Lenz model

Like the Cooke model, the Lenz model [77] is a generic model for membranes, but it has been designed for studying internal phase transitions. Therefore, it puts a slightly higher emphasis on conformational degrees of freedom than the Cooke model. Lipids are represented by semiflexible linear chains of seven beads (one for the head group, six for the tail), which interact with truncated Lennard-Jones potentials. Model parameters such as the chain stiffness are inspired by the properties of hydrocarbon tails [78]. The model includes an explicit solvent, which is, however, modeled such that it is simulated very efficiently it interacts only with lipid beads and not with itself ( phantom solvent [79]). 

The model reproduces the most prominent phase transitions of phospholipid monolayers [78] and bilayers [80]. In particular, it reproduces a main transitirm from a fluid membrane phase (L to a tilted gel phase Lpi) with an intermediate ripple phase Pp ), in agreement with experiments. The elastic parameters have been studied in the fluid phase and are in reasonable agreement with those of saturated DPPC (dipalmitoyl-phosphatidylcholine) bilayers. Recently, the Lenz model has been supplemented with a simple cholesterol model [81]. Cholesterol molecules are taken to be shorter and stiffer than lipids, and they have a slight affinity to lipids. Mixtures of lipids and cholesterol were found to develop nanoscale raft domains... 

Fig. 2 Rafts in a two-component lipid bilayer (20,000 lipids, Lenz model). Purple (darker) beads correspond to cholesterol and green (lighter) beads to phospholipids (see [81])...

Second, the characteristic length scale of the rafts is similar to the wavelength of the ripple state in one-component bUayers in the transition region between the fluid and the tilted gel Lp state [199, 200]. Experimentally [201, 202] and in computer simulations [80, 203-207], modulated phases are observed in lipid bUayers that exhibit a tilted gel state, and they are not observed in Upid bUayers with an untUted gel state [201-203,208]. For example, in the Lenz model, rippled states occur in the standard setup with a mismatch between head and taU size [80], but they disappear if the head size is reduced such that the tilt in the gel phase vanishes [208]. 

In the case where the membrane is deformed, the deformation profiles can be compared to a variety of theories [16,17,27, 33, 245-247]. Both in coarse-grained [30,234] and atomistic [248] simulations, it was reported that membrane thickness profiles as a function of the distance to the protein are not strictly monotonic, but exhibit a weakly oscillatory behavior. This feature is not compatible with membrane models that predict an exponential decay [16,17,27], but it is nicely captured by the coupled elastic monolayer models discussed earlier [22, 28, 30]. Coarsegrained simulations of the Lenz model showed that the coupled monolayer models describe the profile data at a quantitative level, with almost no fit parameters except the boundary conditions [30, 244]. 

In membranes containing several inclusions, the membrane thickness deformations induce effective interactions between inclusimis. These have also been studied within the Lenz model [30, 249] and other coarse-grained models [250, 251]. The comparison with the elastic theory is less convincing, due to the fact that... 

Goralczyk, R., Wertz, K., Lenz, B. et al. 2005. Beta-carotene interaction with NNK in the AJ-mouse model Effects on cell proliferation, tumor formation and retinoic acid responsive genes. Biochim Biophys Acta 1740 179-188. 

We appreciate the guidance of Pro . R.W. Lenz in the synthesis of model networks, and the help of Drs. Roberto Russo and Ulku Yilmazer in initial synthesis work. This work was supported in part by a grant from the Center for University of Massachusetts-lndustry Research on Polymers (CUMIRP). We appreciate the donation of the Duragen samples by the General Tire and Rubber Co., the isocyanate samples by the Mobay Chemical Co., and the Butarez samples by the Phillips Petroleum Co. 

Wisel A, Schmidt-Traub H, Lenz J, Strube J. Modelling gradient elution of bioactive multicomponent systems in non-linear ion-excahnge chromatography. Journal of Chromatography A 2003 1006 101-120. 

