Note on the effect of imitation in social behavior

The discussion given by N. Rashevsky (1949) on the effect of imitation in the mathematical biology of social behavior is generalized by assuming the distributions involved to be normal rather than Laplace distributions, and also by showing how most of the results can be derived without assuming any specific form for the distributions. In particular, it is demonstrated that it is possible, in a sufficiently large population, to have a stable behavior pattern which is quite independent of the desires of the population or of their inherent pattern of response.     

Note on an inequality for the coefficients in legendre polynomial expansions and its application to the theory of liquid phase transitions

It is shown that if themth derivative of a function is positive, and it has a Legendre polynomial expansion with coefficients,A _n, then (A _m)/(2m+1)≧(A _n)/(2n+1) forn>m. This result is applied to the theory of liquid phase transitions.     

On dominance relations and the structure of animal societies: III The condition for a score structure

The necessary and sufficient condition is given forn integers to be the score structure of a society with a dominance relation. A proof is also given for a theorem showing that there are members who dominate every other member either directly or indirectly through a single intermediate member.     

On some problems of random nets

The probability problems connected with random nets are restated as probabilities of drawings from an urn containing black and white balls. A partial difference equation is obtained and its solution is given. For large nets a series expression is obtained for the connectivity γ, and this is shown to be equivalent to the transcendental equation obtained by R. Solomonoff and A. Rapport (1951).     

Protein, lipid and water organization in bacteriorhodopsin crystals: a molecular view of the purple membrane at 1.9 A resolution.

BACKGROUND: Bacteriorhodopsin (bR) from Halobacterium salinarum is a proton pump that converts the energy of light into a proton gradient that drives ATP synthesis. The protein comprises seven transmembrane helices and in vivo is organized into purple patches, in which bR and lipids form a crystalline two-dimensional array. Upon absorption of a photon, retinal, which is covalently bound to Lys216 via a Schiff base, is isomerized to a 13-cis,15-anti configuration. This initiates a sequence of events - the photocycle - during which a proton is transferred from the Schiff base to Asp85, followed by proton release into the extracellular medium and reprotonation from the cytoplasmic side. RESULTS: The structure of bR in the ground state was solved to 1.9 A resolution from non-twinned crystals grown in a lipidic cubic phase. The structure reveals eight well-ordered water molecules in the extracellular half of the putative proton translocation pathway. The water molecules form a continuous hydrogen-bond network from the Schiff-base nitrogen (Lys216) to Glu194 and Glu204 and includes residues Asp85, Asp212 and Arg82. This network is involved both in proton translocation occurring during the photocycle, as well as in stabilizing the structure of the ground state. Nine lipid phytanyl moieties could be modeled into the electron-density maps. Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) analysis of single crystals demonstrated the presence of four different charged lipid species. CONCLUSIONS: The structure of protein, lipid and water molecules in the crystals represents the functional entity of bR in the purple membrane of the bacteria at atomic resolution. Proton translocation from the Schiff base to the extracellular medium is mediated by a hydrogen-bond network that involves charged residues and water molecules.     

What can AlphaFold do for antimicrobial amyloids?

Amyloids, protein, and peptide assemblies in various organisms are crucial in physiological and pathological processes. Their intricate structures, however, present significant challenges, limiting our understanding of their functions, regulatory mechanisms, and potential applications in biomedicine and technology. This study evaluated the AlphaFold2 ColabFold method's structure predictions for antimicrobial amyloids, using eight antimicrobial peptides (AMPs), including those with experimentally determined structures and AMPs known for their distinct amyloidogenic morphological features. Additionally, two well-known human amyloids, amyloid-β and islet amyloid polypeptide, were included in the analysis due to their disease relevance, short sequences, and antimicrobial properties. Amyloids typically exhibit tightly mated β-strand sheets forming a cross-β configuration. However, certain amphipathic α-helical subunits can also form amyloid fibrils adopting a cross-α structure. Some AMPs in the study exhibited a combination of cross-α and cross-β amyloid fibrils, adding complexity to structure prediction. The results showed that the AlphaFold2 ColabFold models favored α-helical structures in the tested amyloids, successfully predicting the presence of α-helical mated sheets and a hydrophobic core resembling the cross-α configuration. This implies that the AI-based algorithms prefer assemblies of the monomeric state, which was frequently predicted as helical, or capture an α-helical membrane-active form of toxic peptides, which is triggered upon interaction with lipid membranes.     

Protocol for the saMS trial (supportive adjustment for multiple sclerosis): a randomized controlled trial comparing cognitive behavioral therapy to supportive listening for adjustment to multiple sclerosis

Background

Multiple Sclerosis (MS) is an incurable, chronic, potentially progressive and unpredictable disease of the central nervous system. The disease produces a range of unpleasant and debilitating symptoms, which can have a profound impact including disrupting activities of daily living, employment, income, relationships, social and leisure activities, and life goals. Adjusting to the illness is therefore particularly challenging. This trial tests the effectiveness of a Cognitive Behavioural intervention compared to Supportive Listening to assist adjustment in the early stages of MS.

Methods/Design

This is a two arm randomized multi-centre parallel group controlled trial. 122 consenting participants who meet eligibility criteria will be randomly allocated to receive either Cognitive Behavioral Therapy or Supportive Listening. Eight one hour sessions of therapy (delivered over a period of 10 weeks) will be delivered by general nurses trained in both treatments. Self-report questionnaire data will be collected at baseline (0 weeks), mid-therapy (week 5 of therapy), post-therapy (15 weeks) and at six months (26 weeks) and twelve months (52 weeks) follow-up. Primary outcomes are distress and MS-related social and role impairment at twelve month follow-up. Analysis will also consider predictors and mechanisms of change during therapy. In-depth interviews to examine participants' experiences of the interventions will be conducted with a purposively sampled sub-set of the trial participants. An economic analysis will also take place.

Discussion

This trial is distinctive in its aims in that it aids adjustment to MS in a broad sense. It is not a treatment specifically for depression. Use of nurses as therapists makes the interventions potentially viable in terms of being rolled out in the NHS. The trial benefits from incorporating patient input in the development and evaluation stages. The trial will provide important information about the efficacy, cost-effectiveness and acceptability of the interventions as well as mechanisms of psychosocial adjustment.

Trial registration

Current Controlled Trials ISRCTN91377356     

Negative density dependence of seed dispersal and seedling recruitment in a Neotropical palm

Negative density dependence (NDD) of recruitment is pervasive in tropical tree species. We tested the hypotheses that seed dispersal is NDD, due to intraspecific competition for dispersers, and that this contributes to NDD of recruitment. We compared dispersal in the palm Attalea butyracea across a wide range of population density on Barro Colorado Island in Panama and assessed its consequences for seed distributions. We found that frugivore visitation, seed removal and dispersal distance all declined with population density of A. butyracea, demonstrating NDD of seed dispersal due to competition for dispersers. Furthermore, as population density increased, the distances of seeds from the nearest adult decreased, conspecific seed crowding increased and seedling recruitment success decreased, all patterns expected under poorer dispersal. Unexpectedly, however, our analyses showed that NDD of dispersal did not contribute substantially to these changes in the quality of the seed distribution; patterns with population density were dominated by effects due solely to increasing adult and seed density.