Maternal HIV-1 viral load and vertical transmission of infection: the Ariel Project for the prevention of HIV transmission from mother to infant.

Most HIV-1 infections of children result from mother-to-infant transmission, which may occur perinatally or postnatally, as a consequence of breast feeding. In this study, the influence of maternal viral load on transmission of infection to infants from non-breast-feeding mothers was examined using samples of plasma and peripheral blood mononuclear cells (PBMCs) collected at several time points during pregnancy and the 6-month period after delivery. These samples were analyzed by several quantitative methods, including virus cultures of PBMCs and polymerase chain reaction (PCR) assays for HIV-1 RNA in plasma and DNA in PBMCs. The risk of transmission increased slightly with a higher viral load, but transmission and nontransmission occurred over the entire range of values for each assay. No threshold value of virus load was identified which discriminated between transmitters and nontransmitters. We also noted a significant rise in viral load and a decline in CD4+ lymphocytes in the six months after delivery. These findings suggest that a high maternal viral load is insufficient to fully explain vertical transmission of HIV-1. Additional studies are needed to examine the post-partum increase in viremia.

The decay of the latent reservoir of replication-competent HIV-1 is inversely correlated with the extent of residual viral replication during prolonged anti-retroviral therapy.

Replication-competent HIV-1 can be isolated from infected patients despite prolonged plasma virus suppression by anti-retroviral treatment. Recent studies have identified resting, memory CD4+ T lymphocytes as a long-lived latent reservoir of HIV-1 (refs. 4,5). Cross-sectional analyses indicate that the reservoir is rather small, between 103 and 107 cells per patient. In individuals whose plasma viremia levels are well suppressed by anti-retroviral therapy, peripheral blood mononuclear cells containing replication-competent HIV-1 were found to decay with a mean half-life of approximately 6 months, close to the decay characteristics of memory lymphocytes in humans and monkeys. In contrast, little decay was found in a less-selective patient population. We undertook this study to address this apparent discrepancy. Using a quantitative micro-culture assay, we demonstrate here that the latent reservoir decays with a mean half-life of 6.3 months in patients who consistently maintain plasma HIV-1 RNA levels of fewer than 50 copies/ml. Slower decay rates occur in individuals who experience intermittent episodes of plasma viremia. Our findings indicate that the persistence of the latent reservoir of HIV-1 despite prolonged treatment is due not only to its slow intrinsic decay characteristics but also to the inability of current drug regimens to completely block HIV-1 replication.

Risk assessment of recent Egyptian H5N1 influenza viruses.

Highly pathogenic avian influenza (HPAI) viruses of the H5N1 subtype are enzootic in poultry populations in different parts of the world, and have caused numerous human infections in recent years, particularly in Egypt. However, no sustained human-to-human transmission of these viruses has yet been reported. We tested nine naturally occurring Egyptian H5N1 viruses (isolated in 2014-2015) in ferrets and found that three of them transmitted via respiratory droplets, causing a fatal infection in one of the exposed animals. All isolates were sensitive to neuraminidase inhibitors. However, these viruses were not transmitted via respiratory droplets in three additional transmission experiments in ferrets. Currently, we do not know if the efficiency of transmission is very low or if subtle differences in experimental parameters contributed to these inconsistent results. Nonetheless, our findings heighten concern regarding the pandemic potential of recent Egyptian H5N1 influenza viruses.

Design and analysis of serial limiting dilution assays with small sample sizes.

We study the design of serial limiting dilution assays (SLDAs) for estimation of effector cell frequency in settings that restrict severely the amount of material available for assay, and for which the assumption of a single-hit Poisson model is reasonable. For different designs (that is, dilution factor, number of dilution levels, and number of replicates at each level), we evaluate maximum likelihood and minimum chi-square estimators, using four quantitative criteria: probability of a non-informative assay (PNI), bias, coefficient of variation (CV), and mean squared error (MSE). Our results are exact, not simulation-based, nor approximations. We found that differences between these two estimators were insubstantial by comparison with the effect on the estimators of the experimental design. Bias was severe in small assays, and could lead, in extremely small designs, to overestimation of effector frequency by as much as 100%. These four criteria provide a rigorous basis for determining the most effective apportionment of total effort among replicates and dilution levels. By increasing the dilution factor and favoring the number of replicates over the number of dilution levels, the PNI is reduced while bias, CV and MSE are increased; and vice versa. Our study is easily extended to estimation of the density of biologically active particles per volume. It can also be extended to alternatives to the single-hit Poisson model for a serial limiting dilution assay.

