Shooting multiple

Miura and co-workers 121) have successfully induced multiple shoot cultures of C. roseus from seedlings in the presence of 1.0 mg/liter of the cytokinin benzyladenine. Vindoline (3) and catharanthine (4) were predominating alkaloids in the MSC-B-1 line, showing levels of 1.8 and 0.37 mg/g dry weight, respectively in the leaf tissue. In the case of catharanthine (4) this represented a 10-fold increase over the parent plant tissue, and such levels were sustained in the regenerated plants. When the benzyladenine was eliminated, overall growth was reduced, but vindoline (3) and catharanthine (4) concentrations increased to 3.2 and 1.1 mg/g dry weight, respectively. 

Continued work by the same group 123) has led to the first isolation of vinblastine (1) from a multiple shoot culture of C. roseus. The most productive line, MSC-B-1, consisted of two distinctly different tissues, multiple shoots and unorganized tissue, and was maintained growing and productive for 30 months. Vinblastine (1) was isolated by HPLC, and the content was estimated to be 15 jjig/g dry weight. Production of this alkaloid was greater than that in the callus culture but less than that observed for the parent plant, even though the levels of catharanthine (4) and vindoline (3) were about the same. 

P. Deuflhard. A Modified Method for the Solution of Ill-Conditioned Systems of Nonlinear Equations with Application to Multiple Shooting. Numer. Math., 32 289-315,1974. 

Primacords are used principally for multiple shooting of drill holes ranging in diam from ca 3 to 4 in. For certain specialized types of blasting, however smaller holes, on the order of 1.5 in diam may be initiated in the same manner. The number of holes that can be fired simultaneously is practically unlimited... 

Meiners, M.S., Thomas, J.C., Bohnert, H.J. Cushman, J.C. (1991). Regeneration of multiple shoots and plants from M. crystallinum. Plant Cell Reports 9, 563-6. 

The first one is based on a classical variation method. This approach is also known as an indirect method as it focuses on obtaining the solution of the necessary conditions rather than solving the optimization directly. Solution of these conditions often results in a two-point boundary value problem (TPBVP), which is accepted that it is difficult to solve [15], Although several numerical techniques have been developed to address the solution of TPBVP, e.g. control vector iteration (CVI) and single/multiple shooting method, these methods are generally based on an iterative integration of the state and adjoint equations and are usually inefficient [16], Another difficulty relies on the fact that it requires an analytical differentiation to derive the necessary conditions. 

Graf S, Knorr D (1993) Multiple shoot cultures of Mentha canadensis for biotechnological production of flavours. In Schreier P, Winterhalter P (eds) Progress in flavour precursor studies, vol 4. Carol Stream Allured Publishers, p 471... 

Fig. (3). Multiple shoots formed on B5 basal medium containing 0.01 mg/1 NAA and 3 mg/1 BA...

In vitro tissue and cell cultures of lupin plants are not appropriate systems for the study of biosynthesis of lupin alkaloids, because the production ability by in vitro culture is rather low, i.e., 10 2 to lO times compared with that of differentiated plants. The production of the alkaloids of lupinine- and sparteine-groups by cell culture have been reported by us [59] and by Wink s group [60]. We have also successfully produced matrine in green callus culture and in multiple shoots of Sophora flavescens [61]. The producibility of matrine was positively correlated with the chloroplast formation. This indicates that the formation of carbon skeleton of matrine-type alkaloids also likely takes place in chloroplasts in plant cells as postulated in that of sparteine-type alkaloids [62]. 

Deuflhard, P. "Recent Advances in Multiple Shooting Techniques" in Computational Techniques for Ordinary Differential Equations, Caldwell and Sayer, Eds, Academic Press, New York, 1980. 

Rauvolfia serpentina roots are the source used in industrial extraction of the alkaloids. The plant is propagated by root cuttings as it has low seed viability (697). The use of micropropagation is thus of interest, and several authors reported successful procedures for micropropagation (698-701). Mathur et al. (697) reported the micropropagation of colchicine-induced tetraploids. Multiple shoot formation was obtained, as reported by Roja et al. (688), on MS medium containing 1 ppm BAP and 0.1 ppm NAA. 

Antibody was obtained by the immunization of rabbits against a conjugate of vinblastine with bovine serum albumin. The antibody had a high affinity (Ka = 1.2 x 10 L/mol) and specificity for vinblastine. The usable range of standard curve for assay was 0.5-10 ng/ml. Crude alkaloid extracts of tissue cultures could be assayed and many samples could be processed in one time. The vinblastine contents of multiple shoot cultures were lower than that of intact plants but much higher than that of callus cultures. 

Clearly, the longer the integration interval, the greater the numerical difficulties. Many authors have tried to split the integration interval into an appropriate number of subintervals, resulting in the so-called multiple shooting approach. 

In the BzzMath library, the multiple shooting algorithms have not been implemented in a dedicated class. 

The free parameters of the model are fitted to experimental data (the 0-I-D-P-fluorescence rise of dark-adapted tobacco leaves) by means of the multiple shooting algorithm PARFIT as developed by Bock [2] for parameter identification in systems of nonlinear differential equations. We use a multiple experiment structure for measurements at different light intensities. The initial trajectory and the results are shown in Figs. 2 and 3. 

