Rheological properties of mammalian cell culture suspensions: Hybridoma and HeLa cell lines

Data on viscous (eta') and elastic (eta') components of the complex viscosity versus oscillatory angular frequency (0.01 to 4.0 rad/s) with increasing strains were obtained for hybridoma cell (62'D3) and HeLa cell (S3) suspensions in PBS at 0.9 (mL/mL) cell volume fraction using a Weissenberg rheogoniometer equipped with two parallel plate geometry at ambient temperature. Both cell suspensions exhibited shear thinning behavior. From the measured viscoelastic properties, the yield stress was calculated. Hybridoma cell suspension (15 mum as the mean diameter of cells) showed the yield stress at 550 dyne/cm(2) that was 1.8 times higher than the value of HeLa cell suspension (22 mum mean diameter) as measured at the oscillatory angular frequency, 4.0 rad/s. The apparent viscosities of HeLa cell suspension at four concentrations and varying steady shear rate were also determined using the Brookfield rotational viscometer. The yield stress to steady shear test was about 130 dyne/cm(2) for HeLa cell suspension at 0.9 (mL/mL) cell volume fraction. The apparent viscosity was in the range about 1 approximately 1000 Poise depending on the cell concentration and shear rate applied. A modified semiempirical Mooney equation, \documentclass{article}\pagestyle{empty}\begin{document}$ \eta = \eta _0 \exp [K\dot \gamma ;{ - \beta } \phi /(1 - K'\sigma \phi _c /D)] $\end{document} was derived based on the cell concentration, the cell morphology, and the steady shear rate. The beta, shear rate index, was estimated as 0.159 in the range of shear rate, 0.16 to 22.1 s(-1), for the cell volume fractions from 0.6 to 0.9 (mL/mL). In this study, the methods of determining the shear sensitivity and the viscous and the elastic components of mammalian cell suspensions are described under the steady shear field. (c) 1993 John Wiley & Sons, Inc.     

Viscosity of heparin as a function of dielectric constant and of desulfation

The effect of dielectric constant (D) of the solvent on the viscosity of heparin was examined using the relation \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{{\rm sp}} /c = [\eta ]_\infty (1 + k/\sqrt c) $\end{document}, where [η]_∞ is the shielded intrinsic viscosity obtained by extrapolating \documentclass{article}\pagestyle{empty}\begin{document}$ \eta _{{\rm sp}} /c\,{\rm vs}{\rm . }\,1/\sqrt c ) $\end{document} to infinite concentration, and k is an interaction parameter independent of the dielectric constant of the solvent. This equation was previously reported by the authors⁹ for describing the reduced viscosities of strong polyelectrolytes in salt-free polar solvents. It was found that the [η]_∞ of heparin increases linearly with increasing dielectric constant of the solvent whereas the k values were, within experimental error, independent of D in the range 54.7 < D < 93.2 examined. Graded hydrolysis of heparin from its acid form (heparinic acid) at 57°C resulted in samples of varying degree of desulfation with corresponding decrease in biological activity. It was found that both [η]_∞ and k decrease with increasing desulfation.     

Kinetics of ethanol inhibition in alcohol fermentation

The inhibitory effect of ethanol on yeast growth and fermentation has been studied for the strain Saccharomyces cerevisiae ATCC No. 4126 under anaerobic batch conditions. The results obtained reveal that there is no striking difference between the response of growth and ethanol fermentation. Two kinetic models are also proposed to describe the kinetic pattern of ethanol inhibition on the specific rates of growth and ethanol fermentation: \documentclass{article}\pagestyle{empty}\begin{document}$$\begin{array}{*{20}c} {\frac{{\mu _i }}{{\mu _0 }} = 1{\rm } - {\rm }\left( {\frac{P}{{P_m }}} \right);\alpha } \hfill & {\left( {{\rm for}\ {\rm growth}} \right)} \hfill \\ {\frac{{\nu _i }}{{\nu _0 }} = 1{\rm } - {\rm }\left( {\frac{P}{{P'_m }}} \right);\beta } \hfill & {\left( {{\rm for}\ {\rm ethanol}\ {\rm production}} \right)} \hfill \\ \end{array}$$\end{document} The maximum allowable ethanol concentration above which cells do not grow was predicted to be 112 g/L. The ethanol-producing capability of the cells was completely inhibited at 115 g/L ethanol. The proposed models appear to accurately represent the experimental data obtained in this study and the literature data.     

