Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

The chromosome 16q region associated with ankylosing spondylitis includes the candidate gene tumour necrosis factor receptor type 1-associated death domain (TRADD)

Objective: To replicate and refine the reported association of ankylosing spondylitis (AS) with two nonsynonymous single nucleotide polymorphisms (nsSNPs) on chromosome 16q22.1. Methods: Firstly, 730 independent UK patients with AS were genotyped for rs9939768 and rs6979 and allele frequencies were compared with 2879 previously typed historic disease controls. Secondly, the two data sets were combined in meta-analyses. Finally, 5 tagging SNPs, located between rs9939768 and rs6979, were analysed in 1604 cases and 1020 controls. Results: The association of rs6979 with AS was replicated, p=0.03, OR=1.14 (95% CI 1.01 to 1.28), and a trend for association with rs9939768 detected, p=0.06, OR=1.25 (95% CI 0.99 to 1.57). Meta-analyses revealed association of both SNPs with AS, p=0.0008, OR=1.31 (95% CI 1.12 to 1.54) and p=0.0009, OR=1.15 (95% CI 1.06 to 1.23) for rs9939768 and rs6979, respectively. New associations with rs9033 and rs868213 (p=0.00002, OR=1.23 (95% CI 1.12 to 1.36) and p=0.00002 OR=1.45 (95% CI 1.22 to 1.72), respectively, were identified. Conclusions: The region on chromosome 16 that has been replicated in the present work is interesting as the highly plausible candidate gene, tumour necrosis factor receptor type 1 (TNFR1)-associated death domain (TRADD), is located between rs9033 and rs868213. It will require additional work to identify the primary genetic association(s) with AS.

The effect of HLA-DR on susceptibility to rheumatoid arthritis is influenced by the associated lymphotoxin α-tumor necrosis factor haplotype

Objective. HLA-DRB1, a major genetic determinant of susceptibility to rheumatoid arthritis (RA), is located within 1,000 kb of the gene encoding tumor necrosis factor (TNF). Because certain HLA-DRB1*04 subtypes increase susceptibility to RA, investigation of the role of the TNF gene is complicated by linkage disequilibrium (LD) between TNF and DRB1 alleles. By adequately controlling for this LD, we aimed to investigate the presence of additional major histocompatibility complex (MHC) susceptibility genes. Methods. We identified 274 HLA-DRB1*04-positive cases of RA and 271 HLA-DRB1*04-positive population controls. Each subject was typed for 6 single-nucleotide polymorphisms within a 4.5-kb region encompassing TNF and lymphotoxin a (LTA). LTA-TNF haplotypes in these unrelated individuals were determined using a combination of family data and the PHASE software program. Results. Significant differences in LTA-TNF haplotype frequencies were observed between different subtypes of HLA-DRB1*04. The LTA-TNF haplotypes observed were very restricted, with only 4 haplotypes constituting 81% of all haplotypes present. Among individuals carrying DRB1*0401, the LTA-TNF 2 haplotype was significantly underrepresented in cases compared with controls (odds ratio 0.5 [95% confidence interval 0.3-0.8], P = 0.007), while in those with DRB1*0404, the opposite effect was observed (P = 0.007). Conclusion. These findings suggest that the MHC contains genetic elements outside the LTA-TNF region that modify the effect of HLA-DRB1 on susceptibility to RA.

Is there a higher genetic load of susceptibility loci in familial ankylosing spondylitis?