A profile of functionally impaired elderly persons living in the community.

The Health Care Financing Administration, in cooperation with other agencies of the Department of Health and Human Services, conducted surveys in 1982 and 1984 designed to develop a better understanding of the number and circumstances of functionally impaired elderly persons living in the community. This report is based on data from the 1982 Long-Term Care Survey. There were approximately 5 million functionally impaired elderly persons living in the community in 1982. The data show that functionally impaired persons in the community are older, are more often female, have lower incomes, and have a larger proportion of black people than the general elderly population. The data also provide baseline information on what functional impairments are prevalent among them, what means they use to cope with the limitations, and from whom they receive help. The baselines data gathered in 1982 will be supplemented by longitudinal data gathered in the 1984 Long-Term Care Survey.

Effects of concentration and composition of wet corn gluten feed in steam-flaked corn-based finishing diets.

Two finishing experiments were conducted to determine the effects of concentration (Exp. 1) and composition of wet corn gluten feed (Exp. 2) in steam-flaked corn-based diets on feedlot steer performance. In Exp. 1, 192 English x Continental crossbred steer calves (299 +/- 0.6 kg) were used in a completely randomized design with six dietary treatments (four pens per treatment). Treatments were six concentrations of wet corn gluten feed (Sweet Bran, Cargill Inc., Blair, NE; 0, 10, 20, 25, 30, and 35%) replacing steam-flaked corn (DM basis). All diets contained 10% corn silage, 5% supplement, and 3.5% tallow (DM basis). Gain efficiency and ADG were similar (P > 0.25) among treatments. Dry matter intake was lower (P < 0.10) with 0% wet corn gluten feed than with concentrations of 20, 25, and 35% WCGF. Dry matter intake did not differ among treatments containing wet corn gluten feed. In Exp. 2, 160 English x Continental crossbred steer calves (315 +/- 0.6 kg) were used in a completely randomized design with five dietary treatments (four pens/treatment). Treatments were assigned based on four ratios of steep to corn bran/germ meal mix in wet corn gluten feed plus a negative control (CON). Wet corn gluten feed was fed at 25% of the dietary DM and was made by mixing steep and corn bran/germ meal into the diet. The four concentrations of steep in wet corn gluten feed that comprised the ratios were 37.5, 41.7, 45.8, and 50% (DM basis), with the remaining proportion being the bran/germ meal mix. Bran/germ meal mix was comprised of 60% dry corn bran, 24% germ meal, and 16% fine-cracked corn (DM basis). All diets contained 10% corn silage, 5% supplement, and 3.5% tallow (DM basis). Daily gain did not differ (P = 0.18) among treatments. Gain efficiency did not differ between CON and 50% steep; however, G:F was decreased (P < 0.05) for concentrations of 37.5, 41.7, and 45.8% steep compared with CON. A linear improvement (P < 0.05) was observed for G:F as concentration of steep increased as a proportion of wet corn gluten feed. These data suggest that wet corn gluten feed can be used at concentrations up to 35% of the dietary DM without adversely affecting performance, and that steep has more energy than bran/germ meal in steam-flaked corn-based diets.

Effect of organic matter addition to the pen surface and pen cleaning frequency on nitrogen mass balance in open feedlots.