Topography of nucleic acid helices in solutions. 3. Interactions of spermine and spermidine derivatives with polyadenylic-polyuridylic and polyinosinic-polycytidylic acid helices

The synthesis of spermine derivatives (II), \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R}_1 {\rm R}_{\rm 2} {\rm R}_{\rm 3} \mathop {\rm N}\limits^ + \left( {{\rm CH}_2 } \right)_3 \mathop {\rm N}\limits^ + {\rm R}_{\rm 1} {\rm R}_{\rm 2} \left( {{\rm CH}_2 } \right)_2 ]_2 \cdot 4{\rm X}^ - $\end{document}, and spermidine derivatives (III), \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm R}_1 {\rm R}_{\rm 2} {\rm R}_{\rm 3} \mathop {\rm N}\limits^ + \left( {{\rm CH}_2 } \right)_4 \mathop {\rm N}\limits^ + {\rm R}_{\rm 1} {\rm R}_{\rm 2} \left( {{\rm CH}_2 } \right)_3 \mathop {\rm N}\limits^ + {\rm R}_{\rm 1} {\rm R}_{\rm 2} {\rm R}_3 \cdot 3{\rm X}^ - $\end{document}, are reported. The effects of these salts on the helix–coil transition of rA–rU and rI–rC helices were examined. Increasing the size of the hydrophobic substituents, R¹, R², and R³ lowers the degree of stabilization of the helical structure. The disproportionation reaction, 2rA–rU→rA–rU₂ + rA occurs readily with salts II and III, especially when the substituents, R₁, R₂, and R₃ are small, i.e., H or Me. Spermine is found to stabilize the rA–rU² and rI–rC helices to approximately the same extent; however, large differences between the degree of stabilization of rA–rU₂ and rI-rC helices are observed when the substituents R₁, R₂, and R₃ are large hydrophobic groups. Similar results are also obtained for the spermidine series. Finally, differences in the interactions of the salts II and III with rA–rU₂ and rI–rC helices suggest that the latter helix is denser.     

Peptaibol antibiotics: Conformational preferences of synthetic emerimicin fragments

The ir absorption and CD conformational analyses of solutions of the protected 2–9 fragment of the peptaibol antibiotics emerimicins III and IV \documentclass{article}\pagestyle{empty}\begin{document}$ \rlap{--} (Aib_3 \rlap{--} )L - Val - Gly - L - Leu\rlap{--} (Aib_2 \rlap{--} ) $\end{document} and related short sequences are consistent with the presence of a right-handed α-helix for the octapeptide, while the tri-, tetra-, and pentapeptides adopt a 3₁₀-helix, either right- or left-handed, depending on the amino acid sequences. The structural preferences of solid-state \documentclass{article}\pagestyle{empty}\begin{document}$ Z\rlap{--} (Aib_3 \rlap{--} )L - Val - OMe $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ Z\rlap{--} (Aib_3 \rlap{--} )L - Val - Gly - OMe $\end{document} have been determined by x-ray diffraction. In accord with the solution data, incipient 3₁₀-helices, formed by two and three β-turns, have been found for the tetra- and pentapeptides, respectively. The tetrapeptide helix has the left-handed screw sense, while that of the pentapetide is right-handed, thus confirming the conclusions of the CD analysis of the solution.     

