Mutations compensating for the fitness cost of rifampicin resistance in Escherichia coli exert pleiotropic effect on RNA polymerase catalysis.

The spread of drug-resistant bacteria represents one of the most significant medical problems of our time. Bacterial fitness loss associated with drug resistance can be counteracted by acquisition of secondary mutations, thereby enhancing the virulence of such bacteria. Antibiotic rifampicin (Rif) targets cellular RNA polymerase (RNAP). It is potent broad spectrum drug used for treatment of bacterial infections. We have investigated the compensatory mechanism of the secondary mutations alleviating Rif resistance (Rifr) on biochemical, structural and fitness indices. We find that substitutions in RNAP genes compensating for the growth defect caused by ßQ513P and ßT563P Rifr mutations significantly enhanced bacterial relative growth rate. By assaying RNAP purified from these strains, we show that compensatory mutations directly stimulated basal transcriptional machinery (2-9-fold) significantly improving promoter clearance step of the transcription pathway as well as elongation rate. Molecular modeling suggests that compensatory mutations affect transcript retention, substrate loading, and nucleotidyl transfer catalysis. Strikingly, one of the identified compensatory substitutions represents mutation conferring rifampicin resistance on its own. This finding reveals an evolutionary process that creates more virulent species by simultaneously improving the fitness and augmenting bacterial drug resistance.

Analysing the fitness cost of antibiotic resistance to identify targets for combination antimicrobials.

Mutations in the rifampicin (Rif)-binding site of RNA polymerase (RNAP) confer antibiotic resistance and often have global effects on transcription that compromise fitness and stress tolerance of resistant mutants. We suggested that the non-essential genome, through its impact on the bacterial transcription cycle, may represent an untapped source of targets for combination antimicrobial therapies. Using transposon sequencing, we carried out a genome-wide analysis of fitness cost in a clinically common rpoB H526Y mutant. We find that genes whose products enable increased transcription elongation rates compound the fitness costs of resistance whereas genes whose products function in cell wall synthesis and division mitigate it. We validate our findings by showing that the cell wall synthesis and division defects of rpoB H526Y result from an increased transcription elongation rate that is further exacerbated by the activity of the uracil salvage pathway and unresponsiveness of the mutant RNAP to the alarmone ppGpp. We applied our findings to identify drugs that inhibit more readily rpoB H526Y and other RifR alleles from the same phenotypic class. Thus, genome-wide analysis of fitness cost of antibiotic-resistant mutants should expedite the discovery of new combination therapies and delineate cellular pathways that underlie the molecular mechanisms of cost.

Role of bacterial RNA polymerase gate opening dynamics in DNA loading and antibiotics inhibition elucidated by quasi-Markov State Model.

To initiate transcription, the holoenzyme (RNA polymerase [RNAP] in complex with σ factor) loads the promoter DNA via the flexible loading gate created by the clamp and ß-lobe, yet their roles in DNA loading have not been characterized. We used a quasi-Markov State Model (qMSM) built from extensive molecular dynamics simulations to elucidate the dynamics of Thermus aquaticus holoenzyme's gate opening. We showed that during gate opening, ß-lobe oscillates four orders of magnitude faster than the clamp, whose opening depends on the Switch 2's structure. Myxopyronin, an antibiotic that binds to Switch 2, was shown to undergo a conformational selection mechanism to inhibit clamp opening. Importantly, we reveal a critical but undiscovered role of ß-lobe, whose opening is sufficient for DNA loading even when the clamp is partially closed. These findings open the opportunity for the development of antibiotics targeting ß-lobe of RNAP. Finally, we have shown that our qMSMs, which encode non-Markovian dynamics based on the generalized master equation formalism, hold great potential to be widely applied to study biomolecular dynamics.

The DnaK Chaperone System Buffers the Fitness Cost of Antibiotic Resistance Mutations in Mycobacteria.

