A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by Pm(t), which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of Pm(t), which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state (t→∞) or require several parameters to be zero or infinity. Here, we present an approach for calculating Pm(t) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of Pm(t) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.

Worklife and Unemployment: A New Consideration

Do traditional two-state worklife estimates need adjustment for unemployment? To answer, an augmented three-state model classifies individuals as either 1) employed; 2) unemployed; or 3) inactive but not marginally attached. Periods of unemployment may reduce worklives; however, removal of those marginally attached or discouraged from the inactive state raises worklives. The three-state model results are compared to worklife estimates from the same initial data using the traditional two-state model. Results show that in many cases, the two-state model results are a good proxy for the three-state results that control for unemployment.

Distributing Information in Small-World Networks: Four Social Cases of the Process of Contagion in Spain

This case study is part of a research project based in Spain between 2011 and 2014 on the social institutions and affective processes involved in what is normally referred to as social movement. Our purpose is to study how information circulates in small-world networks in which the dynamics are modeled with a stochastic version of Greenberg–Hasting’s excitable model. This is a three-state model in which a node can be in an excited, passive, or susceptible state. Only in the susceptible state does a node interact with its neighbors in the small-world network, and its interaction depends on the probability of contagion. We introduce an infection probability, which is the only parameter in our implementation of Greenberg–Hasting’s model. The small-world network is characterized by a mean connectivity parameter and by a disorder parameter. The resulting dynamics are characterized by the average activity in the network. We have found transitions from inactive to active collective regimes, and we can induce this transition by varying. We search for different dynamics within small-world networks of citizens’ organizations by going through the following steps: identifying alliance patterns; looking for robust small-world attributes and how they are constructed; and interpreting the three modes of our model.

Exact Solution of Kinetic Analysis for Thermally Activated Delayed Fluorescence Materials

The photophysical analysis of thermally activated delayed fluorescence (TADF) materials has become instrumental to providing insight into their stability and performance, which is not only relevant for organic light-emitting diodes (OLED), but also for other applications such as sensing, imaging and photocatalysis. Thus, a deeper understanding of the photophysics underpinning the TADF mechanism is required to push materials design further. Previously reported analyses in the literature of the kinetics of the various processes occurring in a TADF material rely on several a priori assumptions to estimate the rate constants for forward and reverse intersystem crossing (ISC and RISC, respectively). In this report, we demonstrate a method to determine these rate constants using a three-state model together with a steady-state approximation and, importantly, no additional assumptions. Further, we derive the exact rate equations, greatly facilitating a comparison of the TADF properties of structurally diverse emitters and providing a comprehensive understanding of the photophysics of these systems.

Intermolecular Charge-Transfer-Induced Strong Optical Emission from Herringbone H-Aggregates

Superior organic light-emitting transistors (OLETs) materials require two conventionally exclusive properties: strong luminescence and high charge mobilities. We propose a three-state model through localized diabatization to quantitative analyze excited state structures for various herringbone (HB) H-aggregates and demonstrate that for some investigated systems, the low-lying intermolecular charge-transfer (CT) state couples with the bright Frenkel exciton (FE) and forms a dipole-allowed S₁ that lies below the dark state, proceeding strong luminescence. Specifically, such conversion in luminescence properties occurs when the electron- and hole-transfer integrals ( and ) are of the same sign and is notably larger than the excitonic coupling (<i>J</i>), i.e., . This theoretical finding can not only explain and rationalize recent experimental results on DPA and dNaAnt, both with OLET property, but also unravel an exciting scenario where strong luminescence and high charge mobilities are compatible, which will considerably broaden the aperture of novel OLET design.

Intermolecular Charge-Transfer-Induced Strong Optical Emission from Herringbone H-Aggregates

Superior organic light-emitting transistors (OLETs) materials require two conventionally exclusive properties: strong luminescence and high charge mobilities. We propose a three-state model through localized diabatization to quantitative analyze excited state structures for various herringbone (HB) H-aggregates and demonstrate that for some investigated systems, the low-lying intermolecular charge-transfer (CT) state couples with the bright Frenkel exciton (FE) and forms a dipole-allowed S₁ that lies below the dark state, proceeding strong luminescence. Specifically, such conversion in luminescence properties occurs when the electron- and hole-transfer integrals ( and ) are of the same sign and is notably larger than the excitonic coupling (<i>J</i>), i.e., . This theoretical finding can not only explain and rationalize recent experimental results on DPA and dNaAnt, both with OLET property, but also unravel an exciting scenario where strong luminescence and high charge mobilities are compatible, which will considerably broaden the aperture of novel OLET design.

Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

Here, we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this “nanothermodynamics” to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of “atoms” into an ensemble of “regions” of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for particles that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the spins, we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann’s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to the equilibrium thermal fluctuations found in many materials.

Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

Here we investigate how the local properties of particles in a thermal bath may influence the thermodynamics of the bath, and consequently alter the statistical mechanics of subsystems that comprise the bath. We are guided by the theory of small-system thermodynamics, which is based on two primary postulates: that small systems can be treated self-consistently by coupling them to an ensemble of similarly small systems, and that a large ensemble of small systems forms its own thermodynamic bath. We adapt this &ldquo;nanothermodynamics&rdquo; to investigate how a large system may subdivide into an ensemble of smaller subsystems, causing internal heterogeneity across multiple size scales. For the semi-classical ideal gas, maximum entropy favors subdividing a large system of &ldquo;atoms&rdquo; into an ensemble of &ldquo;regions&rdquo; of variable size. The mechanism of region formation could come from quantum exchange symmetry that makes atoms in each region indistinguishable, while decoherence between regions allows atoms in separate regions to be distinguishable by their distinct locations. Combining regions reduces the total entropy, as expected when distinguishable particles become indistinguishable, and as required by a theorem in quantum mechanics for sub-additive entropy. Combining large volumes of small regions gives the usual entropy of mixing for a semi-classical ideal gas, resolving Gibbs paradox without invoking quantum symmetry for atoms that may be meters apart. Other models presented here are based on Ising-like spins, which are solved analytically in one dimension. Focusing on the bonds between the Ising-like spins we find similarity in the equilibrium properties of a two-state model in the nanocanonical ensemble and a three-state model in the canonical ensemble. Thus, emergent phenomena may alter the thermal behavior of microscopic models, and the correct ensemble is necessary for fully-accurate predictions. Another result using Ising-like spins involves simulations that include a nonlinear correction to Boltzmann&rsquo;s factor, which mimics the statistics of indistinguishable states by imitating the dynamics of spin exchange on intermediate lengths. These simulations exhibit 1/f-like noise at low frequencies (f), and white noise at higher f, similar to equilibrium thermal fluctuations found in many materials.

Novel insights into sarcomere regulatory systems control of cardiac thin filament activation

Our review focuses on sarcomere regulatory mechanisms with a discussion of cardiac-specific modifications to the three-state model of thin filament activation from a blocked to closed to open state. We discuss modulation of these thin filament transitions by Ca2+, by crossbridge interactions, and by thick filament–associated proteins, cardiac myosin–binding protein C (cMyBP-C), cardiac regulatory light chain (cRLC), and titin. Emerging evidence supports the idea that the cooperative activation of the thin filaments despite a single Ca2+ triggering regulatory site on troponin C (cTnC) cannot be considered in isolation of other functional domains of the sarcomere. We discuss long- and short-range interactions among these domains with the regulatory units of thin filaments, including proteins at the barbed end at the Z-disc and the pointed end near the M-band. Important to these discussions is the ever-increasing understanding of the role of cMyBP-C, cRLC, and titin filaments. Detailed knowledge of these control processes is critical to the understanding of mechanisms sustaining physiological cardiac state with varying hemodynamic load, to better defining genetic and acquired cardiac disorders, and to developing targets for therapies at the level of the sarcomeres.

Exact Solution of Kinetic Analysis for Thermally Activated Delayed Fluorescence Materials

The photophysical analysis of thermally activated delayed fluorescence (TADF) materials has become instrumental to providing insight into their stability and performance, which is not only relevant for organic light-emitting diodes (OLED), but also for other applications such as sensing, imaging and photocatalysis. Thus, a deeper understanding of the photophysics underpinning the TADF mechanism is required to push materials design further. Previously reported analyses in the literature of the kinetics of the various processes occurring in a TADF material rely on several a priori assumptions to estimate the rate constants for forward and reverse intersystem crossing (ISC and RISC, respectively). In this report, we demonstrate a method to determine these rate constants using a three-state model together with a steady-state approximation and, importantly, no additional assumptions. Further, we derive the exact rate equations, greatly facilitating a comparison of the TADF properties of structurally diverse emitters and providing a comprehensive understanding of the photophysics of these systems.