Computing the partition function for kinetically trapped RNA secondary structures

An RNA secondary structure is locally optimal if there is no lower energy structure that can be obtained by the addition or removal of a single base pair, where energy is defined according to the widely accepted Turner nearest neighbor model. Locally optimal structures form kinetic traps, since any evolution away from a locally optimal structure must involve energetically unfavorable folding steps. Here, we present a novel, efficient algorithm to compute the partition function over all locally optimal secondary structures of a given RNA sequence. Our software, RNAlocopt runs in O(n3) time and O(n2) space. Additionally, RNAlocopt samples a user-specified number of structures from the Boltzmann subensemble of all locally optimal structures. We apply RNAlocopt to show that (1) the number of locally optimal structures is far fewer than the total number of structures--indeed, the number of locally optimal structures approximately equal to the square root of the number of all structures, (2) the structural diversity of this subensemble may be either similar to or quite different from the structural diversity of the entire Boltzmann ensemble, a situation that depends on the type of input RNA, (3) the (modified) maximum expected accuracy structure, computed by taking into account base pairing frequencies of locally optimal structures, is a more accurate prediction of the native structure than other current thermodynamics-based methods. The software RNAlocopt constitutes a technical breakthrough in our study of the folding landscape for RNA secondary structures. For the first time, locally optimal structures (kinetic traps in the Turner energy model) can be rapidly generated for long RNA sequences, previously impossible with methods that involved exhaustive enumeration. Use of locally optimal structure leads to state-of-the-art secondary structure prediction, as benchmarked against methods involving the computation of minimum free energy and of maximum expected accuracy. Web server and source code available at http://bioinformatics.bc.edu/clotelab/RNAlocopt/.     

A model of optimal voluntary muscular control

Summary In the absence of detailed knowledge of how the CNS controls a muscle through its motor fibers, a reasonable hypothesis is that of optimal control. This hypothesis is studied using a simplified mathematical model of a single muscle, based on A. V. Hill's equations, with series elastic element omitted, and with the motor signal represented by a single input variable.Two cost functions were used. The first was total energy expended by the muscle (work plus heat). If the load is a constant force, with no inertia, Hill's optimal velocity of shortening results. If the load includes a mass, analysis by optimal control theory shows that the motor signal to the muscle consists of three phases: (1) maximal stimulation to accelerate the mass to the optimal velocity as quickly as possible, (2) an intermediate level of stimulation to hold the velocity at its optimal value, once reached, and (3) zero stimulation, to permit the mass to slow down, as quickly as possible, to zero velocity at the specified distance shortened. If the latter distance is too small, or the mass too large, the optimal velocity is not reached, and phase (2) is absent. For lengthening, there is no optimal velocity; there are only two phases, zero stimulation followed by maximal stimulation.The second cost function was total time. The optimal control for shortening consists of only phases (1) and (3) above, and is identical to the minimal energy control whenever phase (2) is absent from the latter.Generalization of this model to include viscous loads and a series elastic element are discussed.     

Recovery of the torque-velocity relationship after short exhausting cycling exercise

The effects of fatigue upon the torque-velocity (T-omega) relationship in cycling were studied in 11 subjects. Fatigue was induced by short exhausting exercise, on a cycle ergometer, consisting of 4 all-out sprints without recovery. The linear (T-omega) relationship was determined during each all-out sprint, before, during and after the exhausting exercise. The kinetics of the T-omega relationship had permitted the study of the recovery of optimal torque, optimal velocity and their corresponding maximal power outputs (Pmax), 30 s or 1 min after the short exhausting exercise. Fatigue induced a parallel shift to the left of the T-omega relationship which was partly reversed by a parallel shift to the right during recovery. After 30 s recovery optimal velocity, optimal torque and Pmax were slightly lower than the corresponding values before the exhausting exercise; after 1-min optimal velocity and optimal torque had recovered 99% and 97% of their initial values. These mechanical data suggested that the causes of exhaustion were processes that allowed fast recovery of both optimal velocity and optimal torque.     

