Stochastic ordering for birth–death processes with killing

We consider a birth–death process with killing where transitions from state i may go to either state $i-1$ or state $i+1$ or an absorbing state (killing). Stochastic ordering results on the killing time are derived. In particular, if the killing rate in state i is monotone in i, then the distribution of the killing time with initial state i is stochastically monotone in i. This result is a consequence of the following one for a non-negative tri-diagonal matrix M: if the row sums of M are monotone, so are the row sums of $M^n$ for all $n\ge 2$ .

Structural basis of the protochromic green/red photocycle of the chromatic acclimation sensor RcaE

Cyanobacteriochromes (CBCRs) are bilin-binding photosensors of the phytochrome superfamily that show remarkable spectral diversity. The green/red CBCR subfamily is important for regulating chromatic acclimation of photosynthetic antenna in cyanobacteria and is applied for optogenetic control of gene expression in synthetic biology. It is suggested that the absorption change of this subfamily is caused by the bilin C15-Z/C15-E photoisomerization and a subsequent change in the bilin protonation state. However, structural information and direct evidence of the bilin protonation state are lacking. Here, we report a high-resolution (1.63Å) crystal structure of the bilin-binding domain of the chromatic acclimation sensor RcaE in the red-absorbing photoproduct state. The bilin is buried within a “bucket” consisting of hydrophobic residues, in which the bilin configuration/conformation is C5-Z,syn/C10-Z,syn/C15-E,syn with the A- through C-rings coplanar and the D-ring tilted. Three pyrrole nitrogens of the A- through C-rings are covered in the α-face with a hydrophobic lid of Leu249 influencing the bilin pKa, whereas they are directly hydrogen bonded in the β-face with the carboxyl group of Glu217. Glu217 is further connected to a cluster of waters forming a hole in the bucket, which are in exchange with solvent waters in molecular dynamics simulation. We propose that the “leaky bucket” structure functions as a proton exit/influx pathway upon photoconversion. NMR analysis demonstrated that the four pyrrole nitrogen atoms are indeed fully protonated in the red-absorbing state, but one of them, most likely the B-ring nitrogen, is deprotonated in the green-absorbing state. These findings deepen our understanding of the diverse spectral tuning mechanisms present in CBCRs.

Effect of a Mode of Update on Universality Class for Coupled Logistic Maps: Directed Ising to Ising Class

Ising model at zero temperature leads to a ferromagnetic state asymptotically. There are two such possible states linked by symmetry, and Glauber–Ising dynamics are employed to reach them. In some stochastic or deterministic dynamical systems, the same absorbing state with [Formula: see text] symmetry is reached. This transition often belongs to the directed Ising (DI) class where dynamic exponents and persistence exponent are different. In asymmetrically coupled sequentially updated logistic maps, the transition belongs to the DI class. We study changes in the nature of transition with an update scheme. Even with the synchronous update, the transition still belongs to the DI class. We also study a synchronous probabilistic update scheme in which each site is updated with the probability [Formula: see text]. The order parameter decays with an exponent [Formula: see text] in this scheme. Nevertheless, the dynamic exponent [Formula: see text] is less than [Formula: see text] even for small values of [Formula: see text] indicating a very slow crossover to the Ising class. However, with a random asynchronous update, we recover [Formula: see text]. In the presence of feedback, synchronous update leads to a transition in the DI universality class which changes to Ising class for synchronous probabilistic update.

Structural basis of the protochromic green/red photocycle of the chromatic acclimation sensor RcaE

Cyanobacteriochromes (CBCRs) are bilin-binding photosensors of the phytochrome superfamily that show remarkable spectral diversity. The green/red CBCR subfamily is important for regulating chromatic acclimation of photosynthetic antenna in cyanobacteria and is applied for optogenetic control of gene expression in synthetic biology. They are suggested to combine the bilin C15-Z/C15-E photoisomerization with a change in the bilin protonation state to drive their absorption changes. However, structural information and direct evidence of the bilin protonation state are lacking. Here we report a high-resolution (1.63Å) crystal structure of the bilin-binding domain of the chromatic acclimation sensor RcaE in the red-absorbing photoproduct state. The bilin is buried within a “pan” consisting of hydrophobic residues, where the bilin configuration/conformation is C5-Z,syn/C10-Z,syn/C15-E,syn with the A–C rings co-planar and the D-ring tilted. Three pyrrole nitrogens of the A–C rings are covered in the α-face with a hydrophobic lid of Leu249 influencing the bilin pKa, whereas they are directly hydrogen-bonded in the β-face with the carboxyl group of Glu217. Glu217 is further connected to a cluster of waters forming a hole in the pan, which are in exchange with solvent waters in molecular dynamics simulation. We propose that the “holey pan” structure functions as a proton-exit/influx pathway upon photoconversion. NMR analysis demonstrated that the four pyrrole nitrogen atoms are indeed fully protonated in the red-absorbing state, but one of them, most likely the B-ring nitrogen, is deprotonated in the green-absorbing state. These findings deepen our understanding of the diverse spectral tuning mechanisms present in CBCRs.Significance StatementGreen/red CBCRs are one of the most important CBCR subfamilies owing to their physiological roles in cyanobacteria phylum and optogenetic applications. They are known to utilize a change in the bilin protonation state to drive the marked change in green/red absorption, but the structural basis of the protochromic green/red photocycle are not well understood. Here, we have determined the crystal structure of the chromatic acclimation sensor RcaE of this subfamily in the photoproduct state, demonstrating a unique conformation of the bilin and its interacting residues. In addition, we provide direct evidence of the protonation state of the bilin via NMR analysis. These findings bring insight to our understanding of the molecular mechanisms underlying the spectral diversity of CBCRs.

Multistate life tables using Stata

The mslt command calculates the functions of a multistate life table and plots a graph of conditional and unconditional life expectancies by time. The command provides linear and exponential solutions to estimate the number of individuals, transitions, probabilities, person-years, and years of life in a given cohort and state of occupancy. The input data are time-specific transition rates (or survivorship proportions) between nonabsorbing and at most one absorbing state. In addition to the mean age at transfer between states, mslt calculates the following summary measures: the mean age, the probability of dying, the average duration, and the proportion of life spent in a specific state.