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A signal mixer facilitates rich computation, which has been the building block of modern telecommunication. This frequency mixing produces new signals at the sum and difference frequencies of input signals, enabling powerful operations such as heterodyning and multiplexing. Here, we report that a neuron is a signal mixer. We found through ex vivo and in vivo whole-cell measurements that neurons mix exogenous (controlled) and endogenous (spontaneous) subthreshold membrane potential oscillations, producing new oscillation frequencies, and that neural mixing originates in voltage-gated ion channels. Furthermore, we demonstrate that mixing is evident in human brain activity and is associated with cognitive functions. We found that the human electroencephalogram displays distinct clusters of local and inter-region mixing and that conversion of the salient posterior alpha-beta oscillations into gamma-band oscillations regulates visual attention. Signal mixing may enable individual neurons to sculpt the spectrum of neural circuit oscillations and utilize them for computational operations., Competing Interests: Declaration of interests N.G. and E.S.B. are inventors of a patent on neuromodulation using temporal interference (TI) of kHz electric fields, assigned to MIT. N.G. and E.S.B. are co-founders of TI Solutions AG, a company committed to producing hardware and software solutions to support TI research., (Copyright © 2024 The Author(s). Published by Elsevier Inc. All rights reserved.)

The explosion of data throughout the biomedical sciences provides unprecedented opportunities to learn about the dynamics of evolution and disease progression, but harnessing these large and diverse datasets remains challenging. Here, we describe a highly generalizable statistical platform to infer the dynamic pathways by which many, potentially interacting, traits are acquired or lost over time. We use HyperTraPS (hypercubic transition path sampling) to efficiently learn progression pathways from cross-sectional, longitudinal, or phylogenetically linked data, readily distinguishing multiple competing pathways, and identifying the most parsimonious mechanisms underlying given observations. This Bayesian approach allows inclusion of prior knowledge, quantifies uncertainty in pathway structure, and allows predictions, such as which symptom a patient will acquire next. We provide visualization tools for intuitive assessment of multiple, variable pathways. We apply the method to ovarian cancer progression and the evolution of multidrug resistance in tuberculosis, demonstrating its power to reveal previously undetected dynamic pathways., (Copyright © 2019 Elsevier Inc. All rights reserved.)

To perform well in biotechnology applications, synthetic genetic oscillators must be engineered to allow independent modulation of amplitude and period. This need is currently unmet. Here, we demonstrate computationally how two classic genetic oscillators, the dual-feedback oscillator and the repressilator, can be re-designed to provide independent control of amplitude and period and improve tunability-that is, a broad dynamic range of periods and amplitudes accessible through the input "dials." Our approach decouples frequency and amplitude modulation by incorporating an orthogonal "sink module" where the key molecular species are channeled for enzymatic degradation. This sink module maintains fast oscillation cycles while alleviating the translational coupling between the oscillator's transcription factors and output. We characterize the behavior of our re-designed oscillators over a broad range of physiologically reasonable parameters, explain why this facilitates broader function and control, and provide general design principles for building synthetic genetic oscillators that are more precisely controllable., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

Ammonium assimilation in Escherichia coli is regulated by two paralogous proteins (GlnB and GlnK), which orchestrate interactions with regulators of gene expression, transport proteins, and metabolic pathways. Yet how they conjointly modulate the activity of glutamine synthetase, the key enzyme for nitrogen assimilation, is poorly understood. We combine experiments and theory to study the dynamic roles of GlnB and GlnK during nitrogen starvation and upshift. We measure time-resolved in vivo concentrations of metabolites, total and posttranslationally modified proteins, and develop a concise biochemical model of GlnB and GlnK that incorporates competition for active and allosteric sites, as well as functional sequestration of GlnK. The model predicts the responses of glutamine synthetase, GlnB, and GlnK under time-varying external ammonium level in the wild-type and two genetic knock-outs. Our results show that GlnK is tightly regulated under nitrogen-rich conditions, yet it is expressed during ammonium run-out and starvation. This suggests a role for GlnK as a buffer of nitrogen shock after starvation, and provides a further functional link between nitrogen and carbon metabolisms., (Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

We present a cellular model of lipid biosynthesis in the plasma membrane that couples biochemical and biophysical features of the enzymatic network of the cell-wall-less Mycoplasma Acholeplasma laidlawii. In particular, we formulate how the stored elastic energy of the lipid bilayer can modify the activity of curvature-sensitive enzymes through the binding of amphipathic alpha-helices. As the binding depends on lipid composition, this results in a biophysical feedback mechanism for the regulation of the stored elastic energy. The model shows that the presence of feedback increases the robustness of the steady state of the system, in the sense that biologically inviable nonbilayer states are less likely. We also show that the biophysical and biochemical features of the network have implications as to which enzymes are most efficient at implementing the regulation. The network imposes restrictions on the steady-state balance between bilayer and nonbilayer lipids and on the concentrations of particular lipids. Finally, we consider the influence of the length of the amphipathic alpha-helix on the efficacy of the feedback and propose experimental measurements and extensions of the modeling framework.

We present a perfect sampling algorithm that can be applied to the master equation of gene regulatory networks. The method recasts Gillespie's stochastic simulation algorithm (SSA) in the light of Markov chain Monte Carlo methods and combines it with the dominated coupling from the past (DCFTP) algorithm to provide guaranteed sampling from the stationary distribution. We show how the DCFTP-SSA can be generically applied to genetic networks with feedback formed by the interconnection of linear enzymatic reactions and nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the error and convergence of the DCFTP-SSA, as compared to the standard SSA, through a set of increasingly complex examples. Once the building blocks for gene regulatory networks have been introduced, the algorithm is applied to study properly averaged dynamic properties of two experimentally relevant genetic networks: the toggle switch, a two-dimensional bistable system; and the repressilator, a six-dimensional transcriptional oscillator.

We present a generic computational framework for the simulation of viral capsid assembly which is quantitative and specific. Starting from PDB files containing atomic coordinates, the algorithm builds a coarse-grained description of protein oligomers based on graph rigidity. These reduced protein descriptions are used in an extended Gillespie algorithm to investigate the stochastic kinetics of the assembly process. The association rates are obtained from a diffusive Smoluchowski equation for rapid coagulation, modified to account for water shielding and protein structure. The dissociation rates are derived by interpreting the splitting of oligomers as a process of graph partitioning akin to the escape from a multidimensional well. This modular framework is quantitative yet computationally tractable, with a small number of physically motivated parameters. The methodology is illustrated using two different viruses which are shown to follow quantitatively different assembly pathways. We also show how in this model the quasi-stationary kinetics of assembly can be described as a Markovian cascading process, in which only a few intermediates and a small proportion of pathways are present. The observed pathways and intermediates can be related a posteriori to structural and energetic properties of the capsid oligomers.