On optimal Bayesian classification and risk estimation under multiple classes

A recently proposed optimal Bayesian classification paradigm addresses optimal error rate analysis for small-sample discrimination, including optimal classifiers, optimal error estimators, and error estimation analysis tools with respect to the probability of misclassification under binary classes. Here, we address multi-class problems and optimal expected risk with respect to a given risk function, which are common settings in bioinformatics. We present Bayesian risk estimators (BRE) under arbitrary classifiers, the mean-square error (MSE) of arbitrary risk estimators under arbitrary classifiers, and optimal Bayesian risk classifiers (OBRC). We provide analytic expressions for these tools under several discrete and Gaussian models and present a new methodology to approximate the BRE and MSE when analytic expressions are not available. Of particular note, we present analytic forms for the MSE under Gaussian models with homoscedastic covariances, which are new even in binary classification.     

Individual variation in the ability of Columbian ground squirrels to select an optimal diet

Summary Columbian ground squirrels (Spermophilus columbianus) were examined for ability to select a diet that maximizes daily energy intake (optimal diet) under free-living field conditions. The optimal diet for each squirrel was determined given constraints (e.g. body size, feeding time) on individual foraging behavior. Most squirrels (63%) consumed a diet not significantly different from one that would maximize their daily energy intake. The remainder (37%) approached an energy maximized diet but appeared to make some incorrect foraging decisions. Both males and females appeared to approach energy maximized diets. An individual's deviation from its optimal diet is relatively constant within a season and not significantly affected by immediate environmental influences such as food abundance, thermal conditions and social environment. The energy cost of deviating from an optimal diet may be large enough to affect fitness. These results suggest that the ability to select an optimal diet can be viewed as a behavioral trait that might be subject to natural selection.     

Why "suboptimal" is optimal: Jensen's inequality and ectotherm thermal preferences

Body temperature (T(b)) profoundly affects the fitness of ectotherms. Many ectotherms use behavior to control T(b) within narrow levels. These temperatures are assumed to be optimal and therefore to match body temperatures (Trmax) that maximize fitness (r). We develop an optimality model and find that optimal body temperature (T(o)) should not be centered at Trmax but shifted to a lower temperature. This finding seems paradoxical but results from two considerations relating to Jensen's inequality, which deals with how variance and skew influence integrals of nonlinear functions. First, ectotherms are not perfect thermoregulators and so experience a range of T(b). Second, temperature-fitness curves are asymmetric, such that a T(b) higher than Trmax depresses fitness more than will a T(b) displaced an equivalent amount below Trmax. Our model makes several predictions. The magnitude of the optimal shift (Trmax - To) should increase with the degree of asymmetry of temperature-fitness curves and with T(b) variance. Deviations should be relatively large for thermal specialists but insensitive to whether fitness increases with Trmax ("hotter is better"). Asymmetric (left-skewed) T(b) distributions reduce the magnitude of the optimal shift but do not eliminate it. Comparative data (insects, lizards) support key predictions. Thus, "suboptimal" is optimal.     

Place prioritization for biodiversity conservation using probabilistic surrogate distribution data

We analyse optimal and heuristic place prioritization algorithms for biodiversity conservation area network design which can use probabilistic data on the distribution of surrogates for biodiversity. We show how an Expected Surrogate Set Covering Problem (ESSCP) and a Maximal Expected Surrogate Covering Problem (MESCP) can be linearized for computationally efficient solution. For the ESSCP, we study the performance of two optimization software packages (XPRESS and CPLEX) and five heuristic algorithms based on traditional measures of complementarity and rarity as well as the Shannon and Simpson indices of α‐diversity which are being used in this context for the first time. On small artificial data sets the optimal place prioritization algorithms often produced more economical solutions than the heuristic algorithms, though not always ones guaranteed to be optimal. However, with large data sets, the optimal algorithms often required long computation times and produced no better results than heuristic ones. Thus there is generally little reason to prefer optimal to heuristic algorithms with probabilistic data sets.     

Some effects of energy costs on foraging strategies

We consider the effect of including energy costs on the optimal strategy for animals exploiting a depleting food resource. In the context of central place foraging this leads to the problem of what load size should be brought back to the central place. Two strategies are discussed: (i) maximize gross rate of energy delivery and (ii) maximize net rate of energy delivery. The optimal load size (or optimal patch time) for net maximizers is not always larger than for gross maximizers, as has been claimed. Instead, the difference in optimal load size has the same sign as the difference between metabolic rates of travelling and foraging. We point out that the influence of costs has not always been correctly incorporated in experimental tests of the theory.     

