Purification of plasmid DNA for use in human gene therapy

Two key issues defined the focus of this research in manufacturing plasmid DNA for use In human gene therapy. First, the processing of E.coli bacterial cells to effect the separation of therapeutic plasmid DNA from cellular debris and adventitious material. Second, the affinity purification of the plasmid DNA in a Simple one-stage process. The need arises when considering the concerns that have been recently voiced by the FDA concerning the scalability and reproducibility of the current manufacturing processes in meeting the quality criteria of purity, potency, efficacy, and safety for a recombinant drug substance for use in humans. To develop a preliminary purification procedure, an EFD cross-flow micro-filtration module was assessed for its ability to effect the 20-fold concentration, 6-time diafiltration, and final clarification of the plasmid DNA from the subsequent cell lysate that is derived from a 1 liter E.coli bacterial cell culture. Historically, the employment of cross-flow filtration modules within procedures for harvesting cells from bacterial cultures have failed to reach the required standards dictated by existing continuous centrifuge technologies, frequently resulting in the rapid blinding of the membrane with bacterial cells that substantially reduces the permeate flux. By challenging the EFD module, containing six helical wound tubular membranes promoting centrifugal instabilities known as Dean vortices, with distilled water between the Dean number's of 187Dn and 818Dn,and the transmembrane pressures (TMP) of 0 to 5 psi. The data demonstrated that the fluid dynamics significantly influenced the permeation rate, displaying a maximum at 227Dn (312 Imh) and minimum at 818Dn (130 Imh) for a transmembrane pressure of 1 psi. Numerical studies indicated that the initial increase and subsequent decrease resulted from a competition between the centrifugal and viscous forces that create the Dean vortices. At Dean numbers between 187Dn and 227Dn , the forces combine constructively to increase the apparent strength and influence of the Dean vortices. However, as the Dean number in increases above 227 On the centrifugal force dominates the viscous forces, compressing the Dean vortices into the membrane walls and reducing their influence on the radial transmembrane pressure i.e. the permeate flux reduced. When investigating the action of the Dean vortices in controlling tile fouling rate of E.coli bacterial cells, it was demonstrated that the optimum cross-flow rate at which to effect the concentration of a bacterial cell culture was 579Dn and 3 psi TMP, processing in excess of 400 Imh for 20 minutes (i.e., concentrating a 1L culture to 50 ml in 10 minutes at an average of 450 Imh). The data demonstrated that there was a conflict between the Dean number at which the shear rate could control the cell fouling, and the Dean number at which tile optimum flux enhancement was found. Hence, the internal geometry of the EFD module was shown to sub-optimal for this application. At 579Dn and 3 psi TMP, the 6-fold diafiltration was shown to occupy 3.6 minutes of process time, processing at an average flux of 400 Imh. Again, at 579Dn and 3 psi TMP the clarification of the plasmid from tile resulting freeze-thaw cell lysate was achieved at 120 Iml1, passing 83% (2,5 mg) of the plasmid DNA (6,3 ng μ-1 10.8 mg of genomic DNA (∼23,00 Obp, 36 ng μ-1 ), and 7.2 mg of cellular proteins (5-100 kDa, 21.4 ngμ-1 ) into the post-EFD process stream. Hence the EFD module was shown to be effective, achieving the desired objectives in approximately 25 minutes. On the basis of its ability to intercalate into low molecular weight dsDNA present in dilute cell lysates, and be electrophoresed through agarose, the fluorophore PicoGreen was selected for the development of a suitable dsDNA assay. It was assesseel for its accuracy, and reliability, In determining the concentration and identity of DNA present in samples that were eleclrophoresed through agarose gels. The signal emitted by intercalated PicoGreen was shown to be constant and linear, and that the mobility of the PicaGreen-DNA complex was not affected by the intercalation. Concerning the secondary purification procedure, various anion-exchange membranes were assessed for their ability to capture plasmid DNA from the post-EFD process stream. For a commercially available Sartorius Sartobind Q15 membrane, the reduction in the equilibriumbinding capacity for  ctDNA in buffer of increasing ionic demonstrated that DNA was being.adsorbed by electrostatic  interactions only. However, the problems associated with fluid distribution across the membrane demonstrated that the membrane housing was the predominant cause of the .erratic breakthrough curves. Consequently, this would need to be rectified before such a membrane could be integrated into the current system, or indeed be scaled beyond laboratory scale. However, when challenged with the process material, the data showed that considerable quantities of protein (1150 μg) were adsorbed preferentially to the plasmid DNA (44 μg). This was also shown for derived Pall Gelman UltraBind US450 membranes that had been functionalised by varying molecular weight poly-L~lysine and polyethyleneimine ligands. Hence the anion-exchange membranes were shown to be ineffective in capturing plasmid DNA from the process stream. Finally, work was performed to integrate a sequence-specific DNA·binding protein into a single-stage DNA chromatography, isolating plasmid DNA from E.coli cells whilst minimising the contamination from genomic DNA and cellular protein. Preliminary work demonstrated that the fusion protein was capable of isolating pUC19 DNA into which the recognition sequence for the fusion-protein had been inserted (pTS DNA) when in the presence of the conditioned process material. Althougth the pTS recognition sequence differs from native pUC19 sequences by only 2 bp, the fusion protein was shown to act as a highly selective affinity ligand for pTS DNA alone. Subsequently, the scale of the process was scaled 25-fold and positioned directly following the EFD system. In conclusion, the integration of the EFD micro-filtration system and zinc-finger affinity purification technique resulted in the capture of approximately 1 mg of plasmid DNA was purified from 1L of E.coli  culture in a simple two stage process, resulting in the complete removal of genomic DNA and 96.7% of cellular protein in less than 1 hour of process time.

