Molecular Noise Research Articles

Expression of lncRNAs NEAT1, PACERR, and GAS5 can be associated with disease activity in rheumatoid arthritis patients.

Long non-coding RNAs (lncRNAs) have long been considered molecular noise within the transcriptome, but over time it has been shown that they perform many important biological functions and are associated with various inflammatory and autoimmune diseases, including rheumatoid arthritis (RA). The aim of this study was to evaluate the association between circulating lncRNAs and RA activity. The study included 63 patients with well-established RA (median disease duration 12 years), 51.7 (13); mean (SD) aged, 88.9% women and 25 healthy controls (HCs) 51.8 (8.2) aged, 80% women. Quantitative real-time polymerase chain reaction was used to evaluate the plasma concentration levels of 6 lncRNAs: PACERR, NEAT1, HOTTIP, GAS5, MALAT1 and HIX003209. Among the tested molecules, 5 targets (PACERR, NEAT1, HOTTIP, GAS5 and HIX003209) had decreased concentration in RA patients compared to HCs. LncRNAs NEAT1, PACERR, and GAS5 showed differences between the severe disease activity group (the 28 joint disease activity score, DAS28>5.1) and HCs; (P = 0.02, P = 0.003 and P = 0.04, respectively). The multiple linear regression analysis indicated that GAS5 (P = 0.01) had the greatest impact on disease activity based on DAS28. Circulating plasma lncRNAs may be considered as supporting molecular markers associated with RA activity and may be useful in identifying disease exacerbation.

Dynamics of two feed forward genetic motifs in the presence of molecular noise

Understanding the function of common motifs in gene regulatory networks is an important goal of systems biology. Feed forward loops (FFLs) are an example of such a motif. In FFLs, a gene (X) regulates another gene (Z) both directly and via an intermediary gene (Y). Previous theoretical studies have suggested several possible functions for FFLs, based on their transient responses to changes in input signals (using deterministic models) and their fluctuations around steady state (using stochastic models). In this paper we study stochastic models of the two most common FFLs, “coherent type 1” and “incoherent type 1”. We incorporate molecular noise by treating DNA binding, transcription, translation, and decay as stochastic processes. By comparing the dynamics of these loops with models of alternative networks (in which X does not regulate Y), we explore how FFLs act to process information in the presence of noise. This work highlights the importance of incorporating realistic molecular noise in studying both the transient and steady-state behavior of gene regulatory networks.

A stochastic vs deterministic perspective on the timing of cellular events

Cells are the fundamental units of life, and like all life forms, they change over time. Changes in cell state are driven by molecular processes; of these many are initiated when molecule numbers reach and exceed specific thresholds, a characteristic that can be described as “digital cellular logic”. Here we show how molecular and cellular noise profoundly influence the time to cross a critical threshold—the first-passage time—and map out scenarios in which stochastic dynamics result in shorter or longer average first-passage times compared to noise-less dynamics. We illustrate the dependence of the mean first-passage time on noise for a set of exemplar models of gene expression, auto-regulatory feedback control, and enzyme-mediated catalysis. Our theory provides intuitive insight into the origin of these effects and underscores two important insights: (i) deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells; (ii) molecular noise can significantly shift mean first-passage times, particularly within auto-regulatory genetic feedback circuits.

Spontaneous Stochasticity Amplifies Even Thermal Noise to the Largest Scales of Turbulence in a Few Eddy Turnover Times.

How predictable are turbulent flows? Here, we use theoretical estimates and shell model simulations to argue that Eulerian spontaneous stochasticity, a manifestation of the nonuniqueness of the solutions to the Euler equation that is conjectured to occur in Navier-Stokes turbulence at high Reynolds numbers, leads to universal statistics at finite times, not just at infinite time as for standard chaos. These universal statistics are predictable, even though individual flow realizations are not. Any small-scale noise vanishing slowly enough with increasing Reynolds number can trigger spontaneous stochasticity, and here we show that thermal noise alone, in the absence of any larger disturbances, would suffice. If confirmed for Navier-Stokes turbulence, our findings would imply that intrinsic stochasticity of turbulent fluid motions at all scales can be triggered even by unavoidable molecular noise, with implications for modeling in engineering, climate, astrophysics, and cosmology.

Effects of Molecular Noise on Cell Size Control.