A model for seed size variation among plants

Summary I developed a model for seed size variation among plants assuming that the pollen captured per flower depends on both the allocation to pollen capture mechanisms per flower and the number of flowers on each plant. I showed that the optimal seed size increases with (1) the total resource allocation to reproduction, (2) decreasing outcross pollen availability, (3) decreasing probability of seedling establishment and (4) decreasing selfing rate. However, optimal seed size does not depend on the total resource allocation if the total number of pollen grains captured by a plant increases linearly with its flower number. In addition, the optimal seed size is not always positively correlated with the optimal resource allocation to pollen capture mechanisms per flower. I discussed implications of the results for seasonal decline in seed size and seed size variations among populations, such as alutitudinal variation.     

Contrasting performances of generalist and specialist Myzus persicae (Hemiptera: Aphididae) reveal differential prevalence of maternal effects after host transfer

Transgenerational maternal effects on performance (rm) after host transfer were evaluated in the generalist aphid Myzus persicae s.s., and in its subspecies specialized on tobacco, M. persicae nicotianae Blackman. We tested whether the performance of these taxa, when reared separately on optimal and suboptimal hosts (as sources of different maternal background) and then transferred to optimal hosts, experienced variations along four successive generations. Additionally, to compare the tolerance of both taxa to stress following host transfers, developmental instability (fluctuating asymmetry and body abnormalities) along the four generations was assessed. Taxon, rearing host, and generation affected the performance after host transfer. In the generalist, there was a significant improvement of rm along generations when transferred from suboptimal to optimal host and a significant decrease when transferred from optimal to optimal host; in the specialist, no increase or decrease occurred in any host transfer treatment. Transfer from suboptimal to optimal hosts caused higher losses of remaining replicates along generations than transfers from optimal to optimal hosts, and the specialist showed higher losses than the generalist. The only significant effect detected in comparisons involving fluctuating asymmetry values was that of taxon on length of siphunculi. Frequency of body abnormalities was not affected by treatments. Collectively, these results show a transgenerational weakening of maternal effects in the generalist but not in the specialist aphid, and suggest that rearing the latter in a suboptimal host causes not easily reversible changes that further give rise to constraints in performance.     

Application of radiography of computed tomography in non-small cell lung cancer using prognosis model

ObjectiveStudying the diagnostic value of CT imaging in non-small cell lung cancer (NSCLC), and establishing a prognosis model combined with clinical characteristics is the objective, so as to provide a reference for the survival prediction of NSCLC patients.MethodCT scan data of NSCLC 200 patients were taken as the research object. Through image segmentation, the radiology features of CT images were extracted. The reliability and performance of the prognosis model based on the optimal feature number of specific algorithm and the prognosis model based on the global optimal feature number were compared.Results30-RELF-NB (30 optimal features, RELF feature selection algorithm and NB classifier) has the highest accuracy and AUC (area under the subject characteristic curve) in the prognosis model based on the optimal features of specific algorithm. Among the prognosis models based on global optimal features, 25-NB (25 global optimal features, naive Bayes classification algorithm classifier) has the highest accuracy and AUC. Compared with the prediction model based on feature training of specific feature selection algorithm, the overall performance and stability of the prediction model based on global optimal feature are higher.ConclusionThe prognosis model based on the global optimal feature established in this paper has good reliability and performance, and can be applied to the CT radiology of NSCLC.     

Analysis of internal loops within the RNA secondary structure in almost quadratic time

MOTIVATION: Evaluating all possible internal loops is one of the key steps in predicting the optimal secondary structure of an RNA molecule. The best algorithm available runs in time O(L(3)), L is the length of the RNA. RESULTS: We propose a new algorithm for evaluating internal loops, its run-time is O(M(*)log(2)L), M < L(2) is a number of possible nucleotide pairings. We created a software tool Afold which predicts the optimal secondary structure of RNA molecules of lengths up to 28 000 nt, using a computer with 2 Gb RAM. We also propose algorithms constructing sets of conditionally optimal multi-branch loop free (MLF) structures, e.g. the set that for every possible pairing (x, y) contains an optimal MLF structure in which nucleotides x and y form a pair. All the algorithms have run-time O(M(*)log(2)L).     

