Performance of M06, M06-2X, and M06-HF Density Functionals for Conformationally Flexible Anionic Clusters: M06 Functionals Perform Better than B3LYP for a Model System with Dispersion and Ionic Hydrogen-Bonding Interactions

We present a comparative assessment of the performance of the M06 suite of density functionals (M06, M06-2X, and M06-HF) against an MP2 benchmark for calculating the relative energies and geometric structures of the Cl^–·arginine and Br^–·arginine halide ion–amino acid clusters. Additional results are presented for the popular B3LYP density functional. The Cl^–·arginine and Br^–·arginine complexes are important prototypes for the phenomenon of anion-induced zwitterion formation. Results are presented for the canonical (noncharge separated) and zwitterionic (charge separated) tautomers of the clusters, as well as the numerous conformational isomers of the clusters. We find that all of the M06 functions perform well in terms of predicting the general trends in the conformer relative energies and identifying the global minimum conformer. This is in contrast to the B3LYP functional, which performed significantly less well for the canonical tautomers of the clusters where dispersion interactions contribute more significantly to the conformer energetics. We find that the M06 functional gave the lowest mean unsigned error for the relative energies of the canonical conformers (2.10 and 2.36 kJ/mol for Br^–·arginine and Cl^–·arginine), while M06-2X gave the lowest mean unsigned error for the zwitterionic conformers (0.85 and 1.23 kJ/mol for Br^–·arginine and Cl^–·arginine), thus providing insight into the types of physical systems where each of these functionals should perform best

Long-term impact of vaccination on microfilarial load in the absence of ivermectin treatment.

<p>The green <b>(A)</b>, blue <b>(B)</b> and red <b>(C)</b> lines correspond to, respectively, a pre-control endemicity of 40%, 60%, and 80% microfilarial prevalence. The solid lines indicate the pre-control contribution of each group to the overall microfilarial load, which is the product of multiplying the microfilarial age- and sex specific profiles (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3B</a>) times the proportion of hosts in each demographic stratum, i.e. the proportion of hosts in each age and sex group (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2</a>). The sum total of the age- and sex-specific contributions yields the overall mean microfilarial load. The dotted lines correspond to the values after 15 years of vaccination. The shaded area illustrates the reduction in microfilarial load in those aged less than 20 years. Modelling assumptions are as follows: a vaccination programme targeting initially 1–5 year olds with continuous vaccination of one year olds after the first year of the programme; an initial prophylactic efficacy against the development of incoming worms of 50%; an initial therapeutic efficacy against skin microfilarial load of 90%; a mean duration of protective and therapeutic effects of 20 years (rate of decay = 0.05 per year) and an 80% coverage of vaccination.</p

EPIONCHO’s underlying age- and sex-specific exposure and baseline microfilarial load profiles.

<p><b>(A)</b> The age- and sex-specific exposure profiles to blackfly bites calibrated to reproduce the observed pre-control age-dependent microfilarial loads. <b>(B)</b> The age- and sex-specific microfilarial loads in African savannah settings of northern Cameroon [<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.ref032" target="_blank">32</a>]. Note that the fitting was performed using the individual data, not the binned data shown in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2B</a>. Note also that the legend on panel <b>(B)</b> applies to both panels <b>(A)</b> and <b>(B)</b>.</p

Additional file 2: of Required duration of mass ivermectin treatment for onchocerciasis elimination in Africa: a comparative modelling analysis

A zip-file, which includes the computer simulation program itself (with the JAVA program code embedded in it), batch files used to run the model, PDF documentation of the XML input, and example input and output files. Instructions on how to run the model are provided in Additional file 1 (ONCHOSIM simulation program.zip). (DOCX 15 kb

Model-predicted proportion of bites taken on each age group.

<p>The product of multiplying the age-and sex-specific exposure profiles to blackfly bites (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3A</a>) times the proportion of hosts in each age and sex group according to the demographic characteristics of the population (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2</a>).</p

Additional file 1: of Required duration of mass ivermectin treatment for onchocerciasis elimination in Africa: a comparative modelling analysis

A PDF file, providing a formal mathematical description of the model, instructions on installing and running the model, a complete overview of the probability distributions, functional relationships, and parameter values that are used for this study, and annotated input and output files (Documentation ONCHOSIM v2.58Ap9.pdf). (PDF 1360 kb

Endemicity categories as defined by microfilarial prevalence.

<p>Values adapted from [<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.ref072" target="_blank">72</a>].</p><p>Endemicity categories as defined by microfilarial prevalence.</p

Long-term impact of vaccination on onchocerciasis annual transmission potential and microfilarial load in the absence of ivermectin treatment under different assumptions of initial vaccine efficacy.

<p><b>A:</b> Model assumes an initial vaccine efficacy against the development of incoming worms of 50% and against skin microfilarial load of 90%. <b>B:</b> Model assumes a higher initial vaccine efficacy against the development of incoming worms of 70% and against skin microfilarial load of 95%. Results assume mean duration of prophylactic and therapeutic effects of 20 years (rate of decay = 0.05 per year) and an 80% coverage of vaccination. Annual transmission potential (ATP): the average number of L3 larvae potentially received per person per year.</p><p>Long-term impact of vaccination on onchocerciasis annual transmission potential and microfilarial load in the absence of ivermectin treatment under different assumptions of initial vaccine efficacy.</p

Long-term impact of vaccination on the overall contribution to onwards transmission by age groups in the host population in absence of ivermectin treatment.

<p>The green <b>(A)</b>, blue <b>(B)</b> and red <b>(C)</b> lines correspond to, respectively, a pre-control endemicity of 40%, 60%, and 80% microfilarial prevalence. The solid line indicates the baseline age-specific contribution to the annual transmission potential (ATP, no. L3/person/year). This is obtained as the product of multiplying the following factors: age- and sex-specific microfilarial loads; proportion of the population within each corresponding demographic stratum; proportion of blackfly bites taken on each demographic stratum (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3A</a>); annual biting rate; and the constraining (negative) density-dependent processes, acting on ingested microfilariae within the blackfly vector and on vector survival, that determine L3 output. The dotted lines correspond to the age-specific contributions to the ATP after 15 years of vaccination. The shaded area illustrates the reduction in contribution to transmission by those aged less than 20 years. Modelling assumptions on the initial vaccine efficacy and vaccine duration are as in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g004" target="_blank">Fig 4</a>. The increasing contribution to ATP by older age groups is mainly due to women for whom microfilarial load and exposure to blackfly bites increases with age (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3</a>).</p

Sensitivity of the long-term reduction in microfilarial load in individuals under 20 years of age to the assumed rate of decay of vaccine efficacy.

<p>The mean duration of vaccine prophylactic (against incoming L3 larvae) and therapeutic (against microfilariae) activity is 1/the rate of decay (i.e. 5, 10, 20 and 50 years). We illustrate with a pre-control endemicity of 40% microfilarial prevalence. The solid line indicates the baseline (pre-control) contribution of each group to the overall microfilarial load, which is the product of multiplying the age- and sex-specific microfilarial loads (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3B</a>) times the proportion of the population within each corresponding demographic stratum (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2</a>). The dotted lines correspond to these contributions after 15 years of vaccination for decreasing waning rates of the prophylactic and therapeutic effects of the vaccine; the lower the rate, the greater the reduction in microfilarial loads achieved by the vaccination programme. Other assumptions as in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g004" target="_blank">Fig 4</a>.</p