Cells employ control strategies to maintain a stable size. Dividing at a target size (the "sizer" strategy) is thought to produce the tightest size distribution. However, this result follows from phenomenological models that ignore the molecular mechanisms required to implement the strategy. Here we investigate a simple mechanistic model for exponentially growing cells whose division is triggered at a molecular abundance threshold. We find that size noise inherits the molecular noise and is consequently minimized not by the sizer but by the "adder" strategy, where a cell divides after adding a target amount to its birth size. We derive a lower bound on size noise that agrees with publicly available data from six microfluidic studies on Escherichia coli bacteria.

Coverage and Rate Analysis of LEO Satellite-to-Airplane Communication Networks in Terahertz Band

The low Earth orbit (LEO) satellite constellation in the terahertz (THz) band is one of the promising technologies to provide global coverage and high-rate transmission to the airplane, whose key performance evaluation is required before realistic deployment. In this paper, we consider a downlink THz LEO satellite-airplane network with directional antennas, where the satellites follow a binomial point process on a spherical surface. Incorporating the distinctive THz propagation properties and directional beams in the two scenarios with/without molecular absorption noise, we propose an analytical framework to evaluate the coverage probability and average achievable rate of an arbitrary airplane. The analytical results are expressed in terms of the Laplace transforms of the interference-plus-molecular absorption noise and interference. Specifically, considering a frequency reuse strategy, we first provide the probability distributions of the distances from an arbitrary satellite, the serving satellite and any non-serving satellite to the target airplane, and calculate the probabilities of whether an interfering satellite is blocked by the Earth. Numerical results verify the accuracy of the analytical expressions and show that fewer orthogonal channels and lower LEO satellite altitude lead to better coverage and rate performance. As a key parameter in network design, the number of satellites has two competing effects on coverage and rate, and an optimum satellite number exists. Overall, this study provides theoretical guidance for deploying and planning THz satellite constellations.

Optimal control of gene regulatory networks for morphogen-driven tissue patterning

The generation of distinct cell types in developing tissues depends on establishing spatial patterns of gene expression. Often, this is directed by spatially graded chemical signals-known as morphogens. In the "French Flag model," morphogen concentration instructs cells to acquire specific fates. How this mechanism produces timely and organized cell-fate decisions, despite the presence of changing morphogen levels, molecular noise, and individual variability, is unclear. Moreover, feedback is present at various levels in developing tissues, breaking the link between morphogen concentration, signaling activity, and position. Here, we develop an alternative framework using optimal control theory to tackle the problem of morphogen-driven patterning: intracellular signaling is derived as the control strategy that guides cells to the correct fate while minimizing a combination of signaling levels and time. This approach recovers experimentally observed properties of patterning strategies and offers insight into design principles that produce timely, precise, and reproducible morphogen patterning.

IDESS: a toolbox for identification and automated design of stochastic gene circuits.

One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation. In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks. IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Molecular noise-induced activator-inhibitor duality in enzyme inhibition kinetics.

Classical theories of enzyme inhibition kinetics predict a monotonic decrease in the mean catalytic activity with the increase in inhibitor concentration. The steady-state result, derived from deterministic mass action kinetics, ignores molecular noise in enzyme-inhibition mechanisms. Here, we present a stochastic generalization of enzyme inhibition kinetics to mesoscopic enzyme concentrations by systematically accounting for molecular noise in competitive and uncompetitive mechanisms of enzyme inhibition. Our work reveals an activator-inhibitor duality as a non-classical effect in the transient regime in which inhibitors tend to enhance enzymatic activity. We introduce statistical measures that quantify this counterintuitive response through the stochastic analog of the Lineweaver-Burk plot that shows a merging of the inhibitor-dependent velocity with the Michaelis-Menten velocity. The statistical measures of mean and temporal fluctuations - fractional enzyme activity and waiting time correlations - show a non-monotonic rise with the increase in inhibitors before subsiding to their baseline value. The inhibitor and substrate dependence of the fractional enzyme activity yields kinetic phase diagrams for non-classical activator-inhibitor duality. Our work links this duality to a molecular memory effect in the transient regime, arising from positive correlations between consecutive product turnover times. The vanishing of memory in the steady state recovers all the classical results.

Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise.