A new strategy for selecting and evaluating physical solvents for gas absorption

This work describes how the physical properties of a solvent affect the design variables of a physical gas absorption process. The role of every property in determining the capital and the running cost of a process has been specified. Direct mathematical relationships have been formulated between every item of capital or running cost and the properties which are related to that item. The accuracy of the equations formulated has been checked by comparing their outcome with some actual design data. A good agreement has been found. The equations formulated may be used to evaluate on the basis of economics any suggested new solvents. A group of solvents were selected for evaluation. Their physical properties were estimated or collected as experimental data. The selected ones include three important solvents, the first is polyethylene glycol dimethyl ether (Selexol) which represents the currently most successful one, The other two solvents are acetonyl acetone (B2) and n-formyl morpholine which have been suggested previously as potential credible alternatives to the current ones. The important characteristics of: acetonyl acetone are its high solubility and its low viscosity, while the n-formyl morpholine is characterised by its low vapour pressure and its high selectivity. It was found that acetonyl acetone (B2) is the most attractive solvent for commercial applications particularly for process configurations that:include heat exchangers and strippers. The effect of the process configuration on the selected solvent was investigated in detail and it was found that there is no universal solvent which is the best for any process configuration, but that there is a best solvent for a given process configuration. In previous work, acetonyl acetone was suggested as a commercially promising physical solvent. That suggestion was not fully based on experimental measurement of all the physical properties. The viscosity of acetonyl acetone and its solubility at 1 atm were measured but the vapour pressure and the solubility of C02 and CH4 at high pressure were predicted. In this work, the solubilities of C02, CH4 and C3H8 in acetenyl acetone were measured for a partial pressure range of (2 ~ 22) bar at 25°C, The vapour pressure of this solvent was also measured, and the Antoine equation was formulated from tbe experimental data. The experimental data were found to be not In agreement with the predicted ones, so acetonyl acetone was re-evaluated according to the experimental data. It was found that this solvent can be recommended for further trials in a pilot plant study or for small scale commercial units.

