Analytical study of an exclusive genetic switch

The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be repressed. The model may be thought of as a minimal model of the power struggle between two competing parties. Exact solutions are given for the limits of vanishing binding/unbinding rates and infinite binding/unbinding rates. A mean field theory is introduced which is exact in the limit of vanishing binding/unbinding rates. The mean field theory and numerical simulations reveal that generically bistability occurs and the system is in a symmetry broken state. An exact perturbative solution which in principle allows the nonequilibrium stationary state to be computed is also developed and computed to first and second order.Comment: 28 pages, 6 figure

On the Complexity of Searching in Trees: Average-case Minimization

We focus on the average-case analysis: A function w : V -> Z+ is given which defines the likelihood for a node to be the one marked, and we want the strategy that minimizes the expected number of queries. Prior to this paper, very little was known about this natural question and the complexity of the problem had remained so far an open question. We close this question and prove that the above tree search problem is NP-complete even for the class of trees with diameter at most 4. This results in a complete characterization of the complexity of the problem with respect to the diameter size. In fact, for diameter not larger than 3 the problem can be shown to be polynomially solvable using a dynamic programming approach. In addition we prove that the problem is NP-complete even for the class of trees of maximum degree at most 16. To the best of our knowledge, the only known result in this direction is that the tree search problem is solvable in O(|V| log|V|) time for trees with degree at most 2 (paths). We match the above complexity results with a tight algorithmic analysis. We first show that a natural greedy algorithm attains a 2-approximation. Furthermore, for the bounded degree instances, we show that any optimal strategy (i.e., one that minimizes the expected number of queries) performs at most O(\Delta(T) (log |V| + log w(T))) queries in the worst case, where w(T) is the sum of the likelihoods of the nodes of T and \Delta(T) is the maximum degree of T. We combine this result with a non-trivial exponential time algorithm to provide an FPTAS for trees with bounded degree

Maximizing Maximal Angles for Plane Straight-Line Graphs

Let $G=(S, E)$ be a plane straight-line graph on a finite point set $S\subset\R^2$ in general position. The incident angles of a vertex $p \in S$ of $G$ are the angles between any two edges of $G$ that appear consecutively in the circular order of the edges incident to $p$. A plane straight-line graph is called $\phi$-open if each vertex has an incident angle of size at least $\phi$. In this paper we study the following type of question: What is the maximum angle $\phi$ such that for any finite set $S\subset\R^2$ of points in general position we can find a graph from a certain class of graphs on $S$ that is $\phi$-open? In particular, we consider the classes of triangulations, spanning trees, and paths on $S$ and give tight bounds in most cases.Comment: 15 pages, 14 figures. Apart of minor corrections, some proofs that were omitted in the previous version are now include

Optimizing information flow in small genetic networks. I

In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable randomness of individual molecular events. Here we explore how cells can maximize their control power in the presence of these physical limits; formally, we solve the theoretical problem of maximizing the information transferred from inputs to outputs when the number of available molecules is held fixed. We start with the simplest version of the problem, in which a single transcription factor protein controls the readout of one or more genes by binding to DNA. We further simplify by assuming that this regulatory network operates in steady state, that the noise is small relative to the available dynamic range, and that the target genes do not interact. Even in this simple limit, we find a surprisingly rich set of optimal solutions. Importantly, for each locally optimal regulatory network, all parameters are determined once the physical constraints on the number of available molecules are specified. Although we are solving an over--simplified version of the problem facing real cells, we see parallels between the structure of these optimal solutions and the behavior of actual genetic regulatory networks. Subsequent papers will discuss more complete versions of the problem

Transcriptomic and proteomic analyses of Desulfovibrio vulgaris biofilms: carbon and energy flow contribute to the distinct biofilm growth state.

BackgroundDesulfovibrio vulgaris Hildenborough is a sulfate-reducing bacterium (SRB) that is intensively studied in the context of metal corrosion and heavy-metal bioremediation, and SRB populations are commonly observed in pipe and subsurface environments as surface-associated populations. In order to elucidate physiological changes associated with biofilm growth at both the transcript and protein level, transcriptomic and proteomic analyses were done on mature biofilm cells and compared to both batch and reactor planktonic populations. The biofilms were cultivated with lactate and sulfate in a continuously fed biofilm reactor, and compared to both batch and reactor planktonic populations.ResultsThe functional genomic analysis demonstrated that biofilm cells were different compared to planktonic cells, and the majority of altered abundances for genes and proteins were annotated as hypothetical (unknown function), energy conservation, amino acid metabolism, and signal transduction. Genes and proteins that showed similar trends in detected levels were particularly involved in energy conservation such as increases in an annotated ech hydrogenase, formate dehydrogenase, pyruvate:ferredoxin oxidoreductase, and rnf oxidoreductase, and the biofilm cells had elevated formate dehydrogenase activity. Several other hydrogenases and formate dehydrogenases also showed an increased protein level, while decreased transcript and protein levels were observed for putative coo hydrogenase as well as a lactate permease and hyp hydrogenases for biofilm cells. Genes annotated for amino acid synthesis and nitrogen utilization were also predominant changers within the biofilm state. Ribosomal transcripts and proteins were notably decreased within the biofilm cells compared to exponential-phase cells but were not as low as levels observed in planktonic, stationary-phase cells. Several putative, extracellular proteins (DVU1012, 1545) were also detected in the extracellular fraction from biofilm cells.ConclusionsEven though both the planktonic and biofilm cells were oxidizing lactate and reducing sulfate, the biofilm cells were physiologically distinct compared to planktonic growth states due to altered abundances of genes/proteins involved in carbon/energy flow and extracellular structures. In addition, average expression values for multiple rRNA transcripts and respiratory activity measurements indicated that biofilm cells were metabolically more similar to exponential-phase cells although biofilm cells are structured differently. The characterization of physiological advantages and constraints of the biofilm growth state for sulfate-reducing bacteria will provide insight into bioremediation applications as well as microbially-induced metal corrosion