Microorganisms (mainly bacteria and yeast) are frequently used as hosts for genetic constructs in synthetic biology applications. Molecular noise might have a significant effect on the dynamics of gene regulation in microbial cells, mainly attributed to the low copy numbers of mRNA species involved. However, the inclusion of molecular noise in the automated design of biocircuits is not a common practice due to the computational burden linked to the chemical master equation describing the dynamics of stochastic gene regulatory circuits. Here, we address the automated design of synthetic gene circuits under the effect of molecular noise combining a mixed integer nonlinear global optimization method with a partial integro-differential equation model describing the evolution of stochastic gene regulatory systems that approximates very efficiently the chemical master equation. We demonstrate the performance of the proposed methodology through a number of examples of relevance in synthetic biology, including different bimodal stochastic gene switches, robust stochastic oscillators, and circuits capable of achieving biochemical adaptation under noise.

Disruption in the regulation of casein kinase 2 in circadian rhythm leads to pathological states: cancer, diabetes and neurodegenerative disorders.

Circadian rhythm maintains the sleep-wake cycle in biological systems. Various biological activities are regulated and modulated by the circadian rhythm, disruption of which can result in onset of diseases. Robust rhythms of phosphorylation profiles and abundances of PERIOD (PER) proteins are thought to be the master keys that drive circadian clock functions. The role of casein kinase 2 (CK2) in circadian rhythm via its direct interactions with the PER protein has been extensively studied; however, the exact mechanism by which it affects circadian rhythms at the molecular level is not known. Here, we propose an extended circadian rhythm model in Drosophila that incorporates the crosstalk between the PER protein and CK2. We studied the regulatory role of CK2 in the dynamics of PER proteins involved in circadian rhythm using the stochastic simulation algorithm. We observed that variations in the concentration of CK2 in the circadian rhythm model modulates the PER protein dynamics at different cellular states, namely, active, weakly active, and rhythmic death. These oscillatory states may correspond to distinct pathological cellular states of the living system. We find molecular noise at the expression level of CK2 to switch normal circadian rhythm to any of the three above-mentioned circadian oscillatory states. Our results suggest that the concentration levels of CK2 in the system has a strong impact on its dynamics, which is reflected in the time evolution of PER protein. We believe that our findings can contribute towards understanding the molecular mechanisms of circadian dysregulation in pathways driven by the PER mutant genes and their pathological states, including cancer, obesity, diabetes, neurodegenerative disorders, and socio-psychological disease.

A Cationic Copolymer Enhances Responsiveness andRobustness ofDNA Circuits.

Toehold-mediated DNA circuits are extensively employed to construct diverse DNA nanodevices and signal amplifiers. However, operations of these circuits are slow and highly susceptive to molecular noise such as the interference from bystander DNA strands. Herein, this work investigates the effects of a series of cationic copolymers on DNA catalytic hairpin assembly, a representative toehold-mediated DNA circuit. One copolymer, poly(L -lysine)-graft-dextran, significantly enhances the reaction rate by 30-fold due to its electrostatic interaction with DNA. Moreover, the copolymer considerably alleviates the circuit's dependency on the length and GC content of toehold, thereby enhancing the robustness of circuit operation against molecular noise. The general effectiveness of poly(L -lysine)-graft-dextran is demonstrated through kinetic characterization of a DNA AND logic circuit. Therefore, use of a cationic copolymer is a versatile and efficient approach to enhance the operation rate and robustness of toehold-mediated DNA circuits, paving the way for more flexible design and broader application.

Proofreading does not result in more reliable ligand discrimination in receptor signaling due to its inherent stochasticity

Kinetic proofreading (KPR) has been used as a paradigmatic explanation for the high specificity of ligand discrimination by cellular receptors. KPR enhances the difference in the mean receptor occupancy between different ligands compared to a nonproofread receptor, thus potentially enabling better discrimination. On the other hand, proofreading also attenuates the signal and introduces additional stochastic receptor transitions relative to a nonproofreading receptor. This increases the relative magnitude of noise in the downstream signal, which can interfere with reliable ligand discrimination. To understand the effect of noise on ligand discrimination beyond the comparison of the mean signals, we formulate the task of ligand discrimination as a problem of statistical estimation of the receptor affinity of ligands based on the molecular signaling output. Our analysis reveals that proofreading typically worsens ligand resolution compared to a nonproofread receptor. Furthermore, the resolution decreases further with more proofreading steps under most commonly biologically considered conditions. This contrasts with the usual notion that KPR universally improves ligand discrimination with additional proofreading steps. Our results are consistent across a variety of different proofreading schemes and metrics of performance, suggesting that they are inherent to the KPR mechanism itself rather than any particular model of molecular noise. Based on our results, we suggest alternative roles for KPR schemes such as multiplexing and combinatorial encoding in multi-ligand/multi-output pathways.