Objective Several genetic risk variants for ankylosing spondylitis (AS) have been identified in genome-wide association studies. Our objective was to examine whether familial AS cases have a higher genetic load of these susceptibility variants. Methods Overall, 502 AS patients were examined, consisting of 312 patients who had first-degree relatives (FDRs) with AS (familial) and 190 patients who had no FDRs with AS or spondylarthritis (sporadic). All patients and affected FDRs fulfilled the modified New York criteria for AS. The patients were recruited from 2 US cohorts (the North American Spondylitis Consortium and the Prospective Study of Outcomes in Ankylosing Spondylitis) and from the UK-Oxford cohort. The frequencies of AS susceptibility loci in IL-23R, IL1R2, ANTXR2, ERAP-1, 2 intergenic regions on chromosomes 2p15 and 21q22, and HLA-B27 status as determined by the tag single-nucleotide polymorphism (SNP) rs4349859 were compared between familial and sporadic cases of AS. Association between SNPs and multiplex status was assessed by logistic regression controlling for sibship size. Results HLA-B27 was significantly more prevalent in familial than sporadic cases of AS (odds ratio 4.44 [95% confidence interval 2.06, 9.55], P = 0.0001). Furthermore, the AS risk allele at chromosome 21q22 intergenic region showed a trend toward higher frequency in the multiplex cases (P = 0.08). The frequency of the other AS risk variants did not differ significantly between familial and sporadic cases, either individually or combined. Conclusion HLA-B27 is more prevalent in familial than sporadic cases of AS, demonstrating higher familial aggregation of AS in patients with HLA-B27 positivity. The frequency of the recently described non-major histocompatibility complex susceptibility loci is not markedly different between the sporadic and familial cases of AS.

Evidence of genetic association between TNFRSF1A encoding the p55 tumour necrosis factor receptor, and ankylosing spondylitis in UK Caucasians

Objectives: To replicate the possible genetic association between ankylosing spondylitis (AS) and TNFRSF1A. Methods: TNFRSF1A was re-sequenced in 48 individuals with AS to identify novel polymorphisms. Nine single nucleotide polymorphisms (SNPs) in TNFRSF1A and 5 SNPs in the neighbouring gene SCNN1A were genotyped in 1604 UK Caucasian individuals with AS and 1019 matched controls. An extended study was implemented using additional genotype data on 8 of these SNPs from 1400 historical controls from the 1958 British Birth Cohort. A meta-analysis of previously published results was also undertaken. Results: One novel variant in intron 6 was identified but no new coding variants. No definite associations were seen in the initial study but in the extended study there were weak associations with rs4149576 (p=0.04) and rs4149577 (p=0.007). In the metaanalysis consistent, somewhat stronger associations were seen with rs4149577 (p=0.002) and rs4149578 (p=0.006). Conclusions: These studies confirm the weak genetic associations between AS and TNFRSF1A. In view of the previously reported associations of TNFRSF1A with AS, in Caucasians and Chinese, and the biological plausibility of this candidate gene, replication of this finding in well powered studies is clearly indicated.

Online hidden Markov model parameter estimation and minimax robust quickest change detection in uncertain stochastic processes

Stochastic (or random) processes are inherent to numerous fields of human endeavour including engineering, science, and business and finance. This thesis presents multiple novel methods for quickly detecting and estimating uncertainties in several important classes of stochastic processes. The significance of these novel methods is demonstrated by employing them to detect aircraft manoeuvres in video signals in the important application of autonomous mid-air collision avoidance.

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

Stochastic dynamics of interacting haematopoietic stem cell niche lineages

Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

One practical algorithm for both stochastic and adversarial bandits

We present an algorithm for multiarmed bandits that achieves almost optimal performance in both stochastic and adversarial regimes without prior knowledge about the nature of the environment. Our algorithm is based on augmentation of the EXP3 algorithm with a new control lever in the form of exploration parameters that are tailored individually for each arm. The algorithm simultaneously applies the “old” control lever, the learning rate, to control the regret in the adversarial regime and the new control lever to detect and exploit gaps between the arm losses. This secures problem-dependent “logarithmic” regret when gaps are present without compromising on the worst-case performance guarantee in the adversarial regime. We show that the algorithm can exploit both the usual expected gaps between the arm losses in the stochastic regime and deterministic gaps between the arm losses in the adversarial regime. The algorithm retains “logarithmic” regret guarantee in the stochastic regime even when some observations are contaminated by an adversary, as long as on average the contamination does not reduce the gap by more than a half. Our results for the stochastic regime are supported by experimental validation.

