A determinação dos números de indivíduos mínimos necessários na experimentação genética

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= δ. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = δ2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { δ p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) δ { p1 (1- p2 ) / n= m δ = δ p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.

O problema técnico-econômico da adubação

The authors discuss from the economic point of view the use of a few functions intended to represent the yield y corresponding to a level xof the nutrient. They point out that under conditions of scarce capital what is actually most important is not to obtain the highest profit per hectare but the highest return per cruzeiro spent, so that we should maximize the function z = _R - C_ = _R_ - 1 , C C where R is the gross income and C the cost of production (fixed plus variable, both per hectare). Being C = M + rx, with r the unit price of the nutrient and Af the fixed cost of the crop, wo are led to the equation (M + rx)R' - rR = 0. With R = k + sx + tx², this gives a solution Xo = - Mt - √ M²t² - r t(Ms - Kr)- _____________________ rt on the other hand, with R = PyA [1 - 10-c(x + b)], x0 will be the root of equation (M + rx)cL 10 + r 10c(x + b) = 0 (12). Another solution, pointed out by PESEK and HEADY, is to maximize the function z = sx + tx² _________ m + rx where the numerator is the additional income due to the nutrient, and m is the fixed cost of fertilization. This leads to a solution x+ = - mt - √m²t² - mrst (13) _________________ rt However, we must have x+< _r_-_s_ I if we want to satisfy t _dy_ > r. dx This condition is satisfied only if we have m < _(s__-__r)² (14), - 4 t a restriction apparently not perceived by PESEK and HEADY. A similar reasoning using Mitscherlich's law leads to equation (mcL 10 + r) + cr(L 10)x - r 10cx = 0 (15), with a similar restriction. As an example, data of VIEGAS referring to fertilization of corn (maize) gave the equation y - 1534 + 22.99 x - 0. 1069 x², with x in kg/ha of the cereal. With the prices of Cr$ 5.00 per kilo of maize, Cr$ 26.00 per kilo of P2O3,. and M = Cr$ 5,000.00, we obtain x0 = 61 kg/ha of P(2)0(5). A similar reasoning using Mitscherlich's law leads to x0 = 53 kg/ha. Now, if we take in account only the fixed cost of fertilization m = Cr$ 600.00 per hectare, we obtain from (13) x+ = 51 kg/ha of P2O5, while (14) gives x+ - 41 kg/ha. Note that if m = Cr$ 5,000.00, we obtain by formula (13) x+ = 88 kg/ha of P2O5, a solution which is not valid, since condition (14) is not satisfied.

Structure-function relationships for the interleukin 2 receptor system

Receptors for interleukin 2 (IL-2) esit in at least three forms which differ in their subunit compositio, their affinity for ligand and their ability to mediate a cellular reponse. Type I receptors occur following cellular acitivation and consist of the 55,000 m. w. glycoprotein Tac. These receptors bind IL-2 with a low affinity, do not internalize ligand and have not been definitively associated with any response. Type II receptors, on the other hand, conssit of one or more glycoproteins of 70,000 m. w. which have been termed "beta ([beta]) chains." They bind IL-2 with an intermediate affinity and rapidly internalize the ligand. [Beta] proteins mediate many cellular IL-2-dependent reponses, including the short-term activation of natural killer cells and the induction of Tac protein expression. Type III receptors consist of a ternary complex of the Tac protein, the [beta] chain(s) and IL-2. They are characterized by a paricularly high affinity for ligand association. Type III receptors also internalize ligand and mediate IL-2-dependent responses at low factor concentrations. The identification of two independent IL-2-binding molecules, Tac and [beta], thus provides the elusive molecular explanation for the differences in IL-2 receptor affinity and suggests the potential for selective therapeutic manipulation of IL-2 reponses.

Cost-effectiveness analysis in Chagas' disease vectors control interventions

After a large scale field trial performed in central Brazil envisaging the control of Chagas' disease vectors in an endemic area colonized by Triatoma infestans and T. sordida the cost-effectiveness analysis for each insecticide/formulation was performed. It considered the operational costs and the prices of insecticides and formulations, related to the activity and persistence of each one. The end point was considered to be less than 90% of domicilliary unitis (house + annexes) free of infestation. The results showed good cost-effectiveness for a slow-release emulsifiable suspension (SRES) based on PVA and containing malathion as active ingredient, as well as for the pyrethroids tested in this assay-cyfluthrin, cypermethrin, deltamethrin and permethrin.

A cost-benefit analisys of chagas disease control

Chagas disease transmission can be effetively interrupted by insecticidal control of its triatomine bug vectors. We present here a simple model comparing the costs and benefits of such a programme, designed to eliminate domestic populations of Triatoma infestans throughout its known area of distribution over the seven southernmost countries of Latin America. The model has been simplified to require only four financial estimates relating to the unit cost of housing spraying and benefits due to avoidance of premature death in the acute phase of the disease, avoidance of supportive treatment and care in the chronic phase of the disease, and avoidance of corrective digestive and cardiac surgery. Exceptfor these direct medical costs, al other potential benefits have been ignored. Nevertheless, the model shows that the direct financial benefits of such a programme would far outweigh the costs, and the project would support a remarkably high internal rate of return under the least optimistic estimates.