Transfer coefficients over inclined tube banks

The thesis presents experimental results for shell-side transfer coefficients and pressure drops across four different tube banks, using small-scale models, with yawed tubes, as found in many types of heat exchangers, boilers and nuclear reactors. The tube banks investigated have a staggered tube layout on a rotated square pitch, with a 1.25 pitch-to-diameter ratio. The angle of attack was varied between 45o and 90o. An extensive range of Reynolds number, i.e. 0.5. to 12,600, covering so-called laminar, transition and turbulent flows, was investigated. A diffusion-controlled electrochemical mass transfer technique has been employed to measure mass transfer coefficients. The heat transfer coefficients may be then readily obtained from the mass transfer values by applying the well-established Chilton-Colburn analogy. The results for the normal tube bank, which forms the base case for the study on inclined tube banks, show close agreement with previous work. The transfer coefficients and pressure drops of the inclined tube banks are compared with results from the ideal normal tube bank to examine the effect of inclination angle on heat transfer and pressure drop variations. The variation of the transfer coefficients row-by-row and the entrance and exit effects have also been investigated. An auxilary investigation has been carried out on the role of natural convection. A preliminary correlation of transfer coefficients and pressure drops against the variation in the yaw angle has been attempted. The results are discussed in the light of the few existing theoretical treatments and experimental data for these situations, and recommendations made for future work.

The chromatographic separation of carbohydrate mixtures

The separation performance of a semicontinuous counter-current chromatographic refiner (SCCR7), consisting of twelve 5.4 cm id x 75cm long columns packed with calcium charged cross-linked polysytrene resin (KORELA VO7C), was optimised. An industrial barley syrup was used containing 42% fructose, 52% glucose and 6% maltose and oligosaccharides. The effects of temperature, flow rates and concentration on the distribution coefficients were evaluated and quantified by deriving general relationships. The effects of flow rates, feed composition and concentration on the separation performance of the SCCR7 were identified and general relationships between them and the switch time, which was found to be the controlling parameter, were developed. Fructose rich (FRP) and glucose rich (GRP) product purities of 99.9% were obtained at 18.6% w/v feed concentrations. When a 66% w/v feed concentration was used and product splitting technique was employed, the throughput was 32.1 kg sugar solids/m3 resin/hr. The GRP contained less than 4.5% fructose, the FRP was over 95% pure, and the respective concentrations were 22.56 and 11.29% w/v. Over 94% of the glucose and 95.78% of the fructose in the feed were recovered in the GRP and FRP respectively. By recycling the dilute product split fractions, the GRP and FRP concentrations were increased to 25.4 and 12.96% w/v; the FRP was 90.2% pure and the GRP contained 6.69% w/v fructose. A theoretical link between batch and semicontinuous chromatographic equipments has been determined. A computer simulation was developed predicting successfully the purging concentration profiles at `pseudo-equilibrium', and also certain system design parameters. An important further aspect of the work has been to study the behaviour of chromatographic bioreactor-separators. Such batch systems of 5.4cm id and lengths varying between 30 and 230cm, were used to investigate the effect of scaling up on the conversion of sucrose into dextran and fructose in the presence of the dextransucrase enzyme. Conversions of over 80% were achieved at 4 hr sucrose residence times. The crude dextransucrase was purified using centrifugation, ultrafiltration and cross-flow microfiltration techniques. Better enzyme stability was obtained by first separating the non-solid impurities using cross-flow microfiltration, and then removing the cells from the enzyme immediately before use by continuous centrifugation.

Protein-mediated isolation of plasmid DNA by a zinc finger-glutathione S-transferase affinity linker

The sequence-specific affinity chromatographic isolation of plasmid DNA from crude lysates of E. coli DH5α fermentations is addressed. A zinc finger-GST fusion protein that binds a synthetic oligonucleotide cassette containing the appropriate DNA recognition sequence is described. This cassette was inserted into the Smal site of pUC19 to enable the affinity isolation of the plasmid. It is shown that zinc finger-GST fusion proteins can bind both their DNA recognition sequence and a glutathione-derivatized solid support simultaneously. Furthermore, a simple procedure for the isolation of such plasmids from clarified cell lysates is demonstrated. Cell lysates were clarified by cross-flow Dean vortex microfiltration, and the permeate was incubated with zinc finger-GST fusion protein. The resulting complex was adsorbed directly onto glutathione-Sepharose. Analysis of the glutathione-eluted complex showed that plasmid DNA had been recovered, largely free from contamination by genomic DNA or bacterial cell proteins. © 2002 Wiley Periodicals, Inc.