Vibrational Enhancement of the Effective Donor - Acceptor Coupling

The paper deals with a simple three sites model for charge transfer phenomena in an one-dimensional donor (D) - bridge (B) - acceptor (A) system coupled with vibrational dynamics of the B site. It is found that in a certain range of parameters the vibrational coupling leads to an enhancement of the effective donor - acceptor electronic coupling as a result of the formation of the polaron on the B site. This enhancement of the charge transfer efficiency is maximum at the resonance, where the effective energy of the fluctuating B site coincides with the donor (acceptor) energy.Comment: 5 pages, 3 figure

Selection of chromosomal DNA libraries using a multiplex CRISPR system.

The directed evolution of biomolecules to improve or change their activity is central to many engineering and synthetic biology efforts. However, selecting improved variants from gene libraries in living cells requires plasmid expression systems that suffer from variable copy number effects, or the use of complex marker-dependent chromosomal integration strategies. We developed quantitative gene assembly and DNA library insertion into the Saccharomyces cerevisiae genome by optimizing an efficient single-step and marker-free genome editing system using CRISPR-Cas9. With this Multiplex CRISPR (CRISPRm) system, we selected an improved cellobiose utilization pathway in diploid yeast in a single round of mutagenesis and selection, which increased cellobiose fermentation rates by over 10-fold. Mutations recovered in the best cellodextrin transporters reveal synergy between substrate binding and transporter dynamics, and demonstrate the power of CRISPRm to accelerate selection experiments and discoveries of the molecular determinants that enhance biomolecule function

Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise

The study of fluctuations in gene regulatory networks is extended to the case of Gaussian colored noise. Firstly, the solution of the corresponding Langevin equation with colored noise is expressed in terms of an Ito integral. Then, two important lemmas concerning the variance of an Ito integral and the covariance of two Ito integrals are shown. Based on the lemmas, we give the general formulae for the variances and covariance of molecular concentrations for a regulatory network near a stable equilibrium explicitly. Two examples, the gene auto-regulatory network and the toggle switch, are presented in details. In general, it is found that the finite correlation time of noise reduces the fluctuations and enhances the correlation between the fluctuations of the molecular components.Comment: 10 pages, 4 figure

Genomewide and Enzymatic Analysis Reveals Efficient d-Galacturonic Acid Metabolism in the Basidiomycete Yeast Rhodosporidium toruloides.

Biorefining of renewable feedstocks is one of the most promising routes to replace fossil-based products. Since many common fermentation hosts, such as Saccharomyces cerevisiae, are naturally unable to convert many component plant cell wall polysaccharides, the identification of organisms with broad catabolism capabilities represents an opportunity to expand the range of substrates used in fermentation biorefinery approaches. The red basidiomycete yeast Rhodosporidium toruloides is a promising and robust host for lipid- and terpene-derived chemicals. Previous studies demonstrated assimilation of a range of substrates, from C5/C6 sugars to aromatic molecules similar to lignin monomers. In the current study, we analyzed the potential of R. toruloides to assimilate d-galacturonic acid, a major sugar in many pectin-rich agricultural waste streams, including sugar beet pulp and citrus peels. d-Galacturonic acid is not a preferred substrate for many fungi, but its metabolism was found to be on par with those of d-glucose and d-xylose in R. toruloides A genomewide analysis by combined transcriptome sequencing (RNA-seq) and RB-TDNA-seq revealed those genes with high relevance for fitness on d-galacturonic acid. While R. toruloides was found to utilize the nonphosphorylative catabolic pathway known from ascomycetes, the maximal velocities of several enzymes exceeded those previously reported. In addition, an efficient downstream glycerol catabolism and a novel transcription factor were found to be important for d-galacturonic acid utilization. These results set the basis for use of R. toruloides as a potential host for pectin-rich waste conversions and demonstrate its suitability as a model for metabolic studies with basidiomycetes.IMPORTANCE The switch from the traditional fossil-based industry to a green and sustainable bioeconomy demands the complete utilization of renewable feedstocks. Many currently used bioconversion hosts are unable to utilize major components of plant biomass, warranting the identification of microorganisms with broader catabolic capacity and characterization of their unique biochemical pathways. d-Galacturonic acid is a plant component of bioconversion interest and is the major backbone sugar of pectin, a plant cell wall polysaccharide abundant in soft and young plant tissues. The red basidiomycete and oleaginous yeast Rhodosporidium toruloides has been previously shown to utilize a range of sugars and aromatic molecules. Using state-of-the-art functional genomic methods and physiological and biochemical assays, we elucidated the molecular basis underlying the efficient metabolism of d-galacturonic acid. This study identified an efficient pathway for uronic acid conversion to guide future engineering efforts and represents the first detailed metabolic analysis of pectin metabolism in a basidiomycete fungus

Scheduling Algorithms for Procrastinators

This paper presents scheduling algorithms for procrastinators, where the speed that a procrastinator executes a job increases as the due date approaches. We give optimal off-line scheduling policies for linearly increasing speed functions. We then explain the computational/numerical issues involved in implementing this policy. We next explore the online setting, showing that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is the job's flow time divided by the job's due date minus release time. We show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretch. Then we give the "thrashing" scheduling policy and show that it is a \Theta(1) approximation algorithm for the maximum interval stretch.Comment: 12 pages, 3 figure