A Measure of Plankton Community Similarity Utilizing Variable Weighting of Total Density and Taxonomic Proportionality

Four commonly used formulae for measuring percentage similarity (PS) of biological communities were tested for their usefulness in relating to two plankton community properties, species proportional differences and total density differences. The formula best combining species proportionality and total density in the expression of PS is new: where min (xi,yi) is the lesser percentage (doubly standardized) of a species in two samples X and Y and where 2 q, 2xi and 2yi are the total quantities of all species in samples 8,X and Y, where \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {z_i } ,\,\sum\limits_i {x_i } \,and\sum\limits_i {y_i } $\end{document} are the total quantities of all species in samples Z, X and Y, respectively. Sample 2 contains the highest density of all species in the set; \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {z_i \, > \,(\sum\limits_i {x_i ,\,} \sum\limits_i {y_i } )} $\end{document}. The new expression of PS is simple to use and has the additional advantage of offering the analyst an unlimited choice of weighting factors or importance values for proportionality of species content and total density. The method has been applied to data from Gravenhurst Bay (Ontario) and effectively demonstrates the consequences of phosphorus loading reductions for phytoplankton communities.     

Optical anisotropy of polypeptide chains

Optical anisotropies γ² of N-t-butylacetamide (tBA), N-Methylacetamide (MA), and N, N-dimethylacetamide (DMA) have been determined from the Rayleigh ratios for depolarzed scattering by dilute solutions of the amides in p-dioxane. Traceless optical polarizability tensors \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document} for the amides are derived from these results in conjunction with the Kerr constant for tBA determined by LeGèvre and co-workers. It is shown that the tensor \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document}_i for the glycyle unit in a polypeptide chain may be identified with \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document}MA . Methods for deriving corresponding tensors for other peptide units are indicated and the traceless polarizability tensor \documentclass{article}\pagestyle{empty}\begin{document}$ \widehat{\rm \alpha } $\end{document} for a polypeptide chain in any specified configuration is formulated.     

Polarized fluorescence in an electric field. A model calculation with application to the geometry of the 2-hydroxy-4,4′-diamidinostilbene–DNA complex

Theoretical expressions are derived for the change in the polarized components of the fluorescence, resulting from the orientation of a rigid molecule bearing a chromophore with arbitrary angles for the absorption and transition moments \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _a $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _e $\end{document} with respect to the molecular axis. The break in the symmetry relation H_V = V_H is related to the tilt angle between \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _a $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \vec \mu _e $\end{document}. The theory is applied to a sonicated DNA–2-hydroxy-4,4′-diamidinostilbene complex, in the blue and red emission bands of this peculiar dye. Simultaneous measurements of linear dichroism and fluorescence lead to the determination of an angle of 47° between a fluorescent bound dye and the DNA axis, with no difference for the blue- and red-emitting species, but confirm the presence of nonfluorescent bound dye in a more perpendicular arrangement.     

External-circulation-loop airlift bioreactors: study of the liquid circulating velocity in highly viscous non-Newtonian liquids

In order to obtain further information on the behavior and optimal design of external-circulation-loop airlift (ECL-AL) bioreactors, the liquid circulating velocity, gas holdup and average bubble diameter in the downcomer were studied using highly viscous pseudoplastic solutions of various types of CMC. A few comparative measurements also were made using a viscous Newtonian aqueous sucrose solution. For the liquid velocity measurements, an ultrasonic flow meter (Doppler frequency shift principle) was applied for the first time to the gas/non-Newtonian liquid dispersion in downward flow and satisfactory results were obtained. For viscous liquids, the circulating liquid velocity in the riser section of an ECL-AL (u(LR)) is shown to be dependent mainly on the downcomer-to-riser cross-sectional area ratio (A(d)/A(r)), the effective viscosity (eta(eff)) and the gas superficial velocity (u(GR)) as described by the following equation \documentclass{article}\pagestyle{empty}\begin{document}$$ u_{LR} = 0.23u_{GR};{0.32} (A_d /A_r);{0.97} \eta _{eff};{ - 0.39} $$\end{document} The circulating liquid velocity exerts opposing effects on the mass transfer and liquid-phase mixing performances of ECL-AL fermentors. Therefore, it is proposed that the optimum operating conditions for a given fermentation may be best achieved by means of independently regulating the circulating liquid velocity.     

