Application of mathematical optimization methods in microbiology

Mathematical methods of experiment design have so far found little use in the optimization of microbiological processes. The conventional optimization procedure is still the transformation of functional relationship ofn variables into n unidimensional optimizations; furthermore, the Bos-Wilson gradient method is often used. This paper presents a review of methods used in other fields, and their application in microbiological practice. The methods are classified according to whether they require, besides the simple determination of the objective function (direct search methods), also the finding of its first (gradient methods) or second derivative (Newton-Raphson method). A modified Rosenbrock’s method of direot optimum search and the gradient Box-Wilson method were used in parallel for the optimization of yeast growth on methanol. Their comparison showed that Bosenbrock’s method is more suitable for multiparameter systems.     

Multigradient method for optimization of slow biotechnological processes

A new method (named a "jumping spider") is introduced for the optimization of slow biotechnological processes. The more traditional sequential experimentation (i.e., gradient search, simplex, etc.) is not well suited for slow dynamic processes, e.g., plant cell culture and differentiation. Therefore, a more simultaneous approach is proposed. A large number of initial experiments are performed, on the basis of which several of the initial experiments are selected as starting points. A search is then performed simultaneously from several gradient directions and the optimum is estimated by a quadratic approximation. In simulations, the spider generally climbs up the slopes quickly and the final estimator yields good maximum point estimates even on a complex topography. The spider may even approach more than one local maximum point simultaneously. As a model application, the average xylitol conversion rate of Candida guilliermondii was optimized in relation to cultivation volume (oxygen availability) and the concentration of nitrogen and phosphorus in the medium. A threefold increase in xylitol production was obtained with three experimental steps. (c) 1993 John Wiley & Sons, Inc.     

Computer tomography of the brain in Hamilton.

Computer tomography, a new noninvasive, rapid and easily tolerated technique of brain examination, has been evaluated by analysis of 1000 examinations. It is much more sensitive than conventional radiographic techniques and can resolve soft-tissue structures that differ only slightly in density. It also provides direct visualization of the ventricular system. The range of clinical applications is wide; it is especially useful in differentiating intracerebral hemorrhage from infarction, and in demonstrating many brain tumours, particularly supratentorial, though enhancement with a water-soluble contrast medium injected intravenously is often necessary.     

A survey of non-linear optimization techniques

Optimization means the provision of a set of numerical parameter values which will give the best fit of an equation, or series of equations, to a set of data. For simple systems this can be done by differentiating the equations with respect to each parameter in turn, setting the set of partial differential equations to zero, and solving this set of simultaneous equations (as for exwnple in linear regression). In more complicated cases, however, it may be impossible to differentiate the equations, or very difficultly soluble non-linear equations may result. Many numerical optimization techniques to overcome these difficulties have been developed in the least ten years, and this review explains the logical basis of most of them, without going into the detail of computational procedures.The methods fall naturally into two classes - direct search methods, in which only values of the function to be minimized (or maximized) are used - and gradient methods, which also use derivatives of the function. The author considers all the accepted methods in each class, although warning that gradient methods should not be used unless the analytical differentiation of the function to be minimized is possible.If the solution is constrained, that is, certain values of the parameters are regarded as impossible or certain relations between the parameter values must be obeyed, the problem is more difficult. The second part of the review considers methods which have been proposed for the solution of constrained optimization problems.     