In the present paper, the optimal solutions of the underlying optimal control problems of the Chylla Haase reactor, which have been computed by a new direct multiple shooting method, are discussed. It can be shown that the first of the two products for which physical data are given in [2] can be controlled along its required constant reaction temperature setpoint while, for the second product, this cannot be achieved because of certain mathematical and technical reasons. 

Well, we have picked up their challenge and present optimal solutions for their control problems. In the present paper, a direct multiple shooting... 

For the numerical solution of optimal control problems, there are basically two well-established approaches, the indirect approach, e. g., via the solution of multipoint boxmdary-value problems based on the necessary conditions of optimal control theory, and the direct approach via the solution of constrained nonlinear programming problems based on discretizations of the control and/or the state variables. The application of an indirect method is not advisable if the equations are too complicated or a moderate accuracy of the numerical solution is commensurate with the model accuracy. Therefore, the easier-to-handle direct approach has been chosen here. Direct collocation methods, see, e. g., Stryk [6], as well as direct multiple shooting methods, see, e. g., Bock and Plitt [1], belong to this approach. In view of forthcoming large scale problems, we will focus here on the direct multiple shooting method, since only the control variables have to be discretized for this method. This leads to lower dimensional nonlinear programming problems. 

Based on a multiple shooting method for parameter identification in differential-algebraic equations due to Heim [4], a new implementation of a direct multiple shooting method for optimal control problems has been developed, which enables the solution of problems that can be separated into different phases. In each of these phases, which might be of unknown length, the control behavior due to inequality constraints, the differential equations, even the dimensions of the state and/or the control space can differ. For the optimal control problems under investigation, the different phases are concerned with the different steps of the recipes. 

Bock, H. G., Plitt, K. J. (1984) A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems, Proc. of the 9th IFAC Worldcongress, Budapest, Hungary, Vol. IX, Colloquia 14.2, 09.2... 

This problem is a constrained overdetermined multipoint boundary value problem. Bock [26] has taken a multiple shooting technique to solve this problem. This time interval is devided into pieces (e.g. according to measurement points) ... 

A much better alternative is to explicitly discretize the DAE model as well as any additional path constraints at a finite number of points, and to use multiple shooting togeihei with an infeasible-path optimization method [4, 5, 8]. To this end, choose a multiple shooting mesh... 

Alternatively, collocation has been applied in order to discretize the state differential equations, e.g., see [8, 16]. This allows to treat the DAE discretization exclusively at the level of the NLP problem, but of course it leads to considerably larger optimization problems, especially for stiff systems. Adaptive collocation schemes must be used to control the discretization error. Note that unlike the multiple shooting approach, no use is made of existing advanced DAE solvers. 

OC/DO-problems can be solved very efficiently and reliably by combining the above problem discretization (piecewise control parameterization and multiple shooting state discretization) with a specifically tailored sequential quadratic programming (SQP) algorithm for the solution of the large, but structured NLP problem (2.3). Such a strategy has been implemented in the optimal control code MUSCOD [6, 13]. 

In addition, the Jacobian matrix of F2 in (2.3) has a characteristic block-sparse structure due to the special form of the continuity and consistency conditions (2.2). This multiple shooting structure can be exploited by a condensing algorithm to considerably reduce the size of the QP subproblem, which is then solved by a standard QP solver. Alternatively, the original QP subproblem can be directly solved by specialized, large-scale QP solvers, see e.g. [18]. 

In order to solve (2.3) by means of the GGN or SQP method, the values of the state functions as well as their derivatives with respect to parameters and initial values are required at the end point of each multiple shooting interval. For the calculation of these gradients, the method of internal numerical differentiation (IND) has been proven to be most effective. 

H.-G. Bock and K.-J. Plitt. A multiple shooting algorithm for direct solution of optimal control problems. Preprints of the 9th IFAC World Congress, Budapest, International Federation of Automatic Control, 1984. 

The addition of thiamin HCI (9), Ca-pantothenate (10) and biotin (11) (Figure 2) enhanced the multiple shoot formation. After the formated multiple shoots were transfered to the phytohormone free liquid medium and following were treated a brief exposure to a plant growth hormone auxin, the root formation occurred from the miero shoots. The rooted plants were hardened and transferred to soil. The regeneration potentiality was foimd to be constant throughout the year in long term eultures. 

Depending on the degree of discretization, there are single shooting (or sequential) and multiple shooting strategies in the CVP approach. 

FIGURE 14.2 CVP (a) single shooting (or sequential), (b) multiple shooting. 

In multiple shooting, the integration horizon is divided into time intervals, with the control variables approximated by polynomials in each control interval and differential variables assigned initial values at the beginning of each interval. The DAE system is solved separately within each control interval, as shown in Fignre 14.2b. Profiles for partial derivatives with respect to the optimization variables, as well as the initial conditions of the state variables in each time interval, are obtained through integration of the sensitivity eqnations. These state and sensitivity profiles are solved independently over each time interval and can even be computed in parallel. Additional equations are inclnded in the NLP to enforce continuity of state variables at the time interval boundaries. 

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