several hundred-fold below the minimal inhibitory concentration of susceptible bacteria could enrich for resistant bacteria, even when present at a very low initial fraction. We also show that de novo mutants can be selected at sub-MIC concentrations of antibiotics, and we provide a mathematical model predicting how rapidly such mutants would take over in a susceptible population. These results add another dimension to the evolution of resistance and suggest that the low antibiotic concentrations found in many natural environments are important for enrichment and maintenance of resistance in bacterial populations.

Kick-starting the ratchet: the fate of mutators in an asexual population.

Muller's ratchet operates in asexual populations without intergenomic recombination. In this case, deleterious mutations will accumulate and population fitness will decline over time, possibly endangering the survival of the species. Mutator mutations, i.e., mutations that lead to an increased mutation rate, will play a special role for the behavior of the ratchet. First, they are part of the ratchet and can come to dominance through accumulation in the ratchet. Second, the fitness-loss rate of the ratchet is very sensitive to changes in the mutation rate and even a modest increase can easily set the ratchet in motion. In this article we simulate the interplay between fitness loss from Muller's ratchet and the evolution of the mutation rate from the fixation of mutator mutations. As long as the mutation rate is increased in sufficiently small steps, an accelerating ratchet and eventual extinction are inevitable. If this can be countered by antimutators, i.e., mutations that reduce the mutation rate, an equilibrium can be established for the mutation rate at some level that may allow survival. However, the presence of the ratchet amplifies fluctuations in the mutation rate and, even at equilibrium, these fluctuations can lead to dangerous bursts in the ratchet. We investigate the timescales of these processes and discuss the results with reference to the genome degradation of the aphid endosymbiont Buchnera aphidicola.

Mutational robustness of ribosomal protein genes.

The distribution of fitness effects (DFE) of mutations is of fundamental importance for understanding evolutionary dynamics and complex diseases and for conserving threatened species. DFEs estimated from DNA sequences have rarely been subject to direct experimental tests. We used a bacterial system in which the fitness effects of a large number of defined single mutations in two ribosomal proteins were measured with high sensitivity. The obtained DFE appears to be unimodal, where most mutations (120 out of 126) are weakly deleterious and the remaining ones are potentially neutral. The DFEs for synonymous and nonsynonymous substitutions are similar, suggesting that in some genes, strong fitness constraints are present at the level of the messenger RNA.

Stochastic reaction-diffusion kinetics in the microscopic limit.

Quantitative analysis of biochemical networks often requires consideration of both spatial and stochastic aspects of chemical processes. Despite significant progress in the field, it is still computationally prohibitive to simulate systems involving many reactants or complex geometries using a microscopic framework that includes the finest length and time scales of diffusion-limited molecular interactions. For this reason, spatially or temporally discretized simulations schemes are commonly used when modeling intracellular reaction networks. The challenge in defining such coarse-grained models is to calculate the correct probabilities of reaction given the microscopic parameters and the uncertainty in the molecular positions introduced by the spatial or temporal discretization. In this paper we have solved this problem for the spatially discretized Reaction-Diffusion Master Equation; this enables a seamless and physically consistent transition from the microscopic to the macroscopic frameworks of reaction-diffusion kinetics. We exemplify the use of the methods by showing that a phosphorylation-dephosphorylation motif, commonly observed in eukaryotic signaling pathways, is predicted to display fluctuations that depend on the geometry of the system.

Compensatory gene amplification restores fitness after inter-species gene replacements.

Genes introduced by gene replacements and other types of horizontal gene transfer (HGT) represent a significant presence in many archaeal and eubacterial genomes. Most alien genes are likely to be neutral or deleterious upon arrival and their long-term persistence may require a mechanism that improves their selective contribution. To examine the fate of inter-species gene replacements, we exchanged three native S. typhimurium genes encoding ribosomal proteins with orthologues from various other microbes. The results show that replacement of each of these three genes reduces fitness to such an extent that it would provide an effective barrier against inter-species gene replacements in eubacterial populations. However, these fitness defects could be partially ameliorated by gene amplification that augmented the dosage of the heterologous proteins. This suggests that suboptimal expression is a common fitness constraint for inter-species gene replacements, with fitness costs conferred by either a lower expression level of the alien protein compared with the native protein or a requirement for an increased amount of the alien protein to maintain proper function. Our findings can explain the observation that duplicated genes are over-represented among horizontally transferred genes, and suggest a potential coupling between compensatory gene amplification after HGT and the evolution of new genes.

Contribution of gene amplification to evolution of increased antibiotic resistance in Salmonella typhimurium.

The use of beta-lactam antibiotics has led to the evolution and global spread of a variety of resistance mechanisms, including beta-lactamases, a group of enzymes that degrade the beta-lactam ring. The evolution of increased beta-lactam resistance was studied by exposing independent lineages of Salmonella typhimurium to progressive increases in cephalosporin concentration. Each lineage carried a beta-lactamase gene (bla(TEM-1)) that provided very low resistance. In most lineages, the initial response to selection was an amplification of the bla(TEM-1) gene copy number. Amplification was followed in some lineages by mutations (envZ, cpxA, or nmpC) that reduced expression of the uptake functions, the OmpC, OmpD, and OmpF porins. The initial resistance provided by bla(TEM-1) amplification allowed the population to expand sufficiently to realize rare secondary point mutations. Mathematical modeling showed that amplification often is likely to be the initial response because events that duplicate or further amplify a gene are much more frequent than point mutations. These models show the importance of the population size to appearance of later point mutations. Transient gene amplification is likely to be a common initial mechanism and an intermediate in stable adaptive improvement. If later point mutations (allowed by amplification) provide sufficient adaptive improvement, the amplification may be lost.

Thermodynamic reciprocity of the inhibitor binding to the active site and the interface binding region of IB phospholipase A2.

Interfacial activation of pig pancreatic IB phospholipase A(2) (PLA2) is modeled in terms of the three discrete premicellar complexes (E(i)(#), i = 1, 2, or 3) consecutively formed by the cooperative binding of a monodisperse amphiphile to the i-face (the interface binding region of the enzyme) without or with an occupied active site. Monodisperse PCU, the sn-2-amide analogue of the zwitterionic substrate, is a competitive inhibitor. PCU cooperatively binds to the i-face to form premicellar complexes (E(i), i = 1 or 2) and also binds to the active site of the premicellar complexes in the presence of calcium. In the E(i)I complex formed in the presence of PCU and calcium, one inhibitor molecule is bound to the active site and a number of others are bound to the i-face. The properties of the E(i) complexes with PCU are qualitatively similar to those of E(i)(#) formed with decylsulfate. Decylsulfate binds to the i-face but does not bind to the active site in the presence of calcium, nor does it interfere with the binding of PCU to the active site in the premicellar complexes. Due to the strong coupling between binding at the i-face and at the active site, it is difficult to estimate the primary binding constants for each site in these complexes. A model is developed that incorporates the above boundary conditions in relation to a detailed balance between the complexes. A key result is that a modest effect on cooperative amphiphile binding corresponds to a large change in the affinity of the inhibitor for the active site. We suggest that besides the binding to the active site, PCU also binds to another site and that full activation requires additional amphiphiles on the i-face. Thus, the activation of the inhibitor binding to the active site of the E(2)(#) complex or, equivalently, the shift in the E(1)(#) to E(2)(#) equilibrium by the inhibitor is analogous to the allosteric activation of the substrate binding to the enzyme bound to the interface.

Allosteric effect of amphiphile binding to phospholipase A(2).

In the preceding paper, we showed that the formation of the second premicellar complex of pig pancreatic IB phospholipase A2 (PLA2) can be considered a proxy for interface-activated substrate binding. Here we show that this conclusion is supported by results from premicellar E(i)(#) (i = 1, 2, or 3) complexes with a wide range of mutants of PLA2. Results also show a structural basis for the correlated functional changes during the formation of E(2)(#), and this is interpreted as an allosteric T (inactive) to R (active) transition. For example, the dissociation constant K(2)(#) for decylsulfate bound to E(2)(#) is lower at lower pH, at higher calcium concentrations, or with an inhibitor bound to the active site. Also, the lower limits of the K(2)(#) values are comparable under these conditions. The pH-dependent increase in K(2)(#) with a pK(a) of 6.5 is attributed to E71 which participates in the binding of the second calcium which in turn influences the enzyme binding to phosphatidylcholine interface. Most mutants exhibited kinetic and spectroscopic behavior that is comparable to that of native PLA2 and DeltaPLA2 with a deleted 62-66 loop. However, the DeltaY52L substitution mutant cannot undergo the calcium-, pH-, or interface-dependent changes. We suggest that the Y52L substitution impairs the R to T transition and also hinders the approach of the Michaelis complex to the transition state. This allosteric change may be mediated by the structural motifs that connect the D48-D99 catalytic diad, the substrate-binding slot, and the residues of the i-face. Our interpretation is that the 57-72 loop and the H(48)DNCY(52) segment of PLA2 are involved in transmitting the effect of the cooperative amphiphile binding to the i-face as a structural change in the active site.

Deletion rate evolution and its effect on genome size and coding density.

Deletion rates are thought to be important factors in determining the genome size of organisms in nature. Although it is indisputable that deletions, and thus deletion rates, affect genome size, it is unclear how, or indeed if, genome size is regulated via the deletion rate. Here, we employ a mathematical model to determine the evolutionary fate of deletion rate mutants. Simulations are employed to explore the interactions between deletions, deletion rate mutants, and genome size. The results show that, in this model, the fate of deletion rate mutants will depend on the fraction of essential genomic material, on the frequency of sexual recombination, as well as on the population size of the organism. We find that there is no optimal deletion rate in any state. However, at one critical coding density, all changes in deletion rate are neutral and the rate may drift either up or down. As a consequence, the coding density of the genome is expected to fluctuate around this critical density. Characteristic differences in the impact of deletion rate mutations on prokaryote and eukaryote genomes are described.

Evolution of new gene functions: simulation and analysis of the amplification model.

Creation of new genes and functions is a central feature of evolution. Duplication of existing genes has long been assumed to be the source of new genes, but the precise mechanism has remained unclear. One suggestion is that new genes are created via temporary amplifications, which simultaneously increase both the selective advantage of weak, pre-existing secondary functions and the target for optimizing mutations. This paper examines the amplification model by formalizing it into a mathematical framework. This framework is used to perform stochastic (Monte Carlo) simulations. In addition, experimental data from Salmonella typhimurium LT2 are used to support the modelling, by providing estimates for parameter values. The results show that amplification of tandem repeats is likely to contribute to creation of new genes in nature.