Agrobacterium tumefaciens OAH-01产脲酶发酵培养基优化

氨基甲酸乙酯( EC)是大多数发酵制品中的潜在致癌物,而尿素是EC的最主要前体物质之一,因此需要采取相关措施控制发酵制品中尿素的含量。向酒体中添加脲酶具有安全、高效和处理条件温和等优点,是FDA推荐的降低EC 含量的优先方法。微生物是脲酶的主要来源,可利用其实现脲酶的大规模生产。本文以产脲酶根癌农杆菌Agrobacterium tumefaciens OAH-01为研究对象,考察了该菌株的生长曲线和产酶曲线,证明该菌株产脲酶属生长关联型,且能在较短时间内达到最大产酶量,此外还研究了发酵培养基组成对该菌发酵产酶的影响,通过单因素及正交试验优化确定了最佳发酵培养基组成(g/L)：蛋白胨20,酵母粉5,葡萄糖5,FeCl30.54,Na2HPO40.5, KH2 PO40.5,NiSO40.1,起始 pH 7.0。在最适条件下发酵16 h,菌悬液中脲酶酶活可达1.077 U/mL,为优化前的2.4倍。超声破碎后细胞上清中的脲酶活性为0.419 U/mL,为优化前的4.4倍。     

L-缬氨酸生产菌的选育及其发酵培养基的模式识别优化

以黄色短杆菌TV10为出发菌株 ,经紫外线、硫酸二乙酯逐级诱变处理 ,在含磺胺胍 (SG)、α 氨基丁酸 (α AB)、2 噻唑丙氨酸 ( 2 TA)等氨基酸结构类似物平板上定向筛选 ,获得L 缬氨酸高产菌株TV2 30。应用模式识别方法 ,对L 缬氨酸发酵培养基进行优化。以培养基组成构筑模式空间 ,通过主成分分析 (PCA)揭示模式空间的可视优化区域 ,选择优化点并逆推回到高维空间得到最优培养基组成 ,结果该菌株可积累L 缬氨酸 2 6 .38g·L-1,比初始值提高 7.8%。     

Optimization of a culture medium for xylanase production by Bacillus sp. using statistical experimental designs

The concentrations of oat spelt xylan, casein hydrolysate and NH4Cl in the culture medium for production of xylanase from Bacillus sp. I-1018 were optimized by means of response surface methods. The path of steepest ascent was used to approach the optimal region of the medium composition. The optimum composition of the nutrient medium was then easily determined by using a central composite design and was found to be 3.16g/l of xylan, 1.94g/l casein hydrolysate, 0.8g/l of NH4Cl. The xylanase production was increased by 135% when the strain was grown in the optimized medium compared to initial medium.     

Optimization of a culture medium for xylanase production by Bacillus sp. using statistical experimental designs

The concentrations of oat spelt xylan, casein hydrolysate and NH4Cl in the culture medium for production of xylanase from Bacillus sp. I-1018 were optimized by means of response surface methods. The path of steepest ascent was used to approach the optimal region of the medium composition. The optimum composition of the nutrient medium was then easily determined by using a central composite design and was found to be 3.16g/l of xylan, 1.94g/l casein hydrolysate, 0.8g/l of NH4Cl. The xylanase production was increased by 135% when the strain was grown in the optimized medium compared to initial medium.     

Evaluation of isolation methods and culture conditions for rat bone marrow mesenchymal stem cells

Bone marrow mesenchymal stem cells (bMSCs) are multipotent and preferred for cell therapy. However, the content of bMSCs is very low. To propagate a large number of primary bMSCs rapidly has become a prerequisite for bMSC study and application. Different methods of isolating and culturing bMSC were used and compared among groups: bMSCs of group A are isolated using direct adherence method and cultured by conventional medium changing; of group B are isolated using direct adherence method and cultured by low volume medium changing; of group C are isolated using density gradient centrifugation and cultured by conventional medium changing; of group D are isolated using density gradient centrifugation and cultured by low volume medium changing. The average population doubling time (PDT), average generation time and the cumulative cell doubling level were calculated for every group. bMSCs cultured with complete medium containing 10, 11 and 15 % FBS were allocated into group a, b and c separatedly. Cell numbers were counted everyday under a microscope, the population doubling level curve was plotted and PDT was calculated. The growth curve of bMSC in group a, b and c was made. Both density gradient centrifugation and direct adherence methods obtained relatively pure bMSCs. A larger quantity of primary bMSCs were obtained by direct adherence. bMSC proliferation was faster when cultured via the low volume medium changing method at a serum concentration of 11 % than the other methods. Isolating bMSC by direct adherence and culturing by low volume medium changing at a serum concentration of 11 % is preferential for bMSC propagation.     

