Tuning transcriptional regulation through signaling: A predictive theory of allosteric induction

Allosteric regulation is found across all domains of life, yet we still lack simple, predictive theories that directly link the experimentally tunable parameters of a system to its input-output response. To that end, we present a general theory of allosteric transcriptional regulation using the Monod-Wyman-Changeux model. We rigorously test this model using the ubiquitous simple repression motif in bacteria by first predicting the behavior of strains that span a large range of repressor copy numbers and DNA binding strengths and then constructing and measuring their response. Our model not only accurately captures the induction profiles of these strains but also enables us to derive analytic expressions for key properties such as the dynamic range and $[EC_{50}]$. Finally, we derive an expression for the free energy of allosteric repressors which enables us to collapse our experimental data onto a single master curve that captures the diverse phenomenology of the induction profiles.Comment: Substantial revisions for resubmission (3 new figures, significantly elaborated discussion); added Professor Mitchell Lewis as another author for his continuing contributions to the projec

Intrinsic limits to gene regulation by global crosstalk

Gene regulation relies on the specificity of transcription factor (TF) - DNA interactions. In equilibrium, limited specificity may lead to crosstalk: a regulatory state in which a gene is either incorrectly activated due to noncognate TF-DNA interactions or remains erroneously inactive. We present a tractable biophysical model of global crosstalk, where many genes are simultaneously regulated by many TFs. We show that in the simplest regulatory scenario, a lower bound on crosstalk severity can be analytically derived solely from the number of (co)regulated genes and a suitable parameter that describes binding site similarity. Estimates show that crosstalk could present a significant challenge for organisms with low-specificity TFs, such as metazoans, unless they use appropriate regulation schemes. Strong cooperativity substantially decreases crosstalk, while joint regulation by activators and repressors, surprisingly, does not; moreover, certain microscopic details about promoter architecture emerge as globally important determinants of crosstalk strength. Our results suggest that crosstalk imposes a new type of global constraint on the functioning and evolution of regulatory networks, which is qualitatively distinct from the known constraints acting at the level of individual gene regulatory elements

Intermediate coherent-incoherent charge transport: DNA as a case study

We study an intermediate quantum coherent-incoherent charge transport mechanism in metal-molecule-metal junctions using B\"uttiker's probe technique. This tool allows us to include incoherent effects in a controlled manner, and thus to study situations in which partial decoherence affects charge transfer dynamics. Motivated by recent experiments on intermediate coherent-incoherent charge conduction in DNA molecules [L. Xiang {\it et al.}, Nature Chem. 7, 221-226 (2015)], we focus on two representative structures: alternating (GC)$_n$ and stacked G$_n$C$_n$ sequences; the latter structure is argued to support charge delocalization within G segments, and thus an intermediate coherent-incoherent conduction. We begin our analysis with a highly simplified 1-dimensional tight-binding model, while introducing environmental effects through B\"uttiker's probes. This minimal model allows us to gain fundamental understanding of transport mechanisms and derive analytic results for molecular resistance in different limits. We then use a more detailed ladder-model Hamiltonian to represent double-stranded DNA structures---with environmental effects captured by B\"uttiker's probes. We find that hopping conduction dominates in alternating sequences, while in stacked sequences charge delocalization (visualized directly through the electronic density matrix) supports significant resonant-ballistic charge dynamics reflected by an even-odd effect and a weak distance dependence for resistance. Our analysis illustrates that lessons learned from minimal models are helpful for interpreting charge dynamics in DNA.Comment: 16 pages, 14 figure

Can graph-cutting improve microarray gene expression reconstructions?

Microarrays produce high-resolution image data that are, unfortunately, permeated with a great deal of “noise” that must be removed for precision purposes. This paper presents a technique for such a removal process. On completion of this non-trivial task, a new surface (devoid of gene spots) is subtracted from the original to render more precise gene expressions. The graph-cutting technique as implemented has the benefits that only the most appropriate pixels are replaced and these replacements are replicates rather than estimates. This means the influence of outliers and other artifacts are handled more appropriately (than in previous methods) as well as the variability of the final gene expressions being considerably reduced. Experiments are carried out to test the technique against commercial and previously researched reconstruction methods. Final results show that the graph-cutting inspired identification mechanism has a positive significant impact on reconstruction accuracy

Phase diagram of solution of oppositely charged polyelectrolytes

We study a solution of long polyanions (PA) with shorter polycations (PC) and focus on the role of Coulomb interaction. A good example is solutions of DNA and PC which are widely studied for gene therapy. In the solution, each PA attracts many PCs to form a complex. When the ratio of total charges of PA and PC in the solution, $x$, equals to 1, complexes are neutral and they condense in a macroscopic drop. When $x$ is far away from 1, complexes are strongly charged. The Coulomb repulsion is large and free complexes are stable. As $x$ approaches to 1, PCs attached to PA disproportionate themselves in two competing ways. One way is inter-complex disproportionation, in which PCs make some complexes neutral and therefore condensed in a macroscopic drop while other complexes become even stronger charged and stay free. The other way is intra-complex disproportionation, in which PCs make one end of a complex neutral and condensed in a small droplet while the rest of the complex forms a strongly charged tail. Thus each complex becomes a "tadpole". These two ways can also combine together to give even lower free energy. We get a phase diagram of PA-PC solution in a plane of $x$ and inverse screening radius of the monovalent salt, which includes phases or phase coexistence with both kinds of disproportionation.Comment: 29 pages, 10 figures. Major change in results and tex

The influence of horizontal gene transfer on the mean fitness of unicellular populations in static environments

This paper develops a mathematical model describing the influence that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance in an asexually reproducing population of unicellular, prokaryotic organisms. It is assumed that mutation-selection balance is reached in the presence of a fixed background concentration of antibiotic, to which the population must become resistant in order to survive. We analyze the behavior of the model in the limit of low and high antibiotic-induced first-order death rate constants, and find that the highest mean fitness is obtained at low rates of bacterial conjugation. As the rate of conjugation crosses a threshold, the mean fitness decreases to a minimum, and then rises asymptotically to a limiting value as the rate of conjugation becomes infinitely large. However, this limiting value is smaller than the mean fitness obtained in the limit of low conjugation rate. This dependence of the mean fitness on the conjugation rate is fairly small for the parameter ranges we have considered, and disappears as the first-order death rate constant due to the presence of antibiotic approaches zero. For large values of the antibiotic death rate constant, we have obtained an analytical solution for the behavior of the mean fitness that agrees well with the results of simulations. The results of this paper suggest that conjugation-mediated HGT has a slightly deleterious effect on the mean fitness of a population at mutation-selection balance. Therefore, we argue that HGT confers a selective advantage by allowing for faster adaptation to a new or changing environment. The results of this paper are consistent with the observation that HGT can be promoted by environmental stresses on a population.Comment: 27 pages, 4 figure