Chaperones aid in protein folding and maintenance of protein integrity. In doing so, they have the unique ability to directly stabilize resistance-conferring amino acid substitutions in drug targets and to counter the stress imparted by these substitutions, thus supporting heritable antimicrobial resistance (AMR). We asked whether chaperones support AMR in Mycobacterium smegmatis, a saprophytic model of Mycobacterium tuberculosis, the causative agent of tuberculosis (TB). We show that DnaK associates with many drug targets and that DnaK associates more with AMR-conferring mutant RNA polymerase (RNAP) than with wild-type RNAP. In addition, frequency-of-resistance (FOR) and fitness studies reveal that the DnaK system of chaperones supports AMR in antimicrobial targets in mycobacteria, including RNAP and the ribosome. These findings highlight chaperones as potential targets for drugs to overcome AMR in mycobacteria, including M. tuberculosis, as well as in other pathogens.IMPORTANCE AMR is a global problem, especially for TB. Here, we show that mycobacterial chaperones support AMR in M. smegmatis, a nonpathogenic model of M. tuberculosis, the causative agent of TB. In particular, the mycobacterial DnaK system of chaperones supports AMR in the antimicrobial targets RNA polymerase and the ribosome. This is the first report showing a role for protein chaperones in mediating AMR in mycobacteria. Given the widespread role of protein chaperones in enabling genomic diversity, we anticipate that our findings can be extended to other microbes.

Engineered signal-coupled inducible promoters: measuring the apparent RNA-polymerase resource budget.

Inducible promoters are a central regulatory component in synthetic biology, metabolic engineering, and protein production for laboratory and commercial uses. Many of these applications utilize two or more exogenous promoters, imposing a currently unquantifiable metabolic burden on the living system. Here, we engineered a collection of inducible promoters (regulated by LacI-based transcription factors) that maximize the free-state of endogenous RNA polymerase (RNAP). We leveraged this collection of inducible promotors to construct simple two-channel logical controls that enabled us to measure metabolic burden - as it relates to RNAP resource partitioning. The two-channel genetic circuits utilized sets of signal-coupled transcription factors that regulate cognate inducible promoters in a coordinated logical fashion. With this fundamental genetic architecture, we evaluated the performance of each inducible promoter as discrete operations, and as coupled systems to evaluate and quantify the effects of resource partitioning. Obtaining the ability to systematically and accurately measure the apparent RNA-polymerase resource budget will enable researchers to design more robust genetic circuits, with significantly higher fidelity. Moreover, this study presents a workflow that can be used to better understand how living systems adapt RNAP resources, via the complementary pairing of constitutive and regulated promoters that vary in strength.

Bayesian inference and comparison of stochastic transcription elongation models.

Transcription elongation can be modelled as a three step process, involving polymerase translocation, NTP binding, and nucleotide incorporation into the nascent mRNA. This cycle of events can be simulated at the single-molecule level as a continuous-time Markov process using parameters derived from single-molecule experiments. Previously developed models differ in the way they are parameterised, and in their incorporation of partial equilibrium approximations. We have formulated a hierarchical network comprised of 12 sequence-dependent transcription elongation models. The simplest model has two parameters and assumes that both translocation and NTP binding can be modelled as equilibrium processes. The most complex model has six parameters makes no partial equilibrium assumptions. We systematically compared the ability of these models to explain published force-velocity data, using approximate Bayesian computation. This analysis was performed using data for the RNA polymerase complexes of E. coli, S. cerevisiae and Bacteriophage T7. Our analysis indicates that the polymerases differ significantly in their translocation rates, with the rates in T7 pol being fast compared to E. coli RNAP and S. cerevisiae pol II. Different models are applicable in different cases. We also show that all three RNA polymerases have an energetic preference for the posttranslocated state over the pretranslocated state. A Bayesian inference and model selection framework, like the one presented in this publication, should be routinely applicable to the interrogation of single-molecule datasets.

