Time-translational symmetry in statistical dynamics dictates Einstein relation, Green-Kubo formula, and their generalizations.

A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent, components contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. We show that fluctuation-dissipation relations of the two aforementioned components, such as the Einstein relation and the Green-Kubo formula, can be formulated for any stochastic process with a steady state, without additional supposition of the process being Markovian, reversible, or linear. Further, by considering the adjoint process defined by the time reversal at the steady state, we show that reversibility in equilibrium leads to an additional symmetry in the covariance between system's state and drift. Potential directions of further generalizing our results to processes without steady states is briefly discussed.

Ex vivo engineered human plasma cells exhibit robust protein secretion and long-term engraftment in vivo.

Due to their unique longevity and capacity to secrete high levels of protein, plasma B cells have the potential to be used as a cell therapy for protein replacement. Here, we show that ex vivo engineered human plasma cells exhibit single-cell RNA profiles, scanning electron micrograph ultrastructural features, and in vivo homing capacity of long-lived plasma cells. After transferring human plasma cells to immunodeficient mice in the presence of the human cytokines BAFF and IL-6, we observe increases in retention of plasma cells in the bone marrow, with engraftment exceeding a year. The most profound in vivo effects of human IL-6 are observed within 20 days of transfer and could be explained by decreased apoptosis in newly differentiated plasma cells. Collectively, these results show that ex vivo engineered and differentiated human plasma cells have the potential for long-lived in vivo protein secretion, which can be modeled in small animals.

Unified formalism for entropy production and fluctuation relations.

Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables due to reversals can be represented by a change in the probability measure. We consider operators on the space of probability measures that induce changes in the statistical properties of a process, and we formulate entropy production in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy production allows us to achieve an organization of various forms of fluctuation relations: All entropy production has a nonnegative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator of entropy production. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal, and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy production in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuation relations for excess work and heat, discuss the martingale properties of entropy production, and derive the stochastic integral formulas for entropy production in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory.

Adaptive synchronization and anticipatory dynamical systems.

Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and cannot be understood from traditional synchronization consideration of passive oscillatory systems. To understand this anticipatory phenomena, we consider oscillators built from excitable systems with the addition of an adaptive dynamics. With such systems, well-timed post-stimulus responses similar to those from experiments can be obtained. Furthermore, a well-known model of working memory is shown to possess similar anticipatory dynamics when the adaptive mechanism is identified with synaptic facilitation. The last finding suggests that this type of oscillator can be common in neuronal systems with plasticity.