Chemotactic collapse for the Keller-Segel model

 This work is concerned with the system (S) {u _t =Δu − χ∇ (u∇v) for x∈Ω, t>0Γ v _t =Δv+(u−1) for x∈Ω, t>0 where Γ, χ are positive constants and Ω is a bounded and smooth open set in ℝ². On the boundary ∂Ω, we impose no-flux conditions: (N) ∂u∂n =∂v∂n =0 for x∈∂ Ω, t>0 Problem (S), (N) is a classical model to describe chemotaxis corresponding to a species of concentration u(x, t) which tends to aggregate towards high concentrations of a chemical that the species releases. When completed with suitable initial values at t=0 for u(x, t), v(x, t), the problem under consideration is known to be well posed, locally in time. By means of matched asymptotic expansions techniques, we show here that there exist radial solutions exhibiting chemotactic collapse. By this we mean that u(r, t) →Aδ(y) as t→T for some T<∞, where A is the total concentration of the species. Received 9 March 1995; received in revised form 25 December 1995     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

Synthesis of disaccharide neu5Gcα(2–6)galNAcα as a spacer glycoside

The first synthesis of the Neu5Gc analogue of SiaT _n disaccharide, which can be detected in breast tumors by immunochemical methods, is reported. The regioselective sialylation of (3-trifluoroacetamidopropyl)-2-azido-2-deoxy-α-D-galactopyranoside with peracetate of the methyl ester ofN-acetoxyacetyl-neuraminic acid β-ethylthioglycoside in the presence ofN-iodosuccinimide and trifluoromethanesulfonic acid (or its trimethylsilyl ester) resulted in the derivatives of α- and β-sialyl(2→6)galactosaminide in 39 and 32% yields, respectively. The catalytic hydrogenolysis of the azido group and subsequentN- andO-acetylation of the α-anomer gave the peracetate of trifluoroacetamidopropyl glycoside. Removal of the protective groups led to glycoside Neu5Gcα2→6GalNAcα-O(CH₂)₃NH₂. Using the Neu5Gc derivative with acetoxyacetyl groups at positions O9 and O4 as a donor increases the α-selectivity of sialylation to afford the α- and β-anomers in 69 and 8% yields, respectively.     

Seasonal variation in the nitrogenase activity of aPanicum maximum var.trichoglume pasture and identification of associated bacteria

Summary The influence of seasonal variation on nitrogenase (N₂-ase) activity of undisturbed soil-plant cores ofPanicum maximum var.trichoglume was measured using the C₂H₂ reduction assay. The largest N₂-ase activity in the field, 14.7 g N ha⁻¹ day⁻¹, occurred in spring when soil moisture was high, soil temperature was low and nitrogenous fertiliser influence was at a minimum. The potential N₂-ase activity of the cores, measured under controlled conditions, reached a maximum of 27.2 g N ha⁻¹ day⁻¹ and averaged 26.3 g N ha⁻¹ day⁻¹ over the 14 month sampling period. N₂-ase activity was positively correlated (P=0.05) with field soil moisture and negatively correlated with field soil temperature (r=0.59 and −0.78 respectively). Multiple regression showed that 69% of the variation of N₂-ase activity in the field was associated with the combined effects of soil moisture and soil temperature. Nitrogen fixing bacteria were isolated from the roots ofP. maximum and based upon morphology, biochemical tests and fluorescent antibody reaction, were found to be closely related toAzospirillum lipoferum.     

Interaction of maturation delay and nonlinear birth in population and epidemic models

 A population with birth rate function B(N) N and linear death rate for the adult stage is assumed to have a maturation delay T>0. Thus the growth equation N′(t)=B(N(t−T)) N(t−T) e⁻ d ₁ T−dN(t) governs the adult population, with the death rate in previous life stages d ₁≧0. Standard assumptions are made on B(N) so that a unique equilibrium N _e exists. When B(N) N is not monotone, the delay T can qualitatively change the dynamics. For some fixed values of the parameters with d ₁>0, as T increases the equilibrium N _e can switch from being stable to unstable (with numerically observed periodic solutions) and then back to stable. When disease that does not cause death is introduced into the population, a threshold parameter R ₀ is identified. When R ₀<1, the disease dies out; when R ₀>1, the disease remains endemic, either tending to an equilibrium value or oscillating about this value. Numerical simulations indicate that oscillations can also be induced by disease related death in a model with maturation delay. Received: 2 November 1998 / Revised version: 26 February 1999     