A method for cost-effective and rapid characterization of engineered T7-based transcription factors by cell-free protein synthesis reveals insights into the regulation of T7 RNA polymerase-driven expression.

The T7 bacteriophage RNA polymerase (T7 RNAP) serves as a model for understanding RNA synthesis, as a tool for protein expression, and as an actuator for synthetic gene circuit design in bacterial cells and cell-free extract. T7 RNAP is an attractive tool for orthogonal protein expression in bacteria owing to its compact single subunit structure and orthogonal promoter specificity. Understanding the mechanisms underlying T7 RNAP regulation is important to the design of engineered T7-based transcription factors, which can be used in gene circuit design. To explore regulatory mechanisms for T7 RNAP-driven expression, we developed a rapid and cost-effective method to characterize engineered T7-based transcription factors using cell-free protein synthesis and an acoustic liquid handler. Using this method, we investigated the effects of the tetracycline operator's proximity to the T7 promoter on the regulation of T7 RNAP-driven expression. Our results reveal a mechanism for regulation that functions by interfering with the transition of T7 RNAP from initiation to elongation and validates the use of the method described here to engineer future T7-based transcription factors.

Exploring chromatin hierarchical organization via Markov State Modelling.

We propose a new computational method for exploring chromatin structural organization based on Markov State Modelling of Hi-C data represented as an interaction network between genomic loci. A Markov process describes the random walk of a traveling probe in the corresponding energy landscape, mimicking the motion of a biomolecule involved in chromatin function. By studying the metastability of the associated Markov State Model upon annealing, the hierarchical structure of individual chromosomes is observed, and corresponding set of structural partitions is identified at each level of hierarchy. Then, the notion of effective interaction between partitions is derived, delineating the overall topology and architecture of chromosomes. Mapping epigenetic data on the graphs of intra-chromosomal effective interactions helps in understanding how chromosome organization facilitates its function. A sketch of whole-genome interactions obtained from the analysis of 539 partitions from all 23 chromosomes, complemented by distributions of gene expression regulators and epigenetic factors, sheds light on the structure-function relationships in chromatin, delineating chromosomal territories, as well as structural partitions analogous to topologically associating domains and active / passive epigenomic compartments. In addition to the overall genome architecture shown by effective interactions, the affinity between partitions of different chromosomes was analyzed as an indicator of the degree of association between partitions in functionally relevant genomic interactions. The overall static picture of whole-genome interactions obtained with the method presented in this work provides a foundation for chromatin structural reconstruction, for the modelling of chromatin dynamics, and for exploring the regulation of genome function. The algorithms used in this study are implemented in a freely available Python package ChromaWalker (https://bitbucket.org/ZhenWahTan/chromawalker).

An RNA polymerase II-driven Ebola virus minigenome system as an advanced tool for antiviral drug screening.

Ebola virus (EBOV) causes a severe disease in humans with the potential for significant international public health consequences. Currently, treatments are limited to experimental vaccines and therapeutics. Therefore, research into prophylaxis and antiviral strategies to combat EBOV infections is of utmost importance. The requirement for high containment laboratories to study EBOV infection is a limiting factor for conducting EBOV research. To overcome this issue, minigenome systems have been used as valuable tools to study EBOV replication and transcription mechanisms and to screen for antiviral compounds at biosafety level 2. The most commonly used EBOV minigenome system relies on the ectopic expression of the T7 RNA polymerase (T7), which can be limiting for certain cell types. We have established an improved EBOV minigenome system that utilizes endogenous RNA polymerase II (pol II) as a driver for the synthesis of minigenome RNA. We show here that this system is as efficient as the T7-based minigenome system, but works in a wider range of cell types, including biologically relevant cell types such as bat cells. Importantly, we were also able to adapt this system to a reliable and cost-effective 96-well format antiviral screening assay with a Z-factor of 0.74, indicative of a robust assay. Using this format, we identified JG40, an inhibitor of Hsp70, as an inhibitor of EBOV replication, highlighting the potential for this system as a tool for antiviral drug screening. In summary, this updated EBOV minigenome system provides a convenient and effective means of advancing the field of EBOV research.