Kinetics of anaerobic purification of industrial wastewater

As a part of the development of an integral mathematical model describing the up-flow anaerobic sludge blanket (UASB) reactor, the kinetics of the conversion of organic wastes has to be known. We compared the Monod model with the model proposed by Andrews et al. Together with the assumption that the substrate for the anaerobic bacteria is formed by nonionized, volatile fatty acids, the Andrews model is able to describe substrate inhibition and reactor failure due to pH changes.From four batch experiments, with different concentrations of microorganisms, it could be concluded with a reliability of over 95% that the monod model was inadequate and Andrews' model was adequate to describe the measurements. Standard statistical techniques like the X2- and the F-test were used for this purpose.From a parameter sensitivity analysis for the Andrews model it followed that the maximum specific growth rate mu(A) (max) of the bacteria and the inhibition constant K(1) are the parameters which influence the system most. Thus, these parameter were determined experimentally and most accurately. The results are: \documentclass{article}\pagestyle{empty}\begin{document}$$\mu;{A}_{\max} = 16*10;{-4}{\rm h};{-1}\pm 2\%\quad {\rm and}\quad K_l = 0.0158\,{\rm g}\,{\rm HAc/L}\pm 2.5\%$$\end{document} The other parameters were taken from literature. From calculation of the Thiele modulus for the particles it follows that transport limitation of the substrate in the flocus is not significant. The efficiency eta is 0.85 in the worst case.     

Morphometric diffusing capacity and functional anatomy of the book lungs in the spider Tegenaria spp. (Agelenidae)

The presence of both book lungs and a tracheal system in many spiders raises the question of the functional significance of this double respiratory system. The present physiological and morphometric study of the house spider (Tegenaria spp.) reveals that the diffusing capacity (Dto₂) of the lungs alone suffices during rest and following exercise to meet measured rates of oxygen consumption (\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm V}\limits^{\rm.} $\end{document}o₂) at driving pressures (ΔPto ₂) similar to those calculated for vertebrate lungs. During moulting ΔPto ₂ may rise to more than double the vertebrate values, implying the possible insufficiency of book lungs during this critical life phase. Resting \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm V}\limits^{\rm .} $\end{document}o₂ is greatest (92 mm³/h · g) during the early morning and lowest (66 mm³/h · g) near midday: during moulting \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm V}\limits^{\rm .} $\end{document}o₂ rises to 278.7 mm³/h · g. In spiders recovering from exercise \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm V}\limits^{\rm .} $\end{document}o₂ is consistently greater than during rest: neither value is significantly reduced by blockage of the tracheal stigmas. Regression calculations of morphometric values for a hypothetical 100-mg Tegenaria yield a total lung volume of 0.578 mm³, a pulmonary surface area of 69.8 mm², and a surface-to-volume ratio of 120.89 mm²/mm³. In spite of the similar thickness of the chitinous and hypodermal components of the air-hemolymph barrier (each ca. 0.2 μm in nonmoulting animals), the low permeability of chitin for oxygen makes this layer the greater barrier to diffusion. For a 100-mg specimen Dto₂ is 3.5 mm³/h · torr: similar to that of a turtle (Pseudemys) on a gram-body weight basis.     

Solution properties of synthetic polypeptides. 18. Helix-coil transition of poly-N5-(2-hydroxyethyl)L-glutamine

The helix–coil transition of poly-N⁵-(2-hydroxyethyl)L -glutamine (PHEG) in aqueous isopropanol was examined by means of optical rotatory dispersion (ORD) and intrinsic viscosity [η] measurements. The Zimm–Bragg parameters σ and s for the transition were determined from the ORD data as a function of molecular weight. It was found that the transition was characterized by a relatively low cooperativity; the values of \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt \sigma $\end{document} were in the range from 0.039 to 0.066, depending on the solvent composition. These σ values are much larger than those reported for other polypeptide–solvent systems. The transition enthalpy was negative and its magnitude varied with the solvent composition, with a maximum of 620 cal/mol at 40 wt% isopropanol. The curve of [η] versus helical content for a high-molecular-weight sample exhibited a very broad minimum, and this behavior was attributed to the low cooperativity of the transition.     