Global Optimization Approach for Parameter Estimation in Stochastic Dynamic Models of Biosystems.

Mechanistic dynamic models have become an essential tool for understanding biomolecular networks and other biological systems. Biochemical stochasticity can be extremely important in some situations, e.g., at the single-cell level where there is a low copy number of the species involved. In these scenarios, deterministic models are not suitable to characterize the dynamics, so stochastic dynamic models should be considered. Here, we address the challenging problem of parameter estimation in stochastic dynamic models. Despite recent advances, this area is considerably less mature than its deterministic counterpart. We present a novel strategy based on two components: (i) global optimization via a hybrid stochastic-deterministic approach, and (ii) stochastic simulation techniques tailored to the sparsity of the available experimental data. Regarding the latter, for cases of dense population data we make use of a novel approach using a Partial Integro-Differential Equation (PIDE) model solved using a semilagrangian method. In order to further speed up the simulations, we also present efficient parallel implementations for multi-core CPUs and also for graphical processing units (GPUs). Importantly, whereas SDE and Fokker Planck approximations of the Chemical Master Equation (CME) apply when the reactant populations are sufficiently large, the PIDE approximation to the CME is valid for very low copy numbers, and therefore they enable us to tackle parameter estimation for systems with large intrinsic molecular noise, (highly stochastic regimes far from the thermodynamic limit). We test our strategy with four challenging problems: a Lotka-Volterra system, a polarization system in S. cerevisiae, a genetic toggle switch, and a genetic circadian oscillator. Our method could successfully solve these problems in very reasonable computation times (often a few minutes for the first two problems) using standard low-cost hardware, showing very significant speedups with respect to recent alternative methods. The code used to obtain the results reported here is available at https://doi.org/10.5281/zenodo.5195408.

Molecular Noise in Synaptic Communication.

In synaptic molecular communication (MC), the activation of postsynaptic receptors by neurotransmitter (NTs) is governed by a stochastic reaction-diffusion process. This randomness of synaptic MC contributes to the randomness of the electrochemical downstream signal in the postsynaptic cell, called postsynaptic membrane potential (PSP). Since the randomness of the PSP is relevant for neural computation and learning, characterizing the statistics of the PSP is critical. However, the statistical characterization of the synaptic reaction-diffusion process is difficult because the reversible bi-molecular reaction of NTs with receptors renders the system nonlinear. Consequently, there is currently no model available which characterizes the impact of the statistics of postsynaptic receptor activation on the PSP. In this work, we propose a novel statistical model for the synaptic reaction-diffusion process in terms of the chemical master equation (CME). We further propose a novel numerical method which allows to compute the CME efficiently and we use this method to characterize the statistics of the PSP. Finally, we present results from stochastic particle-based computer simulations which validate the proposed models. We show that the biophysical parameters governing synaptic transmission shape the autocovariance of the receptor activation and, ultimately, the statistics of the PSP. Our results suggest that the processing of the synaptic signal by the postsynaptic cell effectively mitigates synaptic noise while the statistical characteristics of the synaptic signal are preserved. The results presented in this paper contribute to a better understanding of the impact of the randomness of synaptic signal transmission on neuronal information processing.

Toehold-Mediated Strand Displacement in Random Sequence Pools.

Toehold-mediated strand displacement (TMSD) has been used extensively for molecular sensing and computing in DNA-based molecular circuits. As these circuits grow in complexity, sequence similarity between components can lead to cross-talk, causing leak, altered kinetics, or even circuit failure. For small non-biological circuits, such unwanted interactions can be designed against. In environments containing a huge number of sequences, taking all possible interactions into account becomes infeasible. Therefore, a general understanding of the impact of sequence backgrounds on TMSD reactions is of great interest. Here, we investigate the impact of random DNA sequences on TMSD circuits. We begin by studying individual interfering strands and use the obtained data to build machine learning models that estimate kinetics. We then investigate the influence of pools of random strands and find that the kinetics are determined by only a small subpopulation of strongly interacting strands. Consequently, their behavior can be mimicked by a small collection of such strands. The equilibration of the circuit with the background sequences strongly influences this behavior, leading to up to 1 order of magnitude difference in reaction speed. Finally, we compare two established and one novel technique that speed up TMSD reactions in random sequence pools: a three-letter alphabet, protection of toeholds by intramolecular secondary structure, or by an additional blocking strand. While all of these techniques were useful, only the latter can be used without sequence constraints. We expect that our insights will be useful for the construction of TMSD circuits that are robust to molecular noise.