Preparation of particle-stabilized emulsions using membrane emulsification

There is currently significant interest in particle-stabilized emulsions for a variety of applications and as precursors to other materials such as micro-capsules or colloidosomes. A prerequisite for many applications is the ability to produce stable droplets with a well-controlled size. The preparation of oil-in-water (o/w) emulsions stabilized by silica colloids has been demonstrated here using membrane ulsification techniques. Emulsions were produced using both a cross-flow membrane device and a rotating membrane reactor. Under the correct conditions, highly stable emulsions with very narrow droplet size distributions can be produced. Investigations into the effects of changing the cross-flow shear rate at a fixed droplet production rate illustrate the fine control over mean droplet size that is possible with these emulsification techniques. Evidence for the importance of particle adsorption kinetics onto growing droplets prior to detachment from the membrane surface was obtained by varying the droplet production rate under fixed shear conditions. The presence of a critical surface coverage by the stabilizing particles to prevent droplet coalescence was clearly seen. Comparison with samples produced using conventional high-shear homogenization highlights the improved control over size distribution available from these membrane techniques.

Mathematical Modeling and Simulation of Radial Temperature Profile of Strontium Bromide Lasers

For metal and metal halide vapor lasers excited by high frequency pulsed discharge, the thermal effect mainly caused by the radial temperature distribution is of considerable importance for stable laser operation and improvement of laser output characteristics. A short survey of the obtained analytical and numerical-analytical mathematical models of the temperature profile in a high-powered He-SrBr2 laser is presented. The models are described by the steady-state heat conduction equation with mixed type nonlinear boundary conditions for the arbitrary form of the volume power density. A complete model of radial heat flow between the two tubes is established for precise calculating the inner wall temperature. The models are applied for simulating temperature profiles for newly designed laser. The author’s software prototype LasSim is used for carrying out the mathematical models and simulations.

Análise da eficácia de um refrigerador doméstico com condensador modificado: revestimento com meio poroso dissipativo

The development of home refrigerators generally are compact and economic reasons for using simplified configuration. The thermodynamic coefficient of performance ( COP ) is limited mainly in the condenser design for reasons of size and arrangement ( layout ) of the project ( design ) and climatic characteristics of the region where it will operate. It is noteworthy that this latter limitation is very significant when it comes to a country of continental size like Brazil with diverse climatic conditions. The COP of the cycle depends crucially on the ability of heat dissipated in the condenser. So in hot climates like the northeast, north, and west-central dispel ability is highly attenuated compared to the south and southeast regions with tropical or subtropical climates when compared with other regions. The dissipation in compact capacitors for applications in domestic refrigeration has been the focus of several studies, that due to its impact on reducing costs and power consumption, and better use of the space occupied by the components of refrigeration systems. This space should be kept to a minimum to allow an increase in the useful storage volume of refrigerator without changing the external dimensions of the product. Due to its low cost manufacturing, wire on tube condensers continue to be the most advantageous option for domestic refrigeration. Traditionally, these heat exchangers are designed to operate under natural convection. Not always, the benefits of greater compactness of capacitors for forced outweigh the burden of pumping air through the external heat exchanger. In this work we propose an improvement in convective condenser changing it to a transfer mechanism combined in series with conductive pipes and wire to a moist convective porous medium and the porous medium to the environment. The porous media used in the coating was composed of a gypsum plaster impregnated fiber about a mesh of natural cellulosic molded tubular wire mesh about the original structure of the condenser , and then dried and calcined to greater adherence and increased porosity. The proposed configuration was installed in domestic refrigeration system ( trough ) and tested under the same conditions of the original configuration . Was also evaluated in the dry condition and humidified drip water under natural and forced with an electro - fan ( fan coil ) convection. Assays were performed for the same 134- refrigerant charge e under the same thermal cooling load. The performance was evaluated in various configurations, showing an improvement of about 72 % compared with the original configuration proposed in humidification and natural convection.