T7 RNA polymerase translocation is facilitated by a helix opening on the fingers domain that may also prevent backtracking.

Here, we studied the complete process of a viral T7 RNA polymerase (RNAP) translocation on DNA during transcription elongation by implementing extensive all-atom molecular dynamics (MD) simulations to construct a Markov state model (MSM). Our studies show that translocation proceeds in a Brownian motion, and the RNAP thermally transits among multiple metastable states. We observed non-synchronized backbone movements of the nucleic acid (NA) chains with the RNA translocation accomplished first, while the template DNA lagged. Notably, both the O-helix and Y-helix on the fingers domain play key roles in facilitating NA translocation through the helix opening. The helix opening allows a key residue Tyr639 to become inserted into the active site, which pushes the RNA-DNA hybrid forward. Another key residue, Phe644, coordinates the downstream template DNA motions by stacking and un-stacking with a transition nucleotide (TN) and its adjacent nucleotide. Moreover, the O-helix opening at pre-translocation (pre-trans) likely resists backtracking. To test this hypothesis, we computationally designed mutants of T7 RNAP by replacing the amino acids on the O-helix with counterpart residues from a mitochondrial RNAP that is capable of backtracking. The current experimental results support the hypothesis.

A computational assessment of pH-dependent differential interaction of T7 lysozyme with T7 RNA polymerase.

BACKGROUND: T7 lysozyme (T7L), also known as N-acetylmuramoyl-L-alanine amidase, is a T7 bacteriophage gene product. It involves two functions: It can cut amide bonds in the bacterial cell wall and interacts with T7 RNA polymerase (T7RNAP) as a part of transcription inhibition. In this study, with the help of molecular dynamics (MD) calculations and computational interaction studies, we investigated the effect of varying pH conditions on conformational flexibilities of T7L and their influence on T7RNAP -T7L interactions. RESULTS: From the MD studies of the T7L at three different pH strengths viz. 5, neutral and 7.9 it was observed that T7L structure at pH 5 exhibited less stable nature with more residue level fluctuations, decrease of secondary structural elements and less compactness as compared to its counterparts: neutral pH and pH 7.9. The T-pad analysis of the MD trajectories identified local fluctuations in few residues that influenced the conformational differences in three pH strengths. From the docking of the minimum energy representative structures of T7L at different pH strengths (obtained from the free energy landscape analysis) with T7RNAP structures at same pH strengths, we saw strong interaction patterns at pH 7.9 and pH 5. The MD analysis of these complexes also confirmed the observations of docking study. From the combined in silico studies, it was observed that there are conformational changes in N-terminal and near helix 1 of T7L at different pH strengths, which are involved in the T7RNAP interaction, thereby varying the interaction pattern. CONCLUSION: Since T7L has been used for developing novel therapeutics and T7RNAP one of the most biologically useful protein in both in-vitro and in vivo experiments, this in silico study of pH dependent conformational differences in T7L and the differential interaction with T7RNAP at different pH can provide a significant insight into the structural investigations on T7L and T7RNAP in varying pH environments.

Dynamics of GreB-RNA polymerase interaction allow a proofreading accessory protein to patrol for transcription complexes needing rescue.

