Probabilistic Kolmogorov complexity with applications to average-case complexity

Understanding the relationship between the worst-case and average-case complexities of NP and of other subclasses of PH is a long-standing problem in complexity theory. Over the last few years, much progress has been achieved in this front through the investigation of meta-complexity: the complexity of problems that refer to the complexity of the input string x (e.g., given a string x, estimate its time-bounded Kolmogorov complexity). In particular, [Shuichi Hirahara, 2021] employed techniques from meta-complexity to show that if DistNP ⊆ AvgP then UP ⊆ DTIME[2^{O(n/log n)}]. While this and related results [Shuichi Hirahara and Mikito Nanashima, 2021; Lijie Chen et al., 2022] offer exciting progress after a long gap, they do not survive in the setting of randomized computations: roughly speaking, "randomness" is the opposite of "structure", and upper bounding the amount of structure (time-bounded Kolmogorov complexity) of different objects is crucial in recent applications of meta-complexity. This limitation is significant, since randomized computations are ubiquitous in algorithm design and give rise to a more robust theory of average-case complexity [Russell Impagliazzo and Leonid A. Levin, 1990]. In this work, we develop a probabilistic theory of meta-complexity, by incorporating randomness into the notion of complexity of a string x. This is achieved through a new probabilistic variant of time-bounded Kolmogorov complexity that we call pK^t complexity. Informally, pK^t(x) measures the complexity of x when shared randomness is available to all parties involved in a computation. By porting key results from meta-complexity to the probabilistic domain of pK^t complexity and its variants, we are able to establish new connections between worst-case and average-case complexity in the important setting of probabilistic computations: - If DistNP ⊆ AvgBPP, then UP ⊆ RTIME[2^O(n/log n)]. - If DistΣ^P_2 ⊆ AvgBPP, then AM ⊆ BPTIME[2^O(n/log n)]. - In the fine-grained setting [Lijie Chen et al., 2022], we get UTIME[2^O(√{nlog n})] ⊆ RTIME[2^O(√{nlog n})] and AMTIME[2^O(√{nlog n})] ⊆ BPTIME[2^O(√{nlog n})] from stronger average-case assumptions. - If DistPH ⊆ AvgBPP, then PH ⊆ BPTIME[2^O(n/log n)]. Specifically, for an

Citrullination regulates pluripotency and histone H1 binding to chromatin.

Citrullination is the post-translational conversion of an arginine residue within a protein to the non-coded amino acid citrulline. This modification leads to the loss of a positive charge and reduction in hydrogen-bonding ability. It is carried out by a small family of tissue-specific vertebrate enzymes called peptidylarginine deiminases (PADIs) and is associated with the development of diverse pathological states such as autoimmunity, cancer, neurodegenerative disorders, prion diseases and thrombosis. Nevertheless, the physiological functions of citrullination remain ill-defined, although citrullination of core histones has been linked to transcriptional regulation and the DNA damage response. PADI4 (also called PAD4 or PADV), the only PADI with a nuclear localization signal, was previously shown to act in myeloid cells where it mediates profound chromatin decondensation during the innate immune response to infection. Here we show that the expression and enzymatic activity of Padi4 are also induced under conditions of ground-state pluripotency and during reprogramming in mouse. Padi4 is part of the pluripotency transcriptional network, binding to regulatory elements of key stem-cell genes and activating their expression. Its inhibition lowers the percentage of pluripotent cells in the early mouse embryo and significantly reduces reprogramming efficiency. Using an unbiased proteomic approach we identify linker histone H1 variants, which are involved in the generation of compact chromatin, as novel PADI4 substrates. Citrullination of a single arginine residue within the DNA-binding site of H1 results in its displacement from chromatin and global chromatin decondensation. Together, these results uncover a role for citrullination in the regulation of pluripotency and provide new mechanistic insights into how citrullination regulates chromatin compaction.Cancer Research UKThis is the author accepted manuscript. The final version is available from the Nature Publishing Group via http://dx.doi.org/10.1038/nature1294