Modellierung der enzymatischen Cellobiosehydrolyse – Vergleich linearer und nichtlinearer Parameterbestimmung

Experimental kinetic data (initial rate and high conversion) on the hydrolysis of cellobiose by 1,4-β-glucosidace (Gliocladium sp.) have been analysed and a competitive inhibition by glucose has been proposed. The determination of kinetic parameters from integral data is based upon algorithms for non-linear optimization and numerical integration. The values of kinetic constants \documentclass{article}\pagestyle{empty}\begin{document}$(v_{\max } = 1.02\frac{{\mu {\rm M}_{{\rm glucose}} }}{{{\rm mg}_{{\rm protein}} \cdot \min }},K_M = 2.6{\rm mM/l, and }K_P = 1.2{\rm mM/l)}$\end{document} agree well with the initialrate results. An important distinction is the confidence limit of parameters. Linear regression analysis shows a virtual accuracy and can lead to wrong conclusions.     

Topological classification and enumeration of RNA structures by genus

To an RNA pseudoknot structure is naturally associated a topological surface, which has its associated genus, and structures can thus be classified by the genus. Based on earlier work of Harer–Zagier, we compute the generating function $\mathbf{D}_{g,\sigma }(z)=\sum _{n}\mathbf{d}_{g,\sigma }(n)z^n$ for the number $\mathbf{d}_{g,\sigma }(n)$ of those structures of fixed genus $g$ and minimum stack size $\sigma $ with $n$ nucleotides so that no two consecutive nucleotides are basepaired and show that $\mathbf{D}_{g,\sigma }(z)$ is algebraic. In particular, we prove that $\mathbf{d}_{g,2}(n)\sim k_g\,n^{3(g-\frac{1}{2})} \gamma _2^n$ , where $\gamma _2\approx 1.9685$ . Thus, for stack size at least two, the genus only enters through the sub-exponential factor, and the slow growth rate compared to the number of RNA molecules implies the existence of neutral networks of distinct molecules with the same structure of any genus. Certain RNA structures called shapes are shown to be in natural one-to-one correspondence with the cells in the Penner–Strebel decomposition of Riemann’s moduli space of a surface of genus $g$ with one boundary component, thus providing a link between RNA enumerative problems and the geometry of Riemann’s moduli space.     

Effects of rheological properties and mass transfer on plant cell bioreactor performance: production of tropane alkaloids

Volumetric mass transfer coefficients, K(L)a were measured over an aeration rate range from 0.1 to 1.0 vvm in a 1.2-L draft-tube-type airlift bioreactor for different Datura stramonium cell concentrations and correlated with superficial air velocity and rheological properties of the cell suspension. The measured K(L)a values (17-40 h(-1)) for a cell volume fraction of 0.2 (v/v) were approximately 2 times higher than those for the highest cell concentrations tested (cell volume fraction 0.7-0.8 v/v). Cell suspensions exhibited yield stress and pseudoplastic behavior. This behavior was described by the Casson model. The estimated yield stress values depended upon cell concentration with an exponent of 4.0. An empirical correlation based on the data for plant cell suspensions exhibiting yield stress was developed in order to determine aeration strategy for the plant cell cultivation in draft-tube-type airlift bioreactors: \documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm K}_{\rm L} {\rm a} = {\rm A}({\rm U}_{{\rm gr}});{0.3} ({\rm \eta }_{{\rm eff}});{ - 0.4} $$\end{document} Aeration rates above 1.0 vvm caused a significant drop in cell yield and product content. Maximum growth and production were obtained at 0.6 vvm aeration. The cell and product yields obtained at 1.7 vvm were 2.8 times lower than the maximum values (25 g cell DW/L and 73.8 mg tropane alkaloid/L). The effects of the increased aeration rates on cell yield were also evaluated in terms of Reynolds stress. It was found that there was a relation between cell damage and the estimated Reynolds stress. The Reynolds stress estimated for the same aeration rate decreased with increasing cell concentration, suggesting that cells in the cultures at low cell concentrations are subjected to hydrodynamic damage. In the experiments with the cell cultures having a cell concentration of 0.3 (v/v), approximately 70% reduction in cell concentration was observed when the Reynolds stress was increased from 10 to 50 dyn/cm(2). (c) 1993 John Wiley & Sons, Inc.     