The secondary channel (SC) of multisubunit RNA polymerases (RNAPs) allows access to the active site and is a nexus for the regulation of transcription. Multiple regulatory proteins bind in the SC and reprogram the catalytic activity of RNAP, but the dynamics of these factors' interactions with RNAP and how they function without cross-interference are unclear. In Escherichia coli, GreB is an SC protein that promotes proofreading by transcript cleavage in elongation complexes backtracked by nucleotide misincorporation. Using multiwavelength single-molecule fluorescence microscopy, we observed the dynamics of GreB interactions with elongation complexes. GreB binds to actively elongating complexes at nearly diffusion-limited rates but remains bound for only 0.3-0.5 s, longer than the duration of the nucleotide addition cycle but far shorter than the time needed to synthesize a complete mRNA. Bound GreB inhibits transcript elongation only partially. To test whether GreB preferentially binds backtracked complexes, we reconstituted complexes stabilized in backtracked and nonbacktracked configurations. By verifying the functional state of each molecular complex studied, we could exclude models in which GreB is selectively recruited to backtracked complexes or is ejected from RNAP by catalytic turnover. Instead, GreB binds rapidly and randomly to elongation complexes, patrolling for those requiring nucleolytic rescue, and its short residence time minimizes RNAP inhibition. The results suggest a general mechanism by which SC factors may cooperate to regulate RNAP while minimizing mutual interference.

Handmade microfluidic device for biochemical applications in emulsion.

A simple, inexpensive flow-focusing device has been developed to make uniform droplets for biochemical reactions, such as in vitro transcription and cell-free protein synthesis. The device was fabricated from commercially available components without special equipment. Using the emulsion droplets formed by the device, a class I ligase ribozyme, bcI 23, was successfully synthesized from DNA attached to magnetic microbeads by T7 RNA polymerase. It was also ligated with an RNA substrate on the same microbeads, and detected using flow cytometry with a fluorescent probe. In addition, a single-chain derivative of the lambda Cro protein was expressed using an Escherichia coli cell-free protein synthesis system in emulsion, which was prepared using the flow-focusing device. In both emulsified reactions, usage of the flow-focusing device was able to greatly reduce the coefficient of variation for the amount of RNA or protein displayed on the microbeads, demonstrating the device is advantageous for quantitative analysis in high-throughput screening.

Fitness Cost of Rifampin Resistance in Neisseria meningitidis: In Vitro Study of Mechanisms Associated with rpoB H553Y Mutation.

Rifampin chemoprophylaxis against Neisseria meningitidis infections led to the onset of rifampin resistance in clinical isolates harboring point mutations in the rpoB gene, coding for the RNA polymerase ß chain. These resistant strains are rare in medical practice, suggesting their decreased fitness in the human host. In this study, we isolated rifampin-resistant rpoB mutants from hypervirulent serogroup C strain 93/4286 and analyzed their different properties, including the ability to grow/survive in different culture media and in differentiated THP-1 human monocytes and to compete with the wild-type strain in vitro. Our results demonstrate that different rpoB mutations (H553Y, H553R, and S549F) may have different effects, ranging from low- to high-cost effects, on bacterial fitness in vitro. Moreover, we found that the S549F mutation confers temperature sensitivity, possibly explaining why it is observed very rarely in clinical isolates. Comparative high-throughput RNA sequencing analysis of bacteria grown in chemically defined medium demonstrated that the low-cost H553Y substitution resulted in global transcriptional changes that functionally mimic the stringent response. Interestingly, many virulence-associated genes, including those coding for meningococcal type IV pili, porin A, adhesins/invasins, IgA protease, two-partner secretion system HrpA/HrpB, enzymes involved in resistance to oxidative injury, lipooligosaccharide sialylation, and capsular polysaccharide biosynthesis, were downregulated in the H553Y mutant compared to their level of expression in the wild-type strain. These data might account for the reduced capacity of this mutant to grow/survive in differentiated THP-1 cells and explain the rarity of H553Y mutants among clinical isolates.

Vesicular stomatitis virus polymerase's strong affinity to its template suggests exotic transcription models.