Optimization of culture medium composition for cellulolytic bacteria by mathematical methods

The culture medium composition for cellulolytic bacteria growing on sugar cane wastes was optimized. A modified method of Rosenbrock was employed for shaker culture medium and a factorial plan design for fermentor culture medium optimization. A much more economical and productive medium was obtained for the production of single cell protein (SCP). A biomass concentration of 4.3 g/L was obtained in the optimized medium in batch fermentation, in comparison with 2.8 g/L previously obtained in the traditional medium under similar conditions.     

Evidence of evolutionary optimization of fatty acid length and unsaturation

The lipid composition of cell membranes exerts a crucial influence on cell physiology. Indeed, one double bond triggers membrane fluidity, essential for cell functionality, but additional double bonds increase the susceptibility to peroxidation, which produces reactive compounds that impair the viability of cells. It has therefore been suggested, but never tested in an extensive comparative context, that the composition of membrane fatty acids has been optimized during evolution. A similar prediction has been made for fatty acid chain length, on which susceptibility to peroxidation also depends. Here I tested for stabilizing selection on fatty acid composition by evaluating the fitting of the single stationary peak (SSP) model of evolution to a large data set from 107 species of birds, against alternative evolutionary models. I found that across‐species variation in average chain length and in the proportion of monounsaturated fatty acids (MUFAs), but not in the proportion of polyunsaturated (PUFAs) nor saturated (SFAs) fatty acids, was better explained by SSP models than by other models. Results show optimum values of fatty acid chain length and proportion of MUFAs of 18 C atoms and 25.5% mol, respectively, the strength of stabilizing selection being particularly high in chain length. This is the first evidence of evolutionary optimization in fatty acid composition, suggesting that certain values may have been selected because of their adaptive capacity to minimize susceptibility to lipid peroxidation.     

Sugar beet (Beta vulgaris L.) morphogenesis in vitro: effects of phytohormone type and concentration in the culture medium, type of explants, and plant genotype on shoot regeneration frequency

In vitro regeneration techniques have been optimized for seven strains and cultivars of sugar beet (Beta vulgaris L.) bred in Russia. The frequency of shoot regeneration from somatic cells and tissues of sugar beet varies from 10 to 97% depending on the explant type, culture-medium composition, and genotype. The in vitro regeneration potential has been estimated in plants with different genotypes. The effect of medium composition (phytohormones and carbohydrates) on the frequency of the formation of a morphogenic callus competent for plant regeneration has been determined. The effect of the types and concentrations of various cytokines (zeatin, kinetin, and 6-benzylaminopurine) on direct shoot regeneration from cotyledon nodes has been estimated. The culture-medium composition has been optimized for direct shoot regeneration from petioles. The effects of different concentrations of abscisic acid on the frequency of shoot regeneration from a morphogenic callus has been studied. Micropropagation has been used to obtain petiole explants and reproduce the shoots obtained by direct regeneration from cotyledon nodes, petioles, and calluses. Improved shoot-regeneration methods can be used for both agrobacterial and bioballistic genetic transformation of the sugar beet genotypes studied.     

Sugar beet (Beta vulgaris L.) morphogenesis in vitro: Effects of phytohormone type and concentration in the culture medium, type of explants, and plant genotype on shoot regeneration frequency

In vitro regeneration techniques have been optimized for seven strains and cultivars of sugar beet (Beta vulgaris L.) bred in Russia. The frequency of shoot regeneration from somatic cells and tissues of sugar beet varies from 10 to 97% depending on the explant type, culture-medium composition, and genotype. The in vitro regeneration potential has been estimated in plants with different genotypes. The effect of medium composition (phytohormones and carbohydrates) on the frequency of the formation of a morphogenic callus competent for plant regeneration has been determined. The effect of the types and concentrations of various cytokines (zeatin, kinetin, and 6-benzylaminopurine) on direct shoot regeneration from cotyledon nodes has been estimated. The culture-medium composition has been optimized for direct shoot regeneration from petioles. The effects of different concentrations of abscisic acid on the frequency of shoot regeneration from a morphogenic callus has been studied. Micropropagation has been used to obtain petiole explants and reproduce the shoots obtained by direct regeneration from cotyledonnodes, petioles, and calluses. Improved shoot-regeneration methods can be used for both agrobacterial and bioballistic genetic transformation of the sugar beet genotypes studied.     