Optimal age and size at maturity in annuals and perennials with determinate growth

Summary A model predicting optimal age and size at maturity is presented, exploring the conflict between growth and energy allocation to reproduction. According to the model, the factors promoting delayed maturity and large adult body size are as follows: (1) high rate of somatic growth, (2) high percentage increase in reproductive rate with body size increase, (3) long life expectancy at maturity for annuals or large number of expected productive days (when either growth or reproduction is possible) for perennials with growth ceasing at maturity, (4) life expectancy increasing with body size. All these factors are combined in the mathematical formula predicting optimal age and size at maturity, which allows for quantitative predictions. The optimal schedule of growth and reproduction may be achieved by natural selection, developmental plasticity, or when one species replaces another. Sexual size dimorphism is also discussed, resulting from different optimal age at maturity for either sex.     

Adaptation to spatially heterogeneous modifying and adaptive environments

The development of an individual's phenotype is influenced by environmental factors (the modifying environment) which may differ from those factors (the adaptive environment) that decide on the adaptational value of the developed phenotype. The shapes of adaptationally optimal norms of reaction are therefore essentially determined by associations between these two environmental components together with the degree of adaptational sensitivity of the developed phenotypes. Two complementary aspects of optimality are accounted for: (a) environments can be optimal for a given norm of reaction and (b) norms of reaction can be optimal for a given environment. The results are obtained for random distribution of genotypes over environmental conditions and under the physiologically reasonable premise that fitness is a function of the costs of modification and adaptation. It turned out that the associations of adaptive and modifying environments are the primary sources of adaptational optimization. More specifically, it is shown that (i) independence between the two environmental components constitutes an adaptationally optimal environment only for norms of reaction in which all phenotypes are adaptively insensitive; (ii) if costs of modification do not depend on the environment, and if the two environmental components are not associated, adaptationally optimal norms of reaction can always be realized through phenogenetic invariance; (iii) as a rule, adaptively sensitive phenotypes developed under strong environmental associations necessitate phenogenetic plasticity for the optimal norm of reaction; (iv) a norm of reaction which is adaptationally optimal in its adaptationally optimal environment can always be realized through phenogenetic invariance, if costs of modification do not vary with the environment. These results reveal an important role of patterns of adaptive sensitivity of phenotypes, which may even surpass that of shapes of norms of reaction in adaptational processes.     

Optimal Dynamic Allocation of Conservation Funding Among Priority Regions

The optimal allocation of conservation resources between biodiverse conservation regions has generally been calculated using stochastic dynamic programming, or using myopic heuristics. These solutions are hard to interpret and may not be optimal. To overcome these two limitations, this paper approaches the optimal conservation resource allocation problem using optimal control theory. A solution using Pontryagin’s maximum principle provides novel insight into the general properties of efficient conservation resource allocation strategies, and allows more extensive testing of the performance of myopic heuristics. We confirmed that a proposed heuristic (minimize short-term loss) yields near-optimal results in complex allocation situations, and found that a qualitative allocation feature observed in previous analyses (bang-bang allocation) is a general property of the optimal allocation strategy.     

Framework for online optimization of recombinant protein expression in high-cell-density Escherichia coli cultures using GFP-fusion monitoring

A framework for the online optimization of protein induction using green fluorescent protein (GFP)-monitoring technology was developed for high-cell-density cultivation of Escherichia coli. A simple and unstructured mathematical model was developed that described well the dynamics of cloned chloramphenicol acetyltransferase (CAT) production in E. coli JM105 was developed. A sequential quadratic programming (SQP) optimization algorithm was used to estimate model parameter values and to solve optimal open-loop control problems for piecewise control of inducer feed rates that maximize productivity. The optimal inducer feeding profile for an arabinose induction system was different from that of an isopropyl-beta-D-thiogalactopyranoside (IPTG) induction system. Also, model-based online parameter estimation and online optimization algorithms were developed to determine optimal inducer feeding rates for eventual use of a feedback signal from a GFP fluorescence probe (direct product monitoring with 95-minute time delay). Because the numerical algorithms required minimal processing time, the potential for product-based and model-based online optimal control methodology can be realized.     

