Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment

The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window T. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time T. The large deviation properties of any time-additive observable of the Markov trajectory before extinction can be derived from the level 2.5 via the decomposition of the time-additive observable in terms of the empirical density and the empirical flows. This general formalism is described for continuous-time Markov chains, with applications to population birth–death model in a stable or in a switching environment, and for diffusion processes in dimension d.

Approximating quasi-stationary distributions with interacting reinforced random walks

We propose two numerical schemes for approximating quasi-stationary distributions (QSD) of finite state Markov chains with absorbing states. Both schemes are described in terms of interacting chains where the interaction is given in terms of the total time occupation measure of all particles in the system and has the impact of reinforcing transitions, in an appropriate fashion, to states where the collection of particles has spent more time. The schemes can be viewed as combining the key features of the two basic simulation-based methods for approximating QSD originating from the works of Fleming and Viot (1979) and Aldous, Flannery and Palacios (1998), respectively. The key difference between the two schemes studied here is that in the first method one starts with $a(n)$ particles at time $0$ and number of particles stays constant over time whereas in the second method we start with one particle and at most one particle is added at each time instant in such a manner that there are $a(n)$ particles at time $n$. We prove almost sure convergence to the unique QSD and establish Central Limit Theorems for the two schemes under the key assumption that $a(n)=o(n)$. Exploratory numerical results are presented to illustrate the performance.

Construction and Analysis of Queuing and Reliability Models Using Random Graphs

In this paper, the use of the construction of random processes on graphs allows us to expand the models of the theory of queuing and reliability by constructing. These problems are important because the emphasis on the legal component largely determines functioning of these models. The considered models are reliability and queuing. Reliability models arranged according to the modular principle and reliability networks in the form of planar graphs. The queuing models considered here are queuing networks with multi server nodes and failures, changing the parameters of the queuing system in a random environment with absorbing states, and the process of growth of a random network. This is determined by the possibility of using, as traditional probability methods, mathematical logic theorems, geometric images of a queuing network, dual graphs to planar graphs, and a solution to the Dirichlet problem.

Comparative analysis of two paradigm bacteriophytochromes reveals opposite functionalities in two-component signaling

Bacterial phytochrome photoreceptors usually belong to two-component signaling systems which transmit environmental stimuli to a response regulator through a histidine kinase domain. Phytochromes switch between red light-absorbing and far-red light-absorbing states. Despite exhibiting extensive structural responses during this transition, the model bacteriophytochrome from Deinococcus radiodurans (DrBphP) lacks detectable kinase activity. Here, we resolve this long-standing conundrum by comparatively analyzing the interactions and output activities of DrBphP and a bacteriophytochrome from Agrobacterium fabrum (Agp1). Whereas Agp1 acts as a conventional histidine kinase, we identify DrBphP as a light-sensitive phosphatase. While Agp1 binds its cognate response regulator only transiently, DrBphP does so strongly, which is rationalized at the structural level. Our data pinpoint two key residues affecting the balance between kinase and phosphatase activities, which immediately bears on photoreception and two-component signaling. The opposing output activities in two highly similar bacteriophytochromes suggest the use of light-controllable histidine kinases and phosphatases for optogenetics.

Dream to explore: 5-HT2a as adaptive temperature parameter for sophisticated affective inference

Relative to other neuromodulators, serotonin (5-HT) has received far less attention in machine learning and active inference. We will review prior work interpreting 5-HT1a signaling as an uncertainty parameter with opponency to dopamine. We will then discuss how 5-HT2a receptors may promote more exploratory policy selection by enhancing imaginative planning (as sophisticated affective inference). Finally, we will briefly comment on how qualitatively different effects may be observed across low and high levels of 5-HT2a signaling, where the latter may help agents to change self-adversarial policies and break free of maladaptive absorbing states in POMDPs.