Optimizing the medium compositions for accumulation of the novel FR-008/Candicidin derivatives CS101 by a mutant of Streptomyces sp. using statistical experimental methods

Medium compositions for the production of the novel derivatives of FR-008/Candicidin which was produced by a mutant of Streptomyces sp. FR-008 were optimized using two statistical methods including Plackett–Burman design (P–B), which was applied to find the key ingredients for the best medium composition, and response surface methodology (RSM), which was used to determine the optimal concentrations of these components. Results indicated that peptone, copper sulfate and glycerol had significant effects on the production. Under the proposed optimized conditions, the CS101 experimental yield (191.259 mg/L) closely matched the yield (203.536 mg/L) predicted by the statistical model. The optimization of the medium contributed to 10-fold higher antibiotic production than that of the control. It was first revealed that copper could stimulate FR-008/Candicidin and their derivatives synthesis at an optimal concentration in this paper, moreover, the basis of this phenomenon was also explained by investigating the enhancement of the enzymatic pathways.     

Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

Two new PRP conjugate Algorithms are proposed in this paper based on two modified PRP conjugate gradient methods: the first algorithm is proposed for solving unconstrained optimization problems, and the second algorithm is proposed for solving nonlinear equations. The first method contains two aspects of information: function value and gradient value. The two methods both possess some good properties, as follows: 1)β _k ≥ 0 2) the search direction has the trust region property without the use of any line search method 3) the search direction has sufficient descent property without the use of any line search method. Under some suitable conditions, we establish the global convergence of the two algorithms. We conduct numerical experiments to evaluate our algorithms. The numerical results indicate that the first algorithm is effective and competitive for solving unconstrained optimization problems and that the second algorithm is effective for solving large-scale nonlinear equations.     

A rapid heuristic algorithm for finding minimum evolution trees

The minimum sum of branch lengths (S), or the minimum evolution (ME) principle, has been shown to be a good optimization criterion in phylogenetic inference. Unfortunately, the number of topologies to be analyzed is computationally prohibitive when a large number of taxa are involved. Therefore, simplified, heuristic methods, such as the neighbor-joining (NJ) method, are usually employed instead. The NJ method analyzes only a small number of trees (compared with the size of the entire search space); so, the tree obtained may not be the ME tree (for which the S value is minimum over the entire search space). Different compromises between very restrictive and exhaustive search spaces have been proposed recently. In particular, the "stepwise algorithm" (SA) utilizes what is known in computer science as the "beam search," whereas the NJ method employs a "greedy search." SA is virtually guaranteed to find the ME trees while being much faster than exhaustive search algorithms. In this study we propose an even faster method for finding the ME tree. The new algorithm adjusts its search exhaustiveness (from greedy to complete) according to the statistical reliability of the tree node being reconstructed. It is also virtually guaranteed to find the ME tree. The performances and computational efficiencies of ME, SA, NJ, and our new method were compared in extensive simulation studies. The new algorithm was found to perform practically as well as the SA (and, therefore, ME) methods and slightly better than the NJ method. For searching for the globally optimal ME tree, the new algorithm is significantly faster than existing ones, thus making it relatively practical for obtaining all trees with an S value equal to or smaller than that of the NJ tree, even when a large number of taxa is involved.     