Measuring load of phosphate in the environment by passive sampling techniques: An introduction

Phosphorus has a number of indispensable biochemical roles, but its natural deposition and the low solubility of phosphates as well as their rapid transformation to insoluble forms make the element commonly the growth-limiting nutrient, particularly in aquatic ecosystems. Famously, phosphorus that reaches water bodies is commonly the main cause of eutrophication. This undesirable process can severely affect many aquatic biotas in the world. More management practices are proposed but long-term monitoring of phosphorus level is necessary to ensure that the eutrophication won't occur. Passive sampling techniques, which have been developed over the last decades, could provide several advantages to the conventional sampling methods including simpler sampling devices, more cost-effective sampling campaign, providing flow proportional load as well as representative average of concentrations of phosphorus in the environment. Although some types of passive samplers are commercially available, their uses are still scarcely reported in the literature. In Japan, there is limited application of passive sampling technique to monitor phosphorus even in the field of agricultural environment. This paper aims to introduce the relatively new P-sampling techniques and their potential to use in environmental monitoring studies.

Loading compliance of static load bearing exercises performed by transfemoral amputees fitted with an osseointegrated implant

Background To date bone-anchored prostheses are used to alleviate the concerns caused by socket suspended prostheses and to improve the quality of life of transfemoral amputees (TFA). Currently, two implants are commercially available (i.e., OPRA (Integrum AB, Sweden), ILP (Orthodynamics GmbH, Germany)). [1-17]The success of the OPRA technique is codetermined by the rehabilitation program. TFA fitted with an osseointegrated implant perform progressive mechanical loading (i.e. static load bearing exercises (LBE)) to facilitate bone remodelling around the implant.[18, 19] Aim This study investigated the trustworthiness of monitoring the load prescribed (LP) during experimental static LBEs using the vertical force provided by a mechanical bathroom scale that is considered a surrogate of the actual load applied. Method Eleven unilateral TFAs fitted with an OPRA implant performed five trials in four loading conditions. The forces and moments on the three axes of the implant were measured directly with an instrumented pylon including a six-channel transducer. The “axial” and “vectorial” comparisons corresponding to the difference between the force applied on the long axis of the fixation and LP as well as the resultant of the three components of the load applied and LP, respectively were analysed Results For each loading condition, Wilcoxon One-Sample Signed Rank Tests were used to investigate if significant differences (p<0.05) could be demonstrated between the force applied on the long axis and LP, and between the resultant of the force and LP. The results demonstrated that the raw axial and vectorial differences were significantly different from zero in all conditions (p<0.05), except for the vectorial difference for the 40 kg loading condition (p=0.182). The raw axial difference was negative for all the participants in every loading condition, except for TFA03 in the 10 kg condition (11.17 N). Discussion & Conclusion This study showed a significant lack of axial compliance. The load applied on the long axis was significantly smaller than LP in every loading condition. This led to a systematic underloading of the long axis of the implant during the proposed experimental LBE. Monitoring the vertical force might be only partially reflective of the actual load applied, particularly on the long axis of the implant.