Contribution to the probabilistic theory of neural nets: IV. Various models for inhibition

Input-output formulas are derived for a neuron upon which converge single axones of two other neurons, which are subjected to a Poisson shower, where a number of different assumptions are made concerning the mechanism of inhibition. In one assumption so-called “bilateral pre-inhibition” is considered. That is to say, both neuronsN ₁ andN ₂ may exciteN ₃, but if the stimulus of one of them follows within a certain interval σ of the other, the second stimulus is not effective. This model is essentially no different from that involving two excitatory neurons acting upon a neuron having a refractory period. Another mechanism considered involves so-called “pre-and-post” inhibition, in which if two stimuli fromN ₁ andN ₂ fall within σ,both are ineffective. This case being mathematically much more involved than the preceding, an approximation method is used for deriving the input-output formula. Previous papers of this series are denoted by I, II, and III in this paper.     

A note on imitative behavior and information

The equations for imitative behavior developed previously indicate that the imitation effect increases with the numberN ₀ of individuals in the social group. In this note it is pointed out that the above conclusion holds only for not too large values ofN ₀. The above conclusion is based on the tacit assumption that each individual is completely informed about the behavior adopted by every other individual. If, however,N ₀ becomes very large, the information per individual decreases. As a result of this, the effects of imitation either increase withN ₀ less rapidly or actually become independent ofN ₀.     

A note on abstract relational biologies

It is shown that the class of abstract block diagrams of (M, ℜ)-systems which can be constructed out of the objects and mappings of a particular subcategoryG ₀ of the categoryG of all sets depends heavily on the structure ofG ₀, and in particular on the number of sets of mappingsH(A, B) which are empty inG ₀. In the context ofG ₀-systems, there-fore, each particular categoryG ₀ gives rise to a different “abstract biology” in the sense of Rashevsky. A number of theorems illustrating the relation between the structure of a categoryG ₀ and the embeddability of an arbitrary mapping αεG ₀ into an (M, ℜ)-system are proved, and their biological implication is discussed. This research was supported by the United States Air Force through the Air Force Office of Scientific Reserch of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

15N-Determined effect of inoculation with N2 fixing bacteria on nitrogen assimilation in Western Canadian wheats

Summary A two-year field study was undertaken using¹⁵N isotope techniques to differentiate between stimulation of N uptake and N₂ fixation in Western Canadian cultivars of spring wheat (Triticum aestivum L. emend Thell) and durum (T. turgidum L. emend Bowden) in response to inoculation with N₂-fixing bacteria. Bacterial inoculation either had no effect or lowered the % N derived from the fertilizer and the fertilizer use efficiency. Despite the depression of fertilizer uptake, inoculants did not alter the relative uptake from soil and fertilizer-N pools indicating that bacterial inoculation did not alter rooting patterns. Nitrogen-15 isotope dilution indicated that N₂ fixation did occur. In 1984, % plant N derived from the atmosphere (% Ndfa) due to inoculation with Bacillus C-11-25 averaged 23.9% while that withAzospirillum brasilense ATCC 29729 (Cd) averaged 15.5%. In 1985, higher soil N levels reduced these values by approximately one-half. Cultivar x inoculant interactions, while significant, were not consistent across years. However, these interactions did not affect cultivars ‘Cadet’ and ‘Rescue’. In agreement with previous results, ‘Cadet’ performed well with all inoculants in both years while ‘Rescue’ performed poorly. Among 1984 treatments, the N increament in inoculated plants was positively correlated with % Ndfa but no such correlation existed in 1985. N₂ fixation averaged over all cultivars and strains was 17.9 and 6.7 kg N fixed ha⁻¹ in 1984 and 1985, respectively. Highest rates of N₂ fixation were estimated at 52.4 kg N ha⁻¹ for ‘Cadet’ in 1984 and 31.3 kg N ha⁻¹ for ‘Owens’ in 1985, both inoculated with Bacillus C-11-25, an isolate from southern Alberta soils. Inoculation with either ofAzospirillum brasilense strain Cd (ATCC29729) or 245 did not result in as consistent or as high N₂ fixation, suggesting that these wheats had not evolved genetic compatability with this exogenous microorganism. These agronomically significant amounts of N₂ fixation occurred under optimally controlled experimental conditions in the field. It is yet to be determined if N₂ fixation would occur in response to bacterial inoculation under dryland conditions commonly occurring in Western Canada. Contribution from Agriculture Canada Research Station, Lethbridge, Alberta, Canada.     