Potential pitfalls of the PTV concept in dose-to-medium planning optimization

In typical treatment planning of 3D IMRT, the incident energy fluence is optimized to achieve a homogeneous dose distribution to the PTV. The PTV includes the tumour but also healthy tissues that may have a different dose response for the same incident energy fluence, like bony structures included in the PTV (mandibles in head and neck tumours or femoral bones in sarcomas). Dose to medium optimization compensates for this heterogeneous response, leading to a non-homogeneous energy fluence in the PTV and a non-homogeneous dose in the CTV in the presence of geometric errors. We illustrate qualitatively this statement in a cylindrical geometry where the PTV includes a CTV (7 cm diameter) made of water surrounded by ICRU compact bone (1.2 cm thickness); such configuration was chosen to exaggerate the aforementioned effect. Optimization was performed assuming dose equals photon energy fluence times mass energy absorption coefficient. Bone has a 4% lower dose response in a 6 MV flattening filter free spectrum. After optimization either in medium or assuming everything as water composition, the geometry was shifted by 1.2 cm and dose recomputed. As expected, compensating for the under-response of the bone material during optimization in medium leads to an overdosage of the CTV when patient geometric errors are taken into account. Optimization in dose assuming everything as water composition leads to a uniform coverage. Robust optimization or forcing a uniform atomic composition in the PTV margin may resolve this incompatibility between the PTV concept and dose to medium optimization.     

A Conjugate Gradient Algorithm with a Trust Region for Molecular Geometry Optimization

An algorithm is presented for the optimization of molecular geometries and general nonquadratic functions using the nonlinear conjugate gradient method with a restricted step and restart procedure. The algorithm only requires the evaluation of the energy function and its gradient, therefor less memory storage is needed than for other conjugate gradient algorithms. Some numerical results are also presented and the efficiency and behaviour of the algorithm is compared with the standard conjugate gradient method. We also present comparisons of both conjugate gradient and variable metric methods with and without the trust region technique. One of the main conclusions of the present work is that a trust region always improves the converge of any optimization method. A sketch of the algorithm is also given.     

Searching for structural bias in particle swarm optimization and differential evolution algorithms

During the last two decades, a large number of metaheuristics have been proposed, leading to various studies that call for a deeper insight into the behaviour, efficiency and effectiveness of such methods. Among numerous concerns that are briefly reviewed in this paper, the presence of a structural bias (i.e. the tendency, not justified by the fitness landscape, to visit some regions of the search space more frequently than other regions) has recently been detected in simple versions of the genetic algorithm and particle swarm optimization. As of today, it remains unclear how frequently such a behaviour occurs in population-based swarm intelligence and evolutionary computation methods, and to what extent structural bias affects their performance. The present study focuses on the search for structural bias in various variants of particle swarm optimization and differential evolution algorithms, as well as in the traditional direct search methods proposed by Nelder–Mead and Rosenbrock half a century ago. We found that these historical direct search methods are structurally unbiased. However, most tested new metaheuristics are structurally biased, and at least some presence of structural bias can be observed in almost all their variants. The presence of structural bias seems to be stronger in particle swarm optimization algorithms than in differential evolution algorithms. The relationships between the strength of the structural bias and the dimensionality of the search space, the number of allowed function calls and the population size are complex and hard to generalize. For 14 algorithms tested on the CEC2011 real-world problems and the CEC2014 artificial benchmarks, no clear relationship between the strength of the structural bias and the performance of the algorithm was found. However, at least for artificial benchmarks, such old and structurally unbiased methods like Nelder–Mead algorithm performed relatively well. This is a warning that the presence of structural bias in novel metaheuristics may hamper their search abilities.     

A method for rating the individual distinctiveness of domestic cats

Fourteen adult female domestic cats were watched by two observers for 3 months. Ratings of 18 aspects of each cat's behavioural style were obtained independently from each observer. Correlations between observers were statistically significant for 15 of the 18 aspects and seven of the correlation coefficients were greater than 0·7. The ratings were compared with results of direct recording methods, where equivalent measures were available and, in five out of six cases, the results of the ratings and direct methods were significantly correlated. The rating method is, therefore, generally reliable and can be adequately validated. Some assessments of observer ratings which are not obviously and easily related to direct recordings may prove particularly useful in developmental studies of alternative modes of behaviour and the origins of individual differences.