Three finishing trials were conducted to determine the effects of dietary manipulation and management on N losses from open feedlots. In each experiment, 96 steers were assigned randomly to 12 nutrient balance pens. In Trial 1, calves were fed for 180 d during the winter/spring months; in Trial 2, yearlings were fed for 132 d in the summer. In Trials 1 and 2, N losses from pens were compared directly by adding OM to the pen surface or indirectly by feeding digestible ingredients designed to increase OM excretion. The dietary treatment (BRAN) included 30% corn bran (DM basis) replacing dry-rolled corn. Pens where OM was directly added received sawdust applications (SAWDUST) at a rate to match OM excretion from the BRAN diet. These two treatments were compared with a conventional, 75% dry-rolled corn diet (CON). Because CON and SAWDUST diets were identical, performance for both treatments was similar during Trials 1 and 2. The BRAN diet decreased (P < 0.10) gain efficiency during Trials 1 and 2 by 9.5% relative to CON. Fecal N excretion was greater (P < 0.01) for calves and yearlings when BRAN was fed compared with CON. Adding OM to the pen surface increased (P < 0.01) the amount of N in manure removed from pens and reduced (P < 0.10) N losses in Trial 1. Nitrogen losses were not significantly different among treatments in Trial 2. In Trial 3, calves were fed for 166 d during the winter/spring months. A 2 x 2 factorial design was used to evaluate pen cleaning frequency and diets similar to CON and BRAN. Pens were either cleaned monthly or once at the end of the feeding period. Daily DMI was greater (P = 0.01) and ADG was lower (P < 0.01) when cattle were fed BRAN compared with CON. Responses from all three trials indicate a negative effect of BRAN on gain efficiency. Dietary treatment and cleaning frequency interacted for N balance in the feedlot. Nitrogen losses decreased and manure N increased (P < 0.10) for cattle fed BRAN compared with CON when pens were cleaned monthly. Feeding BRAN did not affect total manure N, but resulted in higher N losses when pens were cleaned only once. For all trials, BRAN increased the amount of N remaining in composted manure. Adding OM to pen surfaces and/or cleaning pens more frequently may decrease N losses from open feedlot pens and from compost, although responses seem influenced by ambient temperature or season.

Effect of corn bran and steep inclusion in finishing diets on diet digestibility, cattle performance, and nutrient mass balance.

One metabolism trial and 2 finishing trials were conducted to evaluate the effects of adding corn bran and steep liquor (steep) in replacement of dry-rolled corn (DRC) on diet digestibility, cattle performance, and nutrient mass balance in open feedlot pens. The metabolism trial (Exp. 1) used 8 ruminally cannulated heifers in a 4 × 4 Latin square design and the 2 finishing trials used 128 steer calves fed for 167 d (Exp. 2) and 256 yearling steers fed for 126 d (Exp. 3). Dietary treatments for all trials included a DRC-based control (CON), 30% corn bran (30/0), 30% corn bran plus 15% steep (30/15), and 45% corn bran plus 15% steep (45/15), in which by-products replaced DRC and molasses in the diet (DM basis). Diets were not isonitrogenous or isoenergetic. In the metabolism trial, feeding the by-product diets produced greater rumen pH (5.95) than CON (5.76; P < 0.01). Total tract DM and OM digestibility were greater for heifers fed CON than the by-product diets (P < 0.01). Dry matter and NDF ruminal disappearance (%/h) of corn bran were numerically less for cattle fed the CON diet than the by-product diets (2.36 vs. 2.84 and 0.72 vs. 1.66, respectively). In the performance trials, steers fed the by-product diets consumed more DM (P = 0.06) and G:F was either similar for all diets in Exp. 2 (P = 0.56) or less for cattle fed 30/0 than the other diets in Exp. 3 (P = 0.05). Percent N loss was reduced in Exp. 2 by including corn bran in diets compared with CON (P < 0.01). However, in Exp. 3, no differences in percent N loss were detected among treatments (P = 0.16), but more N was removed in the manure from pens where steers were fed by-products (P = 0.01). Although steep did not improve diet digestibility, it was beneficial in maintaining cattle performance in the feedlot studies. Feeding corn bran in combination with steep increased manure N removed and N in compost, but decreased percent N lost during the winter months only.

Phosphorus requirement and excretion of finishing beef cattle fed different concentrations of phosphorus.

