Zero Entropy Interval Maps And MMLS-MMA Property

We prove that the flow generated by any interval map with zero topological entropy is minimally mean-attractable (MMA) and minimally mean-L-stable (MMLS). One of the consequences is that any oscillating sequence is linearly disjoint with all flows generated by interval maps with zero topological entropy. In particular, the M\"obius function is orthogonal to all flows generated by interval maps with zero topological entropy (Sarnak's conjecture for interval maps). Another consequence is a non-trivial example of a flow having the discrete spectrum.Comment: 12 page

Genetic Predisposition for Immune System, Hormone, and Metabolic Dysfunction in Myalgic Encephalomyelitis/Chronic Fatigue Syndrome: A Pilot Study

Introduction: Myalgic Encephalomyelitis/ Chronic Fatigue Syndrome (ME/CFS) is a multifactorial illness of unknown etiology with considerable social and economic impact. To investigate a putative genetic predisposition to ME/CFS we conducted genome-wide single-nucleotide polymorphism (SNP) analysis to identify possible variants.Methods: 383 ME/CFS participants underwent DNA testing using the commercial company 23andMe. The deidentified genetic data was then filtered to include only non-synonymous and nonsense SNPs from exons and microRNAs, and SNPs close to splice sites. The frequencies of each SNP were calculated within our cohort and compared to frequencies from the Kaviar reference database. Functional annotation of pathway sets containing SNP genes with high frequency in ME/CFS was performed using over-representation analysis via ConsensusPathDB. Furthermore, these SNPs were also scored using the Combined Annotation Dependent Depletion (CADD) algorithm to gauge their deleteriousness.Results: 5693 SNPs were found to have at least 10% frequency in at least one cohort (ME/CFS or reference) and at least two-fold absolute difference for ME/CFS. Functional analysis identified the majority of SNPs as related to immune system, hormone, metabolic, and extracellular matrix organization. CADD scoring identified 517 SNPs in these pathways that are among the 10% most deleteriousness substitutions to the human genome

Cooperation and Competition Shape Ecological Resistance During Periodic Spatial Disturbance of Engineered Bacteria

Cooperation is fundamental to the survival of many bacterial species. Previous studies have shown that spatial structure can both promote and suppress cooperation. Most environments where bacteria are found are periodically disturbed, which can affect the spatial structure of the population. Despite the important role that spatial disturbances play in maintaining ecological relationships, it remains unclear as to how periodic spatial disturbances affect bacteria dependent on cooperation for survival. Here, we use bacteria engineered with a strong Allee effect to investigate how the frequency of periodic spatial disturbances affects cooperation. We show that at intermediate frequencies of spatial disturbance, the ability of the bacterial population to cooperate is perturbed. A mathematical model demonstrates that periodic spatial disturbance leads to a tradeoff between accessing an autoinducer and accessing nutrients, which determines the ability of the bacteria to cooperate. Based on this relationship, we alter the ability of the bacteria to access an autoinducer. We show that increased access to an autoinducer can enhance cooperation, but can also reduce ecological resistance, defined as the ability of a population to resist changes due to disturbance. Our results may have implications in maintaining stability of microbial communities and in the treatment of infectious diseases

Using Gene Expression Signatures to Identify Novel Treatment Strategies in Gulf War Illness

Background Gulf War Illness (GWI) is a complex multi-symptom disorder that affects up to one in three veterans of this 1991 conflict and for which no effective treatment has been found. Discovering novel treatment strategies for such a complex chronic illness is extremely expensive, carries a high probability of failure and a lengthy cycle time. Repurposing Food and Drug Administration approved drugs offers a cost-effective solution with a significantly abbreviated timeline. Methods Here, we explore drug re-purposing opportunities in GWI by combining systems biology and bioinformatics techniques with pharmacogenomic information to find overlapping elements in gene expression linking GWI to successfully treated diseases. Gene modules were defined based on cellular function and their activation estimated from the differential expression of each module’s constituent genes. These gene modules were then cross-referenced with drug atlas and pharmacogenomic databases to identify agents currently used successfully for treatment in other diseases. To explore the clinical use of these drugs in illnesses similar to GWI we compared gene expression patterns in modules that were significantly expressed in GWI with expression patterns in those same modules in other illnesses. Results We found 19 functional modules with significantly altered gene expression patterns in GWI. Within these modules, 45 genes were documented drug targets. Illnesses with highly correlated gene expression patterns overlapping considerably with GWI were found in 18 of the disease conditions studied. Brain, muscular and autoimmune disorders composed the bulk of these. Conclusion Of the associated drugs, immunosuppressants currently used in treating rheumatoid arthritis, and hormone based therapies were identified as the best available candidates for treating GWI symptoms

Electronic energy migration in Microtubules

The repeating arrangement of tubulin dimers confers great mechanical strength to microtubules, which are used as scaffolds for intracellular macromolecular transport in cells and exploited in biohybrid devices. The crystalline order in a microtubule, with lattice constants short enough to allow energy transfer between amino acid chromophores, is similar to synthetic structures designed for light harvesting. After photoexcitation, can these amino acid chromophores transfer excitation energy along the microtubule like a natural or artificial light-harvesting system? Here, we use tryptophan autofluorescence lifetimes to probe energy hopping between aromatic residues in tubulin and microtubules. By studying how the quencher concentration alters tryptophan autofluorescence lifetimes, we demonstrate that electronic energy can diffuse over 6.6 nm in microtubules. We discover that while diffusion lengths are influenced by tubulin polymerization state (free tubulin versus tubulin in the microtubule lattice), they are not significantly altered by the average number of protofilaments (13 versus 14). We also demonstrate that the presence of the anesthetics etomidate and isoflurane reduce exciton diffusion. Energy transport as explained by conventional Förster theory (accommodating for interactions between tryptophan and tyrosine residues) does not sufficiently explain our observations. Our studies indicate that microtubules are, unexpectedly, effective light harvesters