Vesicular stomatitis virus (VSV) is the prototype for negative sense non segmented (NNS) RNA viruses which include potent human and animal pathogens such as Rabies, Ebola and measles. The polymerases of NNS RNA viruses only initiate transcription at or near the 3' end of their genome template. We measured the dissociation constant of VSV polymerases from their whole genome template to be 20 pM. Given this low dissociation constant, initiation and sustainability of transcription becomes nontrivial. To explore possible mechanisms, we simulated the first hour of transcription using Monte Carlo methods and show that a one-time initial dissociation of all polymerases during entry is not sufficient to sustain transcription. We further show that efficient transcription requires a sliding mechanism for non-transcribing polymerases and can be realized with different polymerase-polymerase interactions and distinct template topologies. In conclusion, we highlight a model in which collisions between transcribing and sliding non-transcribing polymerases result in release of the non-transcribing polymerases allowing for redistribution of polymerases between separate templates during transcription and suggest specific experiments to further test these mechanisms.

Linking system-wide impacts of RNA polymerase mutations to the fitness cost of rifampin resistance in Pseudomonas aeruginosa.

UNLABELLED: Fitness costs play a key role in the evolutionary dynamics of antibiotic resistance in bacteria by generating selection against resistance in the absence of antibiotics. Although the genetic basis of antibiotic resistance is well understood, the precise molecular mechanisms linking the genetic basis of resistance to its fitness cost remain poorly characterized. Here, we examine how the system-wide impacts of mutations in the RNA polymerase (RNAP) gene rpoB shape the fitness cost of rifampin resistance in Pseudomonas aeruginosa. Rifampin resistance mutations reduce transcriptional efficiency, and this explains 76% of the variation in fitness among rpoB mutants. The pleiotropic consequence of rpoB mutations is that mutants show altered relative transcript levels of essential genes. We find no evidence that global transcriptional responses have an impact on the fitness cost of rifampin resistance as revealed by transcriptome sequencing (RNA-Seq). Global changes in the transcriptional profiles of rpoB mutants compared to the transcriptional profile of the rifampin-sensitive ancestral strain are subtle, demonstrating that the transcriptional regulatory network of P. aeruginosa is robust to the decreased transcriptional efficiency associated with rpoB mutations. On a smaller scale, we find that rifampin resistance mutations increase the expression of RNAP due to decreased termination at an attenuator upstream from rpoB, and we argue that this helps to minimize the cost of rifampin resistance by buffering against reduced RNAP activity. In summary, our study shows that it is possible to dissect the molecular mechanisms underpinning variation in the cost of rifampin resistance and highlights the importance of genome-wide buffering of relative transcript levels in providing robustness against resistance mutations. IMPORTANCE: Antibiotic resistance mutations carry fitness costs. Relative to the characteristics of their antibiotic-sensitive ancestors, resistant mutants show reduced growth rates and competitive abilities. Fitness cost plays an important role in the evolution of antibiotic resistance in the absence of antibiotics; however, the molecular mechanisms underlying these fitness costs is not well understood. We applied a systems-level approach to dissect the molecular underpinnings of the fitness costs associated with rifampin resistance in P. aeruginosa and showed that most of the variation in fitness cost can be explained by the direct effect of resistance mutations on the enzymatic activity of the mutated gene. Pleiotropic changes in transcriptional profiles are subtle at a genome-wide scale, suggesting that the gene regulatory network of P. aeruginosa is robust in the face of the direct effects of resistance mutations.

Transcription factors IIS and IIF enhance transcription efficiency by differentially modifying RNA polymerase pausing dynamics.

Transcription factors IIS (TFIIS) and IIF (TFIIF) are known to stimulate transcription elongation. Here, we use a single-molecule transcription elongation assay to study the effects of both factors. We find that these transcription factors enhance overall transcription elongation by reducing the lifetime of transcriptional pauses and that TFIIF also decreases the probability of pause entry. Furthermore, we observe that both factors enhance the processivity of RNA polymerase II through the nucleosomal barrier. The effects of TFIIS and TFIIF are quantitatively described using the linear Brownian ratchet kinetic model for transcription elongation and the backtracking model for transcriptional pauses, modified to account for the effects of the transcription factors. Our findings help elucidate the molecular mechanisms by which transcription factors modulate gene expression.

