Tensor network method for reversible classical computation.

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)2041-172310.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

A unified model of transcription elongation: what have we learned from single-molecule experiments?

The transcription of the genetic information encoded in DNA into RNA is performed by RNA polymerase (RNAP), a complex molecular motor, highly conserved across species. Despite remarkable progress in single-molecule techniques revealing important mechanistic details of transcription elongation (TE) with up to base-pair resolution, some of the results and interpretations of these studies are difficult to reconcile, and have not yet led to a minimal unified picture of transcription. We propose a simple model that accounts quantitatively for many of the experimental observations. This model belongs to the class of isothermal ratchet models of TE involving the thermally driven stochastic backward and forward motion (backtracking and forward tracking) of RNAP along DNA between single-nucleotide incorporation events. We uncover two essential features for the success of the model. The first is an intermediate state separating the productive elongation pathway from nonelongating backtracked states. The rates of entering and exiting this intermediate state modulate pausing by RNAP. The second crucial ingredient of the model is the cotranscriptional folding of the RNA transcript, sterically inhibiting the extent of backtracking. This model resolves several apparent differences between single-molecule studies and provides a framework for future work on TE.

An allosteric path to transcription termination.

Transcription termination signals in bacteria occur in RNA as a strong hairpin followed by a stretch of U residues at the 3' terminus. To release the transcript, RNA polymerase (RNAP) is thought to translocate forward without RNA synthesis. Here we provide genetic and biochemical evidence supporting an alternative model in which extensive conformational changes across the enzyme lead to termination without forward translocation. In this model, flexible parts of the RNA exit channel (zipper, flap, and zinc finger) assist the initial step of hairpin folding (nucleation). The hairpin then invades the RNAP main channel, causing RNA:DNA hybrid melting, structural changes of the catalytic site, and DNA-clamp opening induced by interaction with the G(trigger)-loop. Our results envision the elongation complex as a flexible structure, not a rigid body, and establish basic principles of the termination pathway that are likely to be universal in prokaryotic and eukaryotic systems.

Thermodynamic and kinetic modeling of transcriptional pausing.

We present a statistical mechanics approach for the prediction of backtracked pauses in bacterial transcription elongation derived from structural models of the transcription elongation complex (EC). Our algorithm is based on the thermodynamic stability of the EC along the DNA template calculated from the sequence-dependent free energy of DNA-DNA, DNA-RNA, and RNA-RNA base pairing associated with (i) the translocational and size fluctuations of the transcription bubble; (ii) changes in the associated DNA-RNA hybrid; and (iii) changes in the cotranscriptional RNA secondary structure upstream of the RNA exit channel. The calculations involve no adjustable parameters except for a cutoff used to discriminate paused from nonpaused complexes. When applied to 100 experimental pauses in transcription elongation by Escherichia coli RNA polymerase on 10 DNA templates, the approach produces statistically significant results. We also present a kinetic model for the rate of recovery of backtracked paused complexes. A crucial ingredient of our model is the incorporation of kinetic barriers to backtracking resulting from steric clashes of EC with the cotranscriptionally generated RNA secondary structure, an aspect not included explicitly in previous attempts at modeling the transcription elongation process.

Optimal path to epigenetic switching.

We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a numerical solution of the master equation.

A ratchet mechanism of transcription elongation and its control.

RNA chain elongation is a highly processive and accurate process that is finely regulated by numerous intrinsic and extrinsic signals. Here we describe a general mechanism that governs RNA polymerase (RNAP) movement and response to regulatory inputs such as pauses, terminators, and elongation factors. We show that E.coli RNAP moves by a complex Brownian ratchet mechanism, which acts prior to phosphodiester bond formation. The incoming substrate and the flexible F bridge domain of the catalytic center serve as two separate ratchet devices that function in concert to drive forward translocation. The adjacent G loop domain controls F bridge motion, thus keeping the proper balance between productive and inactive states of the elongation complex. This balance is critical for cell viability since it determines the rate, processivity, and fidelity of transcription.