Thermal effects on neurons during stimulation of the brain

All electric and magnetic stimulation of the brain deposits thermal energy in the brain. This occurs through either Joule heating of the conductors carrying current through electrodes and magnetic coils, or through dissipation of energy in the conductive brain. Objective. Although electrical interaction with brain tissue is inseparable from thermal effects when electrodes are used, magnetic induction enables us to separate Joule heating from induction effects by contrasting AC and DC driving of magnetic coils using the same energy deposition within the conductors. Since mammalian cortical neurons have no known sensitivity to static magnetic fields, and if there is no evidence of effect on spike timing to oscillating magnetic fields, we can presume that the induced electrical currents within the brain are below the molecular shot noise where any interaction with tissue is purely thermal. Approach. In this study, we examined a range of frequencies produced from micromagnetic coils operating below the molecular shot noise threshold for electrical interaction with single neurons. Main results. We found that small temperature increases and decreases of 1 ∘C caused consistent transient suppression and excitation of neurons during temperature change. Numerical modeling of the biophysics demonstrated that the Na-K pump, and to a lesser extent the Nernst potential, could account for these transient effects. Such effects are dependent upon compartmental ion fluxes and the rate of temperature change. Significance. A new bifurcation is described in the model dynamics that accounts for the transient suppression and excitation; in addition, we note the remarkable similarity of this bifurcation’s rate dependency with other thermal rate-dependent tipping points in planetary warming dynamics. These experimental and theoretical findings demonstrate that stimulation of the brain must take into account small thermal effects that are ubiquitously present in electrical and magnetic stimulation. More sophisticated models of electrical current interaction with neurons combined with thermal effects will lead to more accurate modulation of neuronal activity.

Molecular Communication in Inhomogeneous Diffusion Channels

We consider an inhomogeneous diffusion channel (IDC) for molecular communication, where the diffusivities vary in space. We first study the statistical properties of molecular noise. These properties can be fully characterized by two IDC parameters related to a space-dependent diffusion coefficient and a constant drift velocity. We then characterize a noise power for the IDC by introducing the concept of geometric noise power since the molecular noise can be a heavy-tailed distribution. Finally, we derive the bit error rate of molecular communication with timing modulation in terms of two IDC parameters.

Microfluidic-Based Bacterial Molecular Computing on a Chip

Biocomputing systems based on engineered bacteria can lead to novel tools for environmental monitoring and detection of metabolic diseases. In this paper, we propose a Bacterial Molecular Computing on a Chip (BMCoC) using microfluidic and electrochemical sensing technologies. The computing can be flexibly integrated into the chip, but we focus on engineered bacterial AND Boolean logic gate and ON-OFF switch sensors that produces secondary signals to change the pH and dissolved oxygen concentrations. We present a prototype with experimental results that shows the electrochemical sensors can detect small pH and dissolved oxygen concentration changes created by the engineered bacterial populations’ molecular signals. Additionally, we present a theoretical model analysis of the BMCoC computation reliability when subjected to unwanted effects, i.e., molecular signal delays and noise, and electrochemical sensors threshold settings that are based on either standard or blind detectors. Our numerical analysis found that the variations in the production delay and the molecular output signal concentration can impact on the computation reliability for the AND logic gate and ON-OFF switch. The molecular communications of synthetic engineered cells for logic gates integrated with sensing systems can lead to a new breed of biochips that can be used for numerous diagnostic applications.

Combining single-cell tracking and omics improves blood stem cell fate regulator identification

AbstractMolecular programs initiating cell fate divergence (CFD) are difficult to identify. Current approaches usually compare cells long after CFD initiation, therefore missing molecular changes at its start. Ideally, single cells that differ in their CFD molecular program but are otherwise identical are compared early in CFD. This is possible in diverging sister cells, which were identical until their mother's division and thus differ mainly in CFD properties. In asymmetrically dividing cells, divergent daughter fates are prospectively committed during division, and diverging sisters can thus be identified at the start of CFD. Using asymmetrically dividing blood stem cells, we developed a pipeline (ie, trackSeq) for imaging, tracking, isolating, and transcriptome sequencing of single cells. Their identities, kinship, and histories are maintained throughout, massively improving molecular noise filtering and candidate identification. In addition to many identified blood stem CFD regulators, we offer here this pipeline for use in CFDs other than asymmetric division.