How nitric oxide donors can protect plants in a changing environment: what we know so far and perspectives

The free radical nitric oxide (NO) plays important roles in plant growth and defense. Owing to its small size and lipophilicity, NO acts as a crucial signaling molecule in plants, crossing cell membranes and enhancing cell communication. Indeed, NO donors have been shown to modulate a variety of physiological processes, such as plant greening, seed germination, iron homeostasis and mitochondrial respiration. Recently, several papers have reported the protective actions upon application of low molecular weight NO donors in plants under abiotic stress. Exogenous NO is able to improve plant tolerance to several abiotic stresses, such as drought, salinity, metal toxicity, and extreme temperatures. This protection is assigned to the NO-mediated redox signaling in plants, which involves interplay with reactive oxygen species and modulation of gene expression and protein function. This review reports and discusses the recent advantages, pitfalls, challenges, and perspectives in the applications of low molecular weight NO donors in plants under abiotic stress. The combination of nanotechnology and NO donors as an efficient approach to protect plants under challenging environments is also discussed

Síntese de óxido nítrico dependente da nitrato redutase na resposta de defesa de Arabidopsis thaliana contra Pseudomonas syringae

Nitrate reductase (NR) was recently shown to play an important role during phytopathogenic interactions by providing substrates for the synthesis of nitric oxide (NO), a key signal for plant defense responses. In order to give additional support to this hypothesis, we compared NO-mediated defense responses of wild-type and NR double-deficient (nia1 nia2) Arabidopsis thaliana plants inoculated with the IBSBF-1115 (ibs) strain of Pseudomonas syringae pv. maculicola (Psm) and with genetically characterized avirulent (avr) or virulent (vir) strains of Psm. Inoculation of wild-type leaves with avr or ibs, but not vir, stimulated NO emission, as measured by the indicator 4,5-diaminofluorescein. NO emission induced by avr was higher than that induced by ibs. Wild-type plants displayed the hypersensitive response (HR) when infiltrated with the strains avr or ibs, although a stronger HR was induced by avr. The vir strain did not induce HR in wild-type plants, and leaves developed severe infection symptoms. nia1 nia2 plants did not show significantly increased NO emission nor did they develop HR to any of the analyzed strains of Psm, but displayed clorotic lesions and higher bacterial growth in their leaves. Overall, these results highlight the importance of NR-dependent NO synthesis for plant defenses against pathogen attack.A nitrato redutase (NR) possui importante papel na interação fitopatogênica por prover os substratos para a síntese do óxido nítrico (NO), um sinalizador essencial para a defesa vegetal. A fim de fornecer suporte adicional a essa hipótese, neste trabalho foram comparadas as respostas de defesa mediadas por NO de plantas de Arabidopsis thaliana selvagens e deficientes para a NR (nia1 nia2) quando inoculadas com a linhagem IBSBF-1115 (ibs) de Pseudomonas syringae pv. maculicola (Psm) e com as linhagens geneticamente caracterizadas como avirulenta (avr) ou virulenta (vir) de Psm. A inoculação de folhas selvagens com avr ou ibs, mas não vir, estimulou a emissão de NO, medida pelo indicador 4,5-diaminofluoresceína. A emissão de NO induzida por avr foi maior que aquela induzida por ibs. Plantas selvagens apresentaram resposta hipersensitiva (RH) quando infiltradas com avr ou ibs, mas uma RH mais forte foi induzida por avr. A linhagem vir não induziu RH nas plantas selvagens, e as folhas desenvolveram sintomas severos da infecção. Plantas nia1 nia2 não tiveram um aumento significativo da emissão de NO nem desenvolveram RH após inoculação com as linhagens analisadas de Psm, apresentando intenso crescimento bacteriano e clorose foliar. Em suma, esses resultados evidenciam a importância da síntese de NO dependente da NR na defesa vegetal ao ataque de patógenos.104107Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq