Protein Editing using a Concerted Transposition Reaction.

Protein engineering through the chemical or enzymatic ligation of polypeptide fragments has proven enormously powerful for studying countless biochemical processes in vitro. In general, this strategy necessitates a protein folding step following ligation of the unstructured fragments, a requirement that constrains the types of systems amenable to the approach. Here, we report an in vitro strategy that allows internal regions of target proteins to be replaced in a single operation. Conceptually, our system is analogous to a DNA transposition reaction, but employs orthogonal pairs of split inteins to swap out a designated region of a host protein with an exogenous molecular cassette. We show using isotopic labeling experiments that this 'protein transposition' reaction is concerted when the kinetics for the embedded intein pairs are suitably matched. Critically, this feature allows for efficient manipulation of protein primary structure in the context of a native fold. The utility of this method is illustrated using several protein systems including the multisubunit chromatin remodeling complex, ACF, where we also show protein transposition can occur in situ within the cell nucleus. By carrying out a molecular 'cut and paste' on a protein or protein complex under native folding conditions, our approach dramatically expands the scope of protein semisynthesis.

Design principles of 3D epigenetic memory systems.

Cells remember their identities, in part, by using epigenetic marks-chemical modifications placed along the genome. How can mark patterns remain stable over cell generations despite their constant erosion by replication and other processes? We developed a theoretical model that reveals that three-dimensional (3D) genome organization can stabilize epigenetic memory as long as (i) there is a large density difference between chromatin compartments, (ii) modifying "reader-writer" enzymes spread marks in three dimensions, and (iii) the enzymes are limited in abundance relative to their histone substrates. Analogous to an associative memory that encodes memory in neuronal connectivity, mark patterns are encoded in a 3D network of chromosomal contacts. Our model provides a unified account of diverse observations and reveals a key role of 3D genome organization in epigenetic memory.

Thermodynamic bounds on ultrasensitivity in covalent switching.

Switch-like motifs are among the basic building blocks of biochemical networks. A common motif that can serve as an ultrasensitive switch consists of two enzymes acting antagonistically on a substrate, one making and the other removing a covalent modification. To work as a switch, such covalent modification cycles must be held out of thermodynamic equilibrium by continuous expenditure of energy. Here, we exploit the linear framework for timescale separation to establish tight bounds on the performance of any covalent-modification switch in terms of the chemical potential difference driving the cycle. The bounds apply to arbitrary enzyme mechanisms, not just Michaelis-Menten, with arbitrary rate constants and thereby reflect fundamental physical constraints on covalent switching.

Size limits the sensitivity of kinetic schemes.

Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. We show how this bound sheds light on and unifies diverse sensitivity mechanisms, including kinetic proofreading and a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, representing in each case a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation and the function of biomolecular condensates.

Functional Transcription Factor Target Networks Illuminate Control of Epithelial Remodelling.

Cell identity is governed by gene expression, regulated by transcription factor (TF) binding at cis-regulatory modules. Decoding the relationship between TF binding patterns and gene regulation is nontrivial, remaining a fundamental limitation in understanding cell decision-making. We developed the NetNC software to predict functionally active regulation of TF targets; demonstrated on nine datasets for the TFs Snail, Twist, and modENCODE Highly Occupied Target (HOT) regions. Snail and Twist are canonical drivers of epithelial to mesenchymal transition (EMT), a cell programme important in development, tumour progression and fibrosis. Predicted "neutral" (non-functional) TF binding always accounted for the majority (50% to 95%) of candidate target genes from statistically significant peaks and HOT regions had higher functional binding than most of the Snail and Twist datasets examined. Our results illuminated conserved gene networks that control epithelial plasticity in development and disease. We identified new gene functions and network modules including crosstalk with notch signalling and regulation of chromatin organisation, evidencing networks that reshape Waddington's epigenetic landscape during epithelial remodelling. Expression of orthologous functional TF targets discriminated breast cancer molecular subtypes and predicted novel tumour biology, with implications for precision medicine. Predicted invasion roles were validated using a tractable cell model, supporting our approach.

Publisher Correction: A space-time tradeoff for implementing a function with master equation dynamics.

The original version of the Supplementary Information associated with this Article contained an error throughout in which all inline references to Theorems, Definitions and Lemmas given in the main Article were incorrectly given as '??'. The HTML has been updated to include a corrected version of the Supplementary Information.

A space-time tradeoff for implementing a function with master equation dynamics.

Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation, even approximately, which raises the question of how they can occur in the real world. Here we show how any function over some "visible" states can be implemented with master equation dynamics-if the dynamics exploits additional, "hidden" states at intermediate times. We also show that any master equation implementing a function can be decomposed into a sequence of "hidden" timesteps, demarcated by changes in what state-to-state transitions have nonzero probability. In many real-world situations there is a cost both for more hidden states and for more hidden timesteps. Accordingly, we derive a "space-time" tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given function.

Self-Organized Resonance during Search of a Diverse Chemical Space.

Recent studies of active matter have stimulated interest in the driven self-assembly of complex structures. Phenomenological modeling of particular examples has yielded insight, but general thermodynamic principles unifying the rich diversity of behaviors observed have been elusive. Here, we study the stochastic search of a toy chemical space by a collection of reacting Brownian particles subject to periodic forcing. We observe the emergence of an adaptive resonance in the system matched to the drive frequency, and show that the increased work absorption by these resonant structures is key to their stabilization. Our findings are consistent with a recently proposed thermodynamic mechanism for far-from-equilibrium self-organization.

A fundamental trade-off in covalent switching and its circumvention by enzyme bifunctionality in glucose homeostasis.

Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.

Controlling seizure-like events by perturbing ion concentration dynamics with periodic stimulation.

We investigate the effects of adding periodic stimulation to a generic, conductance-based neuron model that includes ion concentration dynamics of sodium and potassium. Under conditions of high extracellular potassium, the model exhibits repeating, spontaneous, seizure-like bursting events associated with slow modulation of the ion concentrations local to the neuron. We show that for a range of parameter values, depolarizing and hyperpolarizing periodic stimulation pulses (including frequencies lower than 4 Hz) can stop the spontaneous bursting by interacting with the ion concentration dynamics. Stimulation can also control the magnitude of evoked responses to modeled physiological inputs. We develop an understanding of the nonlinear dynamics of this system by a timescale separation procedure that identifies effective nullclines in the ion concentration parameter space. Our results suggest that the manipulation of ion concentration dynamics via external or endogenous stimulation may play an important role in neuronal excitability, seizure dynamics, and control.