Estimates of annual mean surface temperatures in the late Quaternary of the tropical Atlantic

At least two modes of glacial-interglacial climate change have existed within the tropical Atlantic Ocean during the last 20,000 years. The first mode (defined by cold glacial and warm interglacial conditions) occurred symmetrically north and south of the equator and dominated the eastern boundary currents and tropical upwelling areas. This pattern suggests that mode 1 is driven by a glacial modification of surface winds in both hemispheres. The second mode of oceanic climate change, defined by temperature extremes centered on the deglaciation, was hemispherically asymmetrical, with the northern tropical Atlantic relatively cold and the southern tropical Atlantic relatively warm during deglaciation. A likely cause for this pattern of variation is a reduction of the presently northward cross-equatorial heat flux during deglaciation. No single mechanism accounts for all the data. Potential contributors to oceanic climate changes are linkage to high-latitude climates, modification of monsoonal winds by ice sheet and/or insolation changes, atmospheric CO2 and greenhouse effects, indirect effects of glacial meltwater, and variations in thermohaline overturn of the oceans.

Sea surface temperature reconstruction for sediment core M35003-4 in the western tropical North Atlantic

Planktonic foraminiferal census counts are used to construct high-resolution sea surface temperature (SST) and subsurface (thermocline) temperature records at a core site in the Tobago Basin, Lesser Antilles. The record is used to document climatic variability at this tropical site in comparison to middle- and high-latitude sites and to test current concepts of cross-equatorial heat transports as a major player in interhemispheric climate variability. Temperatures are estimated using transfer function and modern analog techniques. Glacial - maximum cooling of 2.5°-3°C is indicated; maximum cooling by 4°C is inferred for isotope stage 3. The SST record displays millennial-scale variability with temperature jumps of up to 3°C and closely tracks the structure of ice-core Dansgaard/Oeschger cycles. SST variations in part of the record run opposite to the SST evolution at high northern latitude sites, pointing to thermohaline circulation and marine heat transport as an important factor driving SST in the tropical and high-latitude Atlantic, both on orbital and suborbital timescales.

Strength of the Iberian intraplate lithosphere: Cenozoic deformations and seismicity

Previous studies about the strength of the lithosphere in the Iberia centre fail to resolve the depth of earthquakes because of the rheological uncertainties. Therefore, new contributions are considered (the crustal structure from a density model) and several parameters (tectonic regime, mantle rheology, strain rate) are checked in this paper to properly examine the role of lithospheric strength in the intraplate seismicity and the Cenozoic evolution. The strength distribution with depth, the integrated strength, the effective elastic thickness and the seismogenic thickness have been calculated by a finite element modelling of the lithosphere across the Central System mountain range and the bordering Duero and Madrid sedimentary basins. Only a dry mantle under strike-slip/extension and a strain rate of 10-15 s-1, or under extension and 10-16 s-1, causes a strong lithosphere. The integrated strength and the elastic thickness are lower in the mountain chain than in the basins. These anisotropies have been maintained since the Cenozoic and determine the mountain uplift and the biharmonic folding of the Iberian lithosphere during the Alpine deformations. The seismogenic thickness bounds the seismic activity in the upper–middle crust, and the decreasing crustal strength from the Duero Basin towards the Madrid Basin is related to a parallel increase in Plio–Quaternary deformations and seismicity. However, elasto–plastic modelling shows that current African–Eurasian convergence is resolved elastically or ductilely, which accounts for the low seismicity recorded in this region.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Microturbinas em redes de abastecimento de água