Periodically Disturbing the Spatial Structure of Biofilms Can Affect the Production of an Essential Virulence Factor in Pseudomonas aeruginosa

Understanding the environmental factors that affect the production of virulence factors has major implications in evolution and medicine. While spatial structure is important in virulence factor production, observations of this relationship have occurred in undisturbed or continuously disturbed environments. However, natural environments are subject to periodic fluctuations, including changes in physical forces, which could alter the spatial structure of bacterial populations and impact virulence factor production. Using Pseudomonas aeruginosa PA14, we periodically applied a physical force to biofilms and examined production of pyoverdine. Intermediate frequencies of disturbance reduced the amount of pyoverdine produced compared to undisturbed or frequently disturbed conditions. To explore the generality of this finding, we examined how an intermediate disturbance frequency affected pyoverdine production in 21 different strains of P. aeruginosa. Periodic disturbance increased, decreased, or did not change the amount of pyoverdine produced relative to undisturbed populations. Mathematical modeling predicts that interactions between pyoverdine synthesis rate and biofilm density determine the amount of pyoverdine synthesized. When the pyoverdine synthesis rates are high, depletion of the biofilm due to disturbance reduces the accumulation of pyoverdine. At intermediate synthesis rates, production of pyoverdine increases during disturbance as bacteria dispersed into the planktonic state enjoy increased growth and pyoverdine production rates. At low synthesis rates, disturbance does not alter the amount of pyoverdine produced since disturbance-driven access to nutrients does not augment pyoverdine synthesis. Our results suggest that environmental conditions shape robustness in the production of virulence factors and may lead to novel approaches to treat infections

Cytoskeletal Signaling: Is Memory Encoded in Microtubule Lattices by CaMKII Phosphorylation?

Memory is attributed to strengthened synaptic connections among particular brain neurons, yet synaptic membrane components are transient, whereas memories can endure. This suggests synaptic information is encoded and ‘hard-wired’ elsewhere, e.g. at molecular levels within the post-synaptic neuron. In long-term potentiation (LTP), a cellular and molecular model for memory, post-synaptic calcium ion (Ca2+) flux activates the hexagonal Ca2+-calmodulin dependent kinase II (CaMKII), a dodacameric holoenzyme containing 2 hexagonal sets of 6 kinase domains. Each kinase domain can either phosphorylate substrate proteins, or not (i.e. encoding one bit). Thus each set of extended CaMKII kinases can potentially encode synaptic Ca2+ information via phosphorylation as ordered arrays of binary ‘bits’. Candidate sites for CaMKII phosphorylation-encoded molecular memory include microtubules (MTs), cylindrical organelles whose surfaces represent a regular lattice with a pattern of hexagonal polymers of the protein tubulin. Using molecular mechanics modeling and electrostatic profiling, we find that spatial dimensions and geometry of the extended CaMKII kinase domains precisely match those of MT hexagonal lattices. This suggests sets of six CaMKII kinase domains phosphorylate hexagonal MT lattice neighborhoods collectively, e.g. conveying synaptic information as ordered arrays of six “bits”, and thus “bytes”, with 64 to 5,281 possible bit states per CaMKII-MT byte. Signaling and encoding in MTs and other cytoskeletal structures offer rapid, robust solid-state information processing which may reflect a general code for MT-based memory and information processing within neurons and other eukaryotic cells

The Zinc Dyshomeostasis Hypothesis of Alzheimer's Disease

Alzheimer's disease (AD) is the most common form of dementia in the elderly. Hallmark AD neuropathology includes extracellular amyloid plaques composed largely of the amyloid-β protein (Aβ), intracellular neurofibrillary tangles (NFTs) composed of hyper-phosphorylated microtubule-associated protein tau (MAP-tau), and microtubule destabilization. Early-onset autosomal dominant AD genes are associated with excessive Aβ accumulation, however cognitive impairment best correlates with NFTs and disrupted microtubules. The mechanisms linking Aβ and NFT pathologies in AD are unknown. Here, we propose that sequestration of zinc by Aβ-amyloid deposits (Aβ oligomers and plaques) not only drives Aβ aggregation, but also disrupts zinc homeostasis in zinc-enriched brain regions important for memory and vulnerable to AD pathology, resulting in intra-neuronal zinc levels, which are either too low, or excessively high. To evaluate this hypothesis, we 1) used molecular modeling of zinc binding to the microtubule component protein tubulin, identifying specific, high-affinity zinc binding sites that influence side-to-side tubulin interaction, the sensitive link in microtubule polymerization and stability. We also 2) performed kinetic modeling showing zinc distribution in extra-neuronal Aβ deposits can reduce intra-neuronal zinc binding to microtubules, destabilizing microtubules. Finally, we 3) used metallomic imaging mass spectrometry (MIMS) to show anatomically-localized and age-dependent zinc dyshomeostasis in specific brain regions of Tg2576 transgenic, mice, a model for AD. We found excess zinc in brain regions associated with memory processing and NFT pathology. Overall, we present a theoretical framework and support for a new theory of AD linking extra-neuronal Aβ amyloid to intra-neuronal NFTs and cognitive dysfunction. The connection, we propose, is based on β-amyloid-induced alterations in zinc ion concentration inside neurons affecting stability of polymerized microtubules, their binding to MAP-tau, and molecular dynamics involved in cognition. Further, our theory supports novel AD therapeutic strategies targeting intra-neuronal zinc homeostasis and microtubule dynamics to prevent neurodegeneration and cognitive decline