Optimal design and efficiency of two-phase case-control studies with error-prone and error-free exposure measures

This paper addresses optimal design and efficiency of two-phase (2P) case-control studies in which the first phase uses an error-prone exposure measure, Z, while the second phase measures true, dichotomous exposure, X, in a subset of subjects. Optimal design of a separate second phase, to be added to a preexisting study, is also investigated. Differential misclassification is assumed throughout. Results are also applicable to 2P cohort studies with error-prone and error-free measures of disease status but error-free exposure measures. While software based on the mean score method of Reilly and Pepe (1995, Biometrika 82, 299--314) can find optimal designs given pilot data, the lack of simple formulae makes it difficult to generalize about efficiency compared to one-phase (1P) studies based on X alone. Here, formulae for the optimal ratios of cases to controls and first- to second-phase sizes, and the optimal second-phase stratified sampling fractions, given a fixed budget, are given. The maximum efficiency of 2P designs compared to a 1P design is deduced and is shown to be bounded from above by a function of the sensitivities and specificities of Z. The efficiency of 'balanced' separate second-phase designs (Breslow and Cain, 1988, Biometrika 75, 11--20)-in which equal numbers of subjects are chosen from each first-phase strata-compared to optimal design is deduced, enabling situations where balanced designs are nearly optimal to be identified.     

Optimal risk management of human alveolar echinococcosis with vermifuge

In this study, we develop a bioeconomic model of human alveolar echinococcosis (HAE) and formulate the optimal strategies for managing the infection risks in humans by applying optimal control theory. The model has the following novel features: (i) the complex transmission cycle of HAE has been tractably incorporated into the framework of optimal control problems and (ii) the volume of vermifuge spreading to manage the risk is considered a control variable. With this model, we first obtain the stability conditions for the transmission dynamics under the condition of constant control. Second, we explicitly introduce a control variable of vermifuge spreading into the analysis by considering the associated control costs. In this optimal control problem, we have successfully derived a set of conditions for a bang-bang control and singular control, which are mainly characterized by the prevalence of infection in voles and foxes and the remaining time of control. The analytical results are demonstrated by numerical analysis and we discuss the effects of the parameter values on the optimal strategy and the transmission cycle. We find that when the prevalence of infection in foxes is low and the prevalence of infection in voles is sufficiently high, the optimal strategy is to expend no effort in vermifuge spreading.     

Partial characterization of the ouabain-insensitive, Na+-stimulated ATPase activity of kidney basal-lateral plasma membranes

The present paper characterizes the Na+-stimulated ATPase activity present in basal-lateral plasma membranes from guinea-pig kidney proximal tubular cells. These characteristics are compared with those of the (Na+ + K+)-stimulated ATPase activity, and they are: (A) Na+-ATPase activity: (1) requires Mg2+; (2) may be activated by mu molar quantities of Ca2+; (3) optimal ratio Mg:ATP = 5:1-2 and Ka for Mg:ATP = 3:0.60 mM; (4) Ka for Na+:8 mM; (5) does not require K+; (6) is only stimulated by Na+ and Li+ (in a lower extent); (7) is similarly stimulated by the Na+ salt of different anions; (8) hydrolyzes only ATP; (9) optimal temperature: 47 degrees C; (10) optimal pH: 6.9; (11) is ouabain insensitive; (12) is totally inhibited by 1.5 mM ethacrynic acid, 2 mM furosemide and 0.75 mM triflocin. (B) (Na+ + K+)-ATPase activity: (1) also requires Mg2+; (2) is inhibited by Ca2+; (3) optimal ratio Mg:ATP = 1.25:1 and Ka for Mg:ATP = 0.50: 0.40 mM; (4) Ka for Na+: 14 mM (data not shown); (5) needs K+ together with Na+; (6) K+ may be substituted by: Rb+ greater than NH+4 greater than Cs+; (7) is anion insensitive; (8) hydrolyzes mostly ATP and to a lesser extent GTP, ITP, UTP, ADP, CTP; (9) optimal temperature: 52 degrees C; (10) optimal pH: 7.2; (11) 100% inhibited by 1 mM ouabain; (12) 63% inhibited by 1.5 mM ethacrynic acid, 10% inhibited by 2 mM furosemide and insensitive to 0.75 mM triflocin.