Catabolite repression of amylase synthesis in yeast

Amylase synthesis by the yeasts Saccharomycopsis fibuligera and Schwanniomyces castellii and alluvius is repressed by glucose. Steady state continuous culture data for amylase activity, E, biomass concentration, X, and reducing sugar concentration, S, were fitted to the three-parameter catabolite repression model \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{E}{X} = \frac{{[1 + a(S/X)]}}{{[1 + b(S/X)]}}, $\end{document} and biomass productivity, DX, and amylase productivity, DE, were determined for S. castellii and S. alluvius.     

Conformational properties of methionine homo-oligopeptides in solution

A conformational analysis was carried out in solution on a series of L -methionine oligomers having the general formula \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm BOC\rlap{--} (L - Met\rlap{--})}_n {\rm OMe (}n = 2 - 7)$\end{document}. We examined these oligopeptides in TFE, HFIP, EG, and mixed organic–water media. The critical size for helix formation was found to be seven residues in TFE, whereas the β-associated structure appears at the pentamer in EG and TFE–water (20 : 80, v/v). In HFIP, however, the oligomers exist essentially in an unordered conformation.     

Prognose des Stoffhaushaltes von Staugewässern mit Hilfe kontinuierlicher und semikontinuierlicher biologischer Modelle. II. Prüfung der Prognosegenauigkeit. Prediction of the Balance of Matter in Storage Reservoirs by Means of Continuous or Semicontinuous Biological Models. II. Reliability of the Prediction Method

The phosphate removal in small, completely mixed storage reservoirs (preimpoundment basins) mainly is a function of the production of biomass by the phytoplankton. The knowledge of the critical detention time of the water is the most important premise to the prediction. The critical detention time t̄ is computed from the equation: \documentclass{article}\pagestyle{empty}\begin{document}$ \overline t _c = \frac{1}{{\mu ^* - 0,1}} $\end{document} and the growth rate μ* at a given combination of the light intensity J, temperature T and phosphate concentration P is computed from: \documentclass{article}\pagestyle{empty}\begin{document}$ \mu ^* = \frac{{\mu T \cdot \mu J \cdot \mu P}}{{\mu \max ^2 }}\mu \max \cdot \frac{P}{{K_p + P}}\frac{J}{{K_j + J}}\frac{T}{{T_{opt} }}, $\end{document} (μmax = maximum possible growth rate of the dominant species; K_p, K_j and T_opt are constants computed from batch cultures). The quotient \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{\bar t_{act.} }}{{\bar t_c }}(\bar t_{act.} = {\rm actual detention time in the water body)} $\end{document} enables prediction of the phosphate removal. A comparison of the predicted results from semicontinuous cultures and from the preimpoundment basin of the Weida reservoir revealed a satisfactory degree of conformity.     

Patterns of tooth size variability in the dentition of primates

Published data on tooth size in 48 species of non-human primates have been analyzed to determine patterns of variability in the primate dentition. Average coefficients of variation calculated for all species, with males and females combined, are greatest for teeth in the canine region. Incisors tend to be somewhat less variable, and cheek teeth are the least variable. Removing the effect of sexual dimorphism, by pooling coefficients of variation calculated for males and females separately, reduces canine variability but does not alter the basic pattern. Ontogenetic development and position in functional fields have been advanced to explain patterns of variability in the dentition, but neither of these appears to correlate well with patterns documented here. We tentatively suggest another explanation. Variability is inversely proportional to occlusal complexity of the teeth. This suggests that occlusal complexity places an important constraint on relative variability within the dentition. Even when the intensity of natural selection is equal at all tooth positions, teeth with complex occlusal patterns must still be less variable than those with simple occlusion in order to function equally well. Hence variability itself cannot be used to estimate the relative intensity of selection. Low variability of the central cheek teeth ( \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm M}\frac{1}{1} $\end{document} and \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {\rm M}\frac{2}{2} $\end{document}) makes them uniquely important for estimating body size in small samples, and for distinguishing closely related species in the fossil record.