Phosphorus is an expensive nutrient to supplement, and excess may lead to manure P challenges. Therefore, minimizing dietary P to meet requirements is important. Two experiments were conducted to determine the P requirement of finishing cattle (Exp. 1) and to evaluate the effects of feeding different P concentrations on the quantity and route of P excretion (Exp. 2). In Exp. 1, 60 heifers (BW = 278 kg +/- 17 kg) were individually fed 1 of 5 dietary P concentrations (0.10, 0.17, 0.24, 0.31, or 0.38% P). Cattle performance, plasma P concentration, bone characteristics, and bone P concentration were used to determine the P requirement. Intake and ADG increased quadratically (P < 0.01) as dietary P increased. Plasma P in heifers receiving the 0.10% treatment was less (P < 0.01) than the other treatments and suggested that these heifers were experiencing a P deficiency. Total ash weight of the phalanx bones increased linearly (P < 0.01) as dietary P increased. In Exp. 2 using a 5 x 5 Latin square design, 5 different diets varying in P concentration (0.12, 0.27, 0.42, 0.30, and 0.36% P) were fed to steers to evaluate route and quantity of P excreted. Steers excreted little (1.78 g/d on average) P in the urine as a percentage of total P excretion. Steers on the 0.12% P diet excreted very little P in urine (0.50 g/d). Excretion of P was less (P < 0.05) for the cattle fed 0.12% P compared with all other treatments. Results from cattle performance, plasma P concentrations, and bone characteristics indicate that the heifers fed 0.10% P were experiencing a deficiency and the P requirement of finishing heifers is between 0.10 and 0.17% P. Dietary P concentrations of 0.10 to 0.17% P resulted in decreased P excretion. Supplementation of mineral P is unnecessary in grain-based feedlot diets because dietary P will greatly exceed the requirements (<0.17%).

Effect of supplemental energy source and frequency on growing calf performance.

Crossbred heifers (n = 120; 265 kg, SD = 37) were fed individually (84 d) to determine the effect of supplement type, concentration, and frequency on intake and performance and to estimate the energy value of dry distillers grains plus solubles (DDGS) in a high-forage diet. Treatments were arranged in a 3 x 2 x 2 factorial, with 3 supplements, 2 concentrations, and 2 frequencies of supplementation. Supplements including dry-rolled corn (DRC), DRC with corn gluten meal (DRC + CGM), and DDGS were fed at 0.21% (LOW) or 0.81% (HIGH) of BW daily and were provided daily (DAILY) or 3 times weekly (ALT). Heifers were fed to consume grass hay (8.7% CP) ad libitum. Individual DMI, diet composition, BW, and ADG were used to calculate energy values for DDGS and DRC. Supplement type, concentration, frequency, and interactions were tested using the MIXED procedure of SAS, with BW included as a covariate. Supplement x concentration interactions for gain (P = 0.01) and G:F (P < 0.01) were detected. At the LOW concentration, heifers supplemented with DDGS gained more and were more efficient (P /= 0.22) between DDGS and DRC + CGM in HIGH treatments, although both improved (P

Wet corn gluten feed and alfalfa hay levels in dry-rolled corn finishing diets: effects on finishing performance and feedlot nitrogen mass balance.

One-hundred ninety-two crossbred steers (initial BW = 351 +/- 11 kg) were used to determine the effects of removing alfalfa hay (AH) from dry-rolled corn-based diets containing wet corn gluten feed (WCGF) on animal performance and nutrient (N and OM) mass balance in open feedlot pens. Steers were stratified by weight and assigned randomly to 24 pens (2 x 3 factorial) and fed for 132 d from June to October 2002. Experimental diets contained either 0 or 35% WCGF and 0, 3.75, or 7.5% AH, and were formulated to be isonitrogenous. For efficiency of gain, an interaction occurred (P = 0.09) between AH and WCGF. Feed efficiencies of cattle fed 35% WCGF were improved 4.4% (P = 0.10) compared with efficiencies of cattle fed no WCGF at 0% AH; there was a marked improvement in ADG for cattle fed WCGF compared with no WCGF in diets with 0% AH. Within 35% WCGF diets, efficiency decreased as AH inclusion increased (P = 0.06). Efficiency was equal across AH levels when 0% WCGF was fed; however, ADG was decreased when AH was removed. Interactions between AH and WCGF were not detected for other performance or carcass criteria; therefore, main effects of AH and WCGF are discussed. Daily intake, ADG, and HCW increased linearly (P < 0.05) as dietary AH level increased. Feeding 35% WCGF also resulted in greater DMI (P < 0.01) and a tendency for greater ADG and HCW (P < or = 0.10) compared with steers fed no WCGF. Interactions between AH and WCGF were not observed for feedlot N mass balance. As level of AH increased across diets, N intake, N retention, and N excretion increased (P < 0.05). Steers fed 35% WCGF consumed and excreted more N (P < 0.01) than those fed no WCGF. More manure DM (P = 0.11), OM, and N (P < 0.01) were removed from pens housing steers fed 35% WCGF as well as greater OM and N recovery in finished compost. More N (kilogram/steer) was also lost to volatilization as a result of greater N excretion when WCGF was fed. Expressed as a percentage of N excretion, loss of N from pens housing steers fed 0 and 35% WCGF was not different, averaging nearly 80%. These data suggest that AH has less value when dry-rolled corn-based diets contain 35% WCGF and can be decreased from conventional levels. Furthermore, loss of N from open feedlot pens is high during the summer months, and feeding WCGF may not reduce N losses during these times of year.

Influence of corn hybrid traits on digestibility and the efficiency of gain in feedlot cattle.

Two experiments were conducted to determine the influence of chemical and physical corn kernel traits on digestibility and feedlot cattle performance. Seven commercially available corn hybrids representing a range in kernel traits were evaluated for a variety of chemical and physical traits that included test weight, 1,000-grain weight, kernel size, starch, CP, amylose, Stenvert Hardness tests (kernel hardness traits), tangential abrasive dehulling device loss, 12-h in vitro starch disappearance, and rate and extent of in situ DM disappearance. Differences among hybrids existed for all physical kernel traits measured. In Exp. 1, 224 steers in 28 pens were fed the same hybrids for 167 d in a completely randomized design. All diets were formulated to have 12.5% CP and contained 66% dry-rolled corn (DM basis). There were no differences (P >0.20) among corn hybrids for DMI, ADG, or carcass characteristics. However, efficiency of gain (G:F) was influenced by hybrid (P < 0.01) with a difference of 9.5% from the least to the most efficient. In Exp. 2, 7 ruminally cannulated heifers were used in a 7 x 7 Latin square design to determine the effects of these hybrids on nutrient digestibility, VFA concentrations, and ruminal pH. Total-tract OM and starch digestibilities were not different (P >0.15) among hybrids and averaged 77.9 and 95.1%, respectively. Differences (P < 0.05) among hybrids existed for ruminal propionate concentration and the acetate to propionate ratio. Kernel hardness traits correlated (P < 0.05) with G:F were 1,000-grain weight (r = -0.81), Stenvert time to grind (r = -0.83), and the proportion of Stenvert soft to coarse particle height (r = 0.83). Propionate concentration was not correlated (r = 0.45) with G:F but was correlated (P = 0.02) to the Stenvert time to grind (r = -0.83). Cattle fed dry-rolled corn hybrids with greater proportions of soft endosperm had greater concentrations of propionate and gained more efficiently than cattle fed hybrids with a harder endosperm. Selecting for these softer kernel traits may improve the efficiency of gain in feedlot cattle.

Optimal wet corn gluten and protein levels in steam-flaked corn-based finishing diets for steer calves.

A feeding trial evaluated the hypothesis that wet corn gluten feed would improve growth performance of cattle fed steam-flaked corn-based finishing diets and supply required degradable intake protein (DIP). The trial used 360 steer calves (initial BW = 288 +/- 11 kg) housed in 36 pens for 166 d in an incomplete 4 x 3 factorial arrangement of treatments. Pens of steers were assigned to treatments according to a completely randomized design (four replicates per treatment combination). Treatments were wet corn gluten feed (0, 20, 30, or 40% of dietary DM) and CP (13.0, 13.7, or 14.4% of dietary DM) via supplemental urea as DIP. The 0% wet corn gluten feed treatment included only the 13.7% CP diet, and the 40% wet corn gluten feed treatment included only the 13.7 and 14.4% CP diets. Final dietary DIP concentration was 9.0% for 0% wet corn gluten feed; 8.7, 9.5, and 10.2% for 20% wet corn gluten feed; 9.0, 9.7, and 10.3% DIP for 30% wet corn gluten feed; and 10.0 and 10.6% for 40% wet corn gluten feed. Hot carcass weight, ADG, DMI, and G:F responded quadratically (P < or = 0.05) to wet corn gluten feed. The 20, 30, and 40% wet corn gluten feed treatments increased ADG by 7, 6, and 3% and increased DMI by 4, 5, and 5%, respectively, relative to the 0% wet corn gluten feed treatment. Feed efficiency was 102, 101, and 98% of the 0% wet corn gluten feed treatment for 20, 30, and 40% wet corn gluten feed, respectively. Hot carcass weight, ADG, and G:F increased linearly (P < or = 0.05) in response to increased DIP. Nonlinear analysis for DIP over the combined 20 and 30% wet corn gluten feed treatments indicated a DIP requirement of 9.6% of DM for ADG and 9.2% of DM for G:F, corresponding to 14.6 and 14.3% CP for 20% wet corn gluten feed and 14.8 and 14.5% CP for 30% wet corn gluten feed, respectively. Fat thickness, marbling, LM area, and USDA yield grade were not affected (P = 0.12 to 0.99) by wet corn gluten feed or CP. These results show that the inclusion rate of wet corn gluten feed for maximizing ADG and G:F in steam-flaked corn-based finishing diets is approximately 20% of DM. The DIP requirement determined in this trial averaged 9.4% of DM.