A malaria merozoite surface protein (MSP1)-structure, processing and function

Merozoite surface protein-1 (MSP-1, also referred to as P195, PMMSA or MSA 1) is one of the most studied of all malaria proteins. The proteins. The protein is found in all malaria species investigated and structural studies on the gene indicate that parts of the molecule are well-conserved. Studies on Plasmodium falciparum have shown that the protein is in a processed form on the merozoite surface, a result of proteolytic cleavage of the large percursor molecule. Recent studies have identified some of these cleavage sites. During invasion of the new red cell most of the MSP1 molecule is shed from the parasite surface except for a small C-terminal fragment which can be detected in ring stages. Analysis of the structure of this fragment suggests that it contains two growth factor-like domains that may have a functional role.

Impaired renal function in owl monkeys (Aotus nancymai) infected with Plasmodium falciparum

Impaired renal function was observed in sixteen Aotus nancymai 25 and 3 months following infection with the Uganda Palo Alto strain of Plasmodium falciparum. Decrease were noted in the clearance of endogenous creatinine, creatinine excretion, and urine volume while increases were observed in serum urea nitrogen, urine protein, urine potassium, fractional excretion of phosphorus and potassium, and activities of urinary enzymes. The results were suggestive of glomerulonephropathy and chronic renal disease.

Dual function of eosinophils in pathogenesis and protective immunity against parasites

The functional duality of eosinophils, involved in a protective response or in pathogenesis is illustrated in various parasitic infections. In schistosomiasis, eosinophils have been shown to mediate schistosomula killing, in the presence of antibodies. The association of eosinophil-dependent cytotoxic antibody isotypes with resistance of reinfection (IgE and IgA antibodies), whereas in vitro blocking antibody isotypes (IgG4, IgM) were detected in susceptible subjects, suggested a participation of eosinophils in antibody-dependent protective response. However eosinophils could participate to granuloma formation and consequently to the pathological reactions during schistosomiasis. Activation of eosinophils by antibodies, leading to release of granule proteins have been studied in patients with filariasis. Eosinophil peroxidase, EPO was released safter IgE-dependent activation whereas Eosinophil Cationic Protein, ECP, was released after IgG- and IgA-dependent activation of eosinophils, results suggesting a process of differential release mediators. Interactions between eosinophils and interleukins, and specially IL-5 are discussed. Whereas a receptor for IL-5 has been characterized on human eosinophils, recent studies have shown that eosinophils, expressed the messenger RNA encoding IL-5. These results associated to data showing the synthesis of other cytokines indicate that eosinophils are not only the source of cytotoxic mediators involved in the effector phase of immunity but also of growth and regualtory factors, participating to immunoregulation.

A molecular genetic study of the variations in metabolic function during schistosome development

During their complex life cycle schistosomes alternate between the use of stored glycogen and reliance on host glucose to provide for their energy needs. In addition, there is dramatic variation between the relative contribution of aerobic versus anaerobic glucose metabolism during development. We have cloned a set of representative cDNAs that encode proteins involved in glucose uptake, glycolysis, Kreb's cycle and oxidative phosphorylation. The different cDNAs were used as probes to examine the expression of glucose metabolism genes during the schistosome life cycle. Steady state mRNA levels from whole cercariae, isolated cercarial tails, schistosomula and adult worms were analysed on Northern blots and dot blots which were quantified using storage phosphor technology. These studies reveal: (1) Transcripts encoding glycogen metabolic enzymes are expressed to much higher levels in cercarial tails than whole cercariae or schistosomula while the opposite pattern is found for glucose transporters and hexokinase transcripts; (2) Schistosomula contain low levels of transcripts encoding respiratory enzymes but regain the capacity for aerobic glucose metabolism as they mature to adulthood; (3) Male and female adults contain similar levels of the different transcripts involved in glucose metabolism.

From allergy to schistosomes: role of Fc receptors and adhesion molecules in eosinophil effector function

The dual function of eosinophils has been evidenced in protective immunity against parasites as well as in pathological manifestations during allergic disorders. We have demonstrated that a new class of IgE receptors, FcepsilonRII/CD23, was involved in the functional duality of eosinophils and other proinflammatory cells. More recently, we have shown that FcepsilonRI, the high affinity IgE receptor thought to be only expressed by basophils and mast cells, was involved in eosinophil-mediated cytotoxicity against schistosomes as well as in mediator release. These results favour the view that both IgE and its receptors have been primarily associated to a protective immune response, rather than to pathology. Not only IgE receptors but also members belonging to the family of adhesion molecules can participate as co-receptors in eosinophil effector function. The inhibitory role of monoclonal antibodies to LewisX (LeX, CD15) or to selectins in eosinophil-mediated cytotoxicity towards schistosomes and the detection of LeX and 'selectin-like' molecules on schistosomula surface indicate a double interaction mediated by selectins and their carbohydrate ligands between eosinophils and schistosomula. These results suggest new functions for these adhesion molecules, previously known to be involved mainly in cell infiltration.