Identification of IL6R and chromosome 11q13.5 as risk loci for asthma

We aimed to identify novel genetic variants affecting asthma risk, since these might provide novel insights into molecular mechanisms underlying the disease. We did a genome-wide association study (GWAS) in 2669 physician-diagnosed asthmatics and 4528 controls from Australia. Seven loci were prioritised for replication after combining our results with those from the GABRIEL consortium (n=26 475), and these were tested in an additional 25 358 independent samples from four in-silico cohorts. Quantitative multi-marker scores of genetic load were constructed on the basis of results from the GABRIEL study and tested for association with asthma in our Australian GWAS dataset. Two loci were confirmed to associate with asthma risk in the replication cohorts and reached genome-wide significance in the combined analysis of all available studies (n=57 800): rs4129267 (OR 1·09, combined p= 2·4×10-8) in the interleukin-6 receptor (IL6R) gene and rs7130588 (OR 1·09, p=1·8×10-8) on chromosome 11q13.5 near the leucine-rich repeat containing 32 gene (LRRC32, also known as GARP). The 11q13.5 locus was significantly associated with atopic status among asthmatics (OR 1·33, p=7×10-4), suggesting that it is a risk factor for allergic but not non-allergic asthma. Multi-marker association results are consistent with a highly polygenic contribution to asthma risk, including loci with weak effects that might be shared with other immune-related diseases, such as NDFIP1, HLA-B, LPP, and BACH2. The IL6R association further supports the hypothesis that cytokine signalling dysregulation affects asthma risk, and raises the possibility that an IL6R antagonist (tocilizumab) may be effective to treat the disease, perhaps in a genotype-dependent manner. Results for the 11q13.5 locus suggest that it directly increases the risk of allergic sensitisation which, in turn, increases the risk of subsequent development of asthma. Larger or more functionally focused studies are needed to characterise the many loci with modest effects that remain to be identified for asthma. National Health and Medical Research Council of Australia. A full list of funding sources is provided in the webappendix. © 2011 Elsevier Ltd.

Australian data do not support current pharmaceutical benefits scheme criteria for use of tumour necrosis factor-α inhibitors in ankylosing spondylitis

On the basis of local data, we write in support of the conclusions of Smith and Ahern that current Pharmaceu- tical Benefits Scheme (PBS) criteria for tumour necrosis factor (TNF)-a inhibitors in ankylosing spondylitis (AS) are not evidence-based. 1 As a prerequisite to the appropriate use of biological therapy in AS, three aspects of the disease need to be defined: (i) diagnosis, (ii) activity and (iii) therapeutic failure (Table 1)....

The effect of transforming growth factor β1 gene polymorphisms in ankylosing spondylitis

Objectives. To determine whether genetic polymorphisms in or near the transforming growth factor β1 (TGFB1) locus were associated d with susceptibility to or severity of ankylosing spondylitis (AS). Methods. Five intragenic single-nucleotide polymorphisms (SNP) and three microsatellite markers flanking the TGFB1 locus were genotyped. Seven hundred and sixty-two individuals from 184 multiplex families were genotyped for the microsatellite markers and two of the promoter SNPs. One thousand and two individuals from 212 English and 170 Finnish families with AS were genotyped for all five intragenic SNPs. A structured questionnaire was used to assess the age of symptom onset, disease duration and disease severity scores, including the BASDAI (Bath Ankylosing Spondylitis Disease Activity Index) and BASFI (Bath Ankylosing Spondylitis Functional Index). Results. A weak association was noted between the rare TGFB1 + 1632 T allele and AS in the Finnish population (P = 0.04) and in the combined data set (P = 0.03). No association was noted between any other SNPs or SNP haplotype and AS, even among those families with positive non-parametric linkage scores. The TGFB1 +1632 polymorphism was also associated with a younger age of symptom onset (English population, allele 2 associated with age of onset greater by 4.2 yr, P = 0.05; combined data set, allele 2 associated with age of onset greater by 3.2 yr, P = 0.02). A haplotype of coding region SNPs (TGFB1 +869/ +915+1632 alleles 2/1/2) was associated with age of symptom onset in both the English parent-case trios and the combined data set (English data set, haplotype 2/1/2 associated with age of onset greater by 4.9 yr, P = 0.03; combined data set, haplotype 2/1/2 associated with greater age of onset by 4.2 yr, P = 0.006). Weak linkage with AS susceptibility was noted and the peak LOD score was 1.3 at distance 2 cM centromeric to the TGFB1 gene. No other linkage or association was found between quantitative traits and the markers. Conclusion. This study suggests that the polymorphisms within the TGFB1 gene play at most a small role in AS and that other genes encoded on chromosome 19 are involved in susceptibility to the disease.