Fitness costs of rifampicin resistance in Mycobacterium tuberculosis are amplified under conditions of nutrient starvation and compensated by mutation in the ß' subunit of RNA polymerase.

Rifampicin resistance, a defining attribute of multidrug-resistant tuberculosis, is conferred by mutations in the ß subunit of RNA polymerase. Sequencing of rifampicin-resistant (RIF-R) clinical isolates of Mycobacterium tuberculosis revealed, in addition to RIF-R mutations, enrichment of potential compensatory mutations around the double-psi ß-barrel domain of the ß' subunit comprising the catalytic site and the exit tunnel for newly synthesized RNA. Sequential introduction of the resistance allele followed by the compensatory allele in isogenic Mycobacterium smegmatis showed that these mutations respectively caused and compensated a starvation enhanced growth defect by altering RNA polymerase activity. While specific combinations of resistance and compensatory alleles converged in divergent lineages, other combinations recurred among related isolates suggesting transmission of compensated RIF-R strains. These findings suggest nutrient poor growth conditions impose larger selective pressure on RIF-R organisms that results in the selection of compensatory mutations in a domain involved in catalysis and starvation control of RNA polymerase transcription.

Direct assessment of transcription fidelity by high-resolution RNA sequencing.

Cancerous and aging cells have long been thought to be impacted by transcription errors that cause genetic and epigenetic changes. Until now, a lack of methodology for directly assessing such errors hindered evaluation of their impact to the cells. We report a high-resolution Illumina RNA-seq method that can assess noncoded base substitutions in mRNA at 10(-4)-10(-5) per base frequencies in vitro and in vivo. Statistically reliable detection of changes in transcription fidelity through ∼10(3) nt DNA sites assures that the RNA-seq can analyze the fidelity in a large number of the sites where errors occur. A combination of the RNA-seq and biochemical analyses of the positions for the errors revealed two sequence-specific mechanisms that increase transcription fidelity by Escherichia coli RNA polymerase: (i) enhanced suppression of nucleotide misincorporation that improves selectivity for the cognate substrate, and (ii) increased backtracking of the RNA polymerase that decreases a chance of error propagation to the full-length transcript after misincorporation and provides an opportunity to proofread the error. This method is adoptable to a genome-wide assessment of transcription fidelity.

Proteins searching for their target on DNA by one-dimensional diffusion: overcoming the "speed-stability" paradox.

The sequence dependence of DNA-protein interactions that allows proteins to find the correct reaction site also slows down the 1D diffusion of the protein along the DNA molecule, leading to the so-called "speed-stability paradox," wherein fast diffusion along the DNA molecule is seemingly incompatible with stable targeting of the reaction site. Here, we develop diffusion-reaction models that use discrete and continuous Gaussian random 1D diffusion landscapes with or without a high-energy cut-off, and two-state models with a transition to and from a "searching" mode in which the protein diffuses rapidly without recognizing the target. We show the conditions under which such considerations lead to a predicted speed-up of the targeting process, and under which the presence of a "searching" mode in a two-state model is nearly equivalent to the existence of a high-energy cut-off in a one-state model. We also determine the conditions under which the search is either diffusion-limited or reaction-limited, and develop quantitative expressions for the rate of successful targeting as a function of the site-specific reaction rate, the roughness of the DNA-protein interaction potential, and the presence of a "searching" mode. In general, we find that a rough landscape is compatible with a fast search if the highest energy barriers can be avoided by "hopping" or by the protein transitioning to a lower-energy "searching" mode. We validate these predictions with the results of Brownian dynamics, kinetic Metropolis, and kinetic Monte Carlo simulations of the diffusion and targeting process, and apply these concepts to the case of T7 RNA polymerase searching for its target site on T7 DNA.