Figure 16-21 (A) Scheme showing the diiron center of the R2 subunit of E. coli ribonucleotide reductase. Included are the side chains of tyrosine 122, which loses an electron to form a radical, and of histidine 118, aspartate 237, and tryptophan 48. These side chains provide a pathway for radical transfer to the R1 subunit where the chain continues to tyrosines 738 and 737 and cysteine 429.354a c From Andersson et al.35ic (B) Schematic drawing of the active site region of the E. coli class IH ribonucleotide reductase with a plausible position for a model-built substrate molecule. Redrawn from Lenz and Giese373 with permission.

Lenz R, Boelcke C, Peckmann U, Reuss M (1986) In Johnson, A (ed) Proc 1st Modelling Contr Biotechnol Process, Helsinki, Pergamon Press, Oxford, p 85... 

Yermg, D.T., Josse, D., Nicholson, J.D., Khanal, A., McAndrew, C.W., Bahnson, B.J., Lenz, D.E., Cerasoli, D.M. (2004). Stmctiue/fimction analyses of hiunan serum paraoxonase (HuPONl) mutants designed from a DFPase-lrke homology model. Biochim. Biophys. Acta 1702 67-77. 

D. Louden, A. Handley, S. Taylor, I. Sinclair, E. Lenz, and I. D. Wilson, High temperature reversed-phase HPLC using deuterium oxide as a mobile phase for the separation of model pharmaceuticals with multiple on-line spectroscopic analysis (UV, IR, IH-NMR and MS), Analyst 126 (2001), 1625-1629. 

Lenz C-J, Muller F, Schliinzen KH (2000) The sensitivity of mesoscale chemistry transport model results to boundary values. Environ Monit Assess 65 287-298 L6pez SD, Liipkes C, Schliinzen KH (2005) The effects of different k-e-closures on the results of a micro-scale model for the flow in the obstacle layer. Meteorol Z 14 839-848 Muller F, Schliinzen KH, Schatzmann M (2000) Test of numerical solvers for chemical reaction mechanisms in 3D air quality models. Environ Model Softw 15 639-646 Schliinzen KH (1990) Numerical studies on the inland penetration of sea breeze fronts at a coastline with tidally flooded mudflats. Beitr Phys Atmos 63 243-256 Schliinzen KH, Katzfey JJ (2003) Relevance of subgrid-scale land-use effects for mesoscale models. Tellus 55A 232-246... 

Lenz et al. [207] reported studies with model compounds which were in agreement with this expectation. They also reported the over-all second order rate coefficients shown in Table 24. 

According to Lenz and Lund (72), kinetic models for destruction of food components are needed to improve products by minimizing quality changes for new product development and to predict shelf life during storage. Numerous reports and reviews of the kinetics of ascorbic acid destruction can be found in the literature (68-88). A brief overview is presented here to indicate the need for further research in this area. 

Carlotti, E, Giske, J., Werner, F. E., 2000. Modeling zooplankton dynamics. In Harris, R. P., Wiebe P. H., Lenz J., Skjoldal H. R., Huntley M. (Eds.), ICES Zooplankton Methodology Manual. Academic Press, 571-667. 

The model chosen to describe the degradation of polyethylene was random chain scission. Lenz (3,) in his section on degradation reactions of polymers cites work which supports the contention that polyethylene does thermally degrade in a random chain scission manner as opposed to depolymerization. For this model a statistical treatment has been developed by Montroll and Simha (). The extent of reaction may be related to the number average molecular weight by ... 

A comprehensive review of proton NMR of lignin model compounds, synthetic, isolated, and degraded lignins and their derivatives prior to 1968 was made in Ludwig s chapter 8 [145] in Lignins Occurrence, Formation, Structure and Reactions [1], Much of the work reported stemmed from the seminal studies by Ludwig, Nist, and McCarthy published in 1964 [146,147], and the 1968 review by Lenz [148],... 

Simple mathematical expressions have been developed for the Thomas-Fermi, Bohr, Lenz-Jensen, and Moliere screening functions. Several forms exist for the Thomas-Fermi model. The earliest and best known of these is the Sommerfeld asymptotic form,... 

J. Riedrich, F. Lenz, Elastic Electron Scattering from Pb at moderate Momentum Transfers and Model-independent Description of the Nuclear Charge Distribution, Nucl. Phys. A 183 (1972) 523-544. 

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