Nos dias de hoje a sociedade exige níveis qualitativos de vida cada vez mais elevados, o que torna prioritária a conceção de sistemas eficientes, não poluidores, económicos e diversificados que permitam uma gestão integrada e racionalizada de recursos tão escasso como é o da água e da energia. Em sistemas de abastecimento de água, o uso de válvulas redutoras de pressão (VRP) visa a uniformização e controlo de pressões, promovendo uma perda de carga localizada que dissipa a energia hidráulica presente através da redução dos valores de pressão a jusante. Estas são fundamentais no controlo e redução de pressão. A utilização de microturbinas é uma alternativa sustentável para o controle de pressão e, simultaneamente, para a produção de energia elétrica. Trata-se de um método de mitigação para controlar as perdas referidas convergindo no âmbito da eficiência energética. Na perspetiva de promover um aproveitamento de energia nas redes de abastecimento de água, o presente trabalho sugere a substituição de válvulas redutoras de pressão (VRP) por microturbinas. Desse modo, apresenta-se um método automático de seleção de (i) local para implementação e (ii) projeto de microturbinas para sistemas de abastecimento de água. Para a modelação do funcionamento dos sistemas hidráulicos recorre-se ao simulador hidráulico EPANET. Esta ferramenta possibilita avaliação de caudais e pressões em todos os pontos da rede durante um determinado intervalo de tempo. A metodologia desenvolvida permite selecionar o local ideal no sistema hidráulico através de uma análise de cada secção conduta-nó escolhendo-se a melhor opção baseada na produção de energia. Depois da localização procede-se à seleção do tipo de turbina (Kaplan, Francis, Pelton e Cross-flow) que vai depender das características do sistema hidráulico. Na etapa seguinte apresenta-se os resultados obtidos pela turbina nomeadamente a produção de energia elétrica anual, o investimento necessário, o tempo de retorno e a rentabilização ao final de um período de 25 anos. Na última etapa da metodologia, de forma avaliar o comportamento do sistema final, realiza-se uma nova simulação da rede mas tendo em conta a introdução da microturbina no local. Apresentam-se alguns casos de estudo que validam a ferramenta desenvolvida. A metodologia desenvolvida é comparada com um caso de estudo real. Em ambos os exemplos simulados a metodologia aplicada permite obter soluções com ganhos energéticos significativos associados ao sistema. Apenas num dos exemplos se observaram que a implementação da microturbina no sistema hidráulico não seria economicamente rentável.

Lääkeaineiden poisto yhdyskuntajätevesistä katalyyttisillä membraaneilla

Lääkeaineiden poistaminen jätevedestä on tärkeää lääkeainejäämien ympäristöön pääsyn ehkäisemiseksi. Tämän työn tavoitteena on selvittää, soveltuvatko katalyyttiset membraanit lääkeaineiden poistoon jätevedestä ja saadaanko membraanisuodatusta tehostettua katalyyttisellä prosessilla. Työ käsittelee katalyyttisistä prosesseista fotokatalyysiä, joka perustuu valoa absorboivan katalyytin käyttöön. Kirjallisuustyössä tarkastellaan kahden erilaisen fotokatalyyttisen prosessin toimivuutta membraanisuodatuksen kanssa lääkeaineiden poistossa jätevedestä. Lisäksi tutkitaan fotokatalyysissä käytettävän katalyytin ja ultraviolettisäteilyn vaikutusta membraaniin. Tutkimukset ovat osoittaneet, että katalyyttisillä membraaneilla voidaan poistaa lääkeaineita jätevedestä tehokkaasti. Parhaan lääkeaineiden poistotehokkuuden saamiseksi katalyytin määrä on optimoitava hajotusprosessin kannalta. Myös katalyytin sijainti membraanissa vaikuttaa tehokkuuteen. Katalyytti voi sijaita membraanista myös erillään. Tällöin saadaan käsiteltyä myös jatkuvatoimisessa membraanisuodatuksessa syntyvä lääkeaineita sisältävä konsentraattivirta. Kun katalyyttisellä membraanilla hajotetaan lääkeaineita, täytyy prosessin turvallisuuden kannalta olla hyvin selvillä mahdollisista syntyvistä myrkyllisistä välituotteista. Tutkimuksissa on myös todettu, että katalyyttisen membraanin käyttö vähentää membraanin likaantumista.

An experimental investigation by towing tank on VIV of a long flexible cylinder for deepwater riser application

In this study, the dynamic response of a vertical flexible cylinder vibrating at low mode numbers with combined x-y motion was investigated in a towing tank. The uniform flow was simulated by towing the flexible cylinder along the tank in still water; therefore, the turbulence intensity of the free flow was negligible in obtaining more reliable results. A lower branch of dominant frequencies with micro vibration amplitude was found in both cross-flow and in-line directions. This justifiable discrepancy was likely caused by an initial lock-in. The maximum attainable amplitude, modal analysis and x-y trajectory in cross-flow and in-line directions are reported here and compared with previous literature, along with some good agreements and different observations that were obtained from the study. Drag and lift coefficients are also evaluated by making use of a generalized integral transform technique approach, yielding an alternative method to study fluid force acting upon a flexible cylinder.