Assessment of inhomogeneities in an E. coli physical map.

A statistical method based on r-fragments, sums of distances between (r + 1) consecutive restriction enzyme sites, is introduced for detecting nonrandomness in the distribution or too markers in sequence data. The technique is applicable whenever large numbers of markers are available and will detect clumping, excessive dispersion or too much evenness of spacing of the markers. It is particularly adapted to varying the scale on which inhomogeneities can be detected, from nearest neighbor interactions to more distant interactions. The r-fragment procedure is applied primarily to the Kohara et al. (1) physical map of E. coli. Other applications to DAM methylation sites in E. coli and NotI sites in human chromosome 21 are presented. Restriction sites for the eight enzymes used in (1) appear to be randomly distributed, although at widely differing densities. These conclusions are substantially in agreement with the analysis of Churchill et al. (3). Extreme variability in the density of the eight restriction enzyme sites cannot be explained by variability in mono-, di- or trinucleotide frequencies.

A multistage model for the action of cytotoxic T lymphocytes in multicellular conjugates.

We propose a multistage stochastic model to explain data on the kinetics of target cell lysis by cytotoxic T lymphocytes in multicellular conjugates. A novel feature of our model is that we explicitly consider both the lethal hitting stage and the target cell disintegration stage of the cytolytic process. Further, we allow for the possibility that target cell disintegration is itself a complex process composed of many events. The comparison of our model with the data of other investigators suggests that cytotoxic T cells deliver lethal hits at random to undamaged target cells. Having received a lethal hit, the target cell disintegrates over a variable length of time. The disintegration times of target cells from different conjugates appear to be randomly distributed and to be consistent with a model in which disintegration occurs by at least two major, sequential, rate-limiting events. For conjugates containing one lymphocyte and multiple target cells, the mean rate at which a lethally hit target cell disintegrates is found to be independent of the total number of target cells in the conjugate. Our model predicts that in such multicellular conjugates, individual target cells lyse one by one, on average at approximately 30-min intervals, thus agreeing closely with previously reported experimental observations.

Aggregation of cell surface receptors by multivalent ligands.

Using a combination of branching processes and kinetic equations a solution is provided to the problem of describing the size of aggregates formed on cell surfaces when multivalent ligands bind and cross-link multivalent receptors. A criterion is given for the onset of gelation in infinite 2-dimensional systems, which may be relevant to the phenomenon of ligand-induced receptor patching.

Renewal theory, Geiger counters, and the maximum number of receptors bound to a randomly haptenated polymer chain.

Polymers containing small chemical groups (haptens) covalently attached at random along the chain are commonly used to initiate an immune response. Properties of the polymer such as its length, the spacing of the haptens, and the total number of haptens along the chain, correlate with its immune reactivity. Here we model the ability of many finite-sized cell surface receptors to bind simultaneously the haptens conjugated to a polymer chain. The binding sites on two different receptors or on separate parts of a multivalent receptor cannot be arbitrarily close to one another; so, in general, not all haptens along a polymer chain can be simultaneously bound by receptors. We develop an analogy between the steric hindrance among receptors detecting randomly placed haptens and the temporary locking of a Geiger counter that has detected a radioactive decay. Using renewal theory, we compute the probability distribution, and its moments, for the maximum number of haptens that can be simultaneously bound by monovalent receptors. We also model flexible bivalent receptors and obtain the mean and variance of the maximum number of receptors bound to randomly haptenated polymers, and the mean and variance of the maximum number of haptens bound. We demonstrate the importance of our results by applying them to immunological data and showing that, for polymers used in immunology, the effective valence of a polymer may be as much as 50% smaller than its nominal valence.