Structural heterogeneity in biliverdin modulates spectral properties of Sandercyanin fluorescent protein

Sandercyanin, a blue homo-tetrameric lipocalin protein purified from Canadian walleye (Stizostedion vitreus), is the first far-red fluorescent protein reported in vertebrates. Sandercyanin binds non-covalently to biliverdin IXα (BLA) and fluoresces at 675nm on excitation at 375nm and 635nm. Sandercyanin fluorescence can be harnessed for many in vivo applications when engineered into a stable monomeric form. Here, we report the spectral properties and crystal structures of engineered monomeric Sandercyanin-BLA complexes. Compared to wild-type protein, monomeric Sandercyanin (~18kDa) binds BLA with similar affinities and show a broad red- shifted absorbance spectra but possess reduced quantum efficiency. Crystal structures reveal D-ring pyrrole of BLA rotated around the C14-C15 bond, which is stabilized by neighboring aromatic residues and increased water-mediated polar contacts in the BLA-binding pocket. A tetrameric Sandercyanin variant (Tyr-142-Ala) co-displaying red- and far-red absorbing states, and reduced fluorescence shows similar conformational changes in BLA binding pocket. Our results suggest that D-ring flexibility of BLA and its rearrangement reduces the fluorescence quantum-yield of monomeric Sandercyanin. Structures of monomeric Sandercyanin could be utilized as prototypes to generate bright BLA-inducible fluorescent proteins. Further, our study postulates a mechanism for modulating photo-states in BLA- bound lipocalins, known only in phytochromes till date.

The effects of age, gender, education, and APOE on the transitions from a cognitively normal state to mild cognitive impairment and dementia

To determine the effects of a number of risk factors on the transition from a cognitively normal state to mild cognitive impairment (MCI), as transient states, and then to dementia and death, as absorbing states. The study used the data of 8,456 subjects obtained from the Uniform Data Set (UDS) conducted by the National Alzheimer Coordinating Center (NACC), and categorized them into four cognitive states; normal and MCI (transient states), dementia, and death (absorbing states). Then, statistical analysis was conducted to obtain how age, gender, educational attainment, and presence of apolipoprotein 4 allele (APOE) affect the odds of transitioning from one cognitive state to another, and to death as a competing state. Both age and APOE risk had profound effects on the cognitive transition of subjects from one state to another, and to a lesser extent, gender and education attainment. This study has contributed more evidence that risk factors like age, presence of apolipoprotein 4 allele (APOE), and to a lesser extent, education and gender have significant effects in all or some of the transitions from one cognitive state to another among elderly people.

Entropy of killed-resurrected stationary Markov chains

We consider a strictly substochastic matrix or a stochastic matrix with absorbing states. By using quasi-stationary distributions we show that there is an associated canonical Markov chain that is built from the resurrected chain, the absorbing states, and the hitting times, together with a random walk on the absorbing states, which is necessary for achieving time stationarity. Based upon the 2-stringing representation of the resurrected chain, we supply a stationary representation of the killed and the absorbed chains. The entropies of these representations have a clear meaning when one identifies the probability measure of natural factors. The balance between the entropies of these representations and the entropy of the canonical chain serves to check the correctness of the whole construction.

Gene prioritization based on random walks with restarts and absorbing states, to define gene sets regulating drug pharmacodynamics from single-cell analyses

MotivationPrioritizing genes for their role in drug sensitivity, is an important step in understanding drugs mechanisms of action and discovering new molecular targets for co-treatment. To formalize this problem, we consider two sets of genes X and P respectively composing the predictive gene signature of sensitivity to a drug and the genes involved in its mechanism of action, as well as a protein interaction network (PPIN) containing the products of X and P as nodes. We introduce GENetRank, a method to prioritize the genes in X for their likelihood to regulate the genes in P.ResultsGENetRank uses asymmetric random walks with restarts and absorbing states to focus on certain nodes of the PPIN, as well as novel saturation indices providing insights on the visited regions of the PPIN. Using MINT as underlying network, we apply GENetRank to a predicitive gene signature of cancer cells sensitivity to tumor-necrosis-factor-related apoptosis-inducing ligand (TRAIL), performed in single-cells. Our ranking provides biological insights on drug sensitivity and a gene set considerably enriched in genes regulating TRAIL pharmacodynamics when compared to the most significant differentially expressed genes obtained from a statistical analysis framework alone. We also introduce gene expression radars, a visualization tool to assess all pairwise interactions at a glance.Availability and ImplementationGENetRank is made available in the Structural Bioinformatics Library (https://sbl.inria.fr/doc/Genetrank-user-manual.html). It should prove useful for mining gene sets in conjunction with a signaling pathway, whenever other approaches yield relatively large sets of genes.