Mass–density relationship changes along salinity gradient in <Emphasis Type="Italic">Suaeda salsa</Emphasis> L.

Whether and why the biomass–density (M–N) scaling relationship varies along environmental gradients were continuously debated in theoretical ecology. In this study, how soil salinity stress affects on the M–N scaling relationship was investigated by using Suaeda salsa L. in beach of Dongtai, Jiangsu Province, China. The results showed that the exponent of the scaling relationship (b) of low salinity level (−1.259) was smaller than that of middle salinity level (−1.025), which in turn was smaller than that high salinity level (−0.698). The plant height–crown radius (H–r) scaling exponents (∂) decreased with increasing salinity stress, while the canopy coverage–density (C–N) scaling exponents (β) showed an inverse trend. The predict data (b) based on ∂ and β by using the geometric model were statistically indistinguishable from their observed values for the three salinity levels. Moreover, two resources utilization parameters (l mean from root to leaf, a total area of leaves) of metabolic theory, photosynthetic rate, and water-use efficiency were more advantageous to Suaeda salsa L. of high stress than to those of low salinity. Therefore, it was implied that the changes of M–N relationship along salinity gradients may be resulted from their different geometric morphologies and resource utilization in response to salinity stress.     

Prevalence of nitrous oxide reducing capacity in denitrifiers from a variety of habitats

Summary A total of 81 strains isolated by T. N. Gamble from soils from eight countries, fresh water lake sediments and nitrified poultry manure were examined for their ability to grow on N₂O as their electron acceptor, as well as for their tendency to produce N₂O from NO ₃ ⁻ in the absence and presence of acetylene. Seventy-seven of the 81 strains were confirmed as denitrifiers. Fifty-nine of the 77 strains grew on N₂O, while 12 strains produced N₂O but could not utilize it. Six strains reduced NO ₃ ⁻ to N₂ but could not grow on N₂O, suggesting that even if N₂O is always an intermediate product of denitrification, it is not always a freely diffusible intermediate. The organisms, however, would consume N₂O that accumulated early in growth and accumulated N₂O in the presence of acetylene. Thus the total number of N₂O users was 65 strains or 83% of the total tested. This implies that the N₂O reducing capacity of denitrifiers occur widely in nature. A high proportion ofPseudomonas fluorescens biotype II reduced N₂O. The accumulation of N₂O from NO ₃ ⁻ in the presence of acetylene provides strong evidence that N₂O is generally an intermediate in denitrification as well as provides additional support for the usefulness of this chemical as a general inhibitor of N₂O reduction.     

Biologically based risk estimation for radiation-induced CML

Chronic myeloid leukemia (CML) invites biologically based radiation risk modeling because CML is simultaneously well-understood, homogeneous and prevalent. CML is known to be caused by a translocation involving the ABL and BCR genes, almost all CML patients have the BCR-ABL translocation, and CML is prevalent enough that its induction is unequivocally detected among Hiroshima A-bomb survivors. In a previous paper, a linear-quadratic-exponential (LQE) dose- response model was used to estimate the lifetime excess risk of CML in the limit of low doses of γ-rays, R _γ. This estimate assumed that BCR-ABL translocation dose- response curves in stem cells for both neutrons and γ-rays, differ only by a common proportionality constant from dicentric aberration dose-response curves in lymphocytes. In the present paper we challenge this assumption by predicting the BCR-ABL dose response. The predictions are based on the biophysical theory of dual radiation action (TDRA) as it applies to recent BCR-to-ABL distance data in G₀ human lymphocytes; this data shows BCR and ABL geometric distributions that are not uniform and not independent, with close association of the two genes in some cells. The analysis speaks against the previous proportionality assumption. We compute 11 plausible LQE estimates of R _γ, 2 based on the proportionality assumption and 9 based on TDRA predictions. For each estimate of R _γ we also compute an associated estimate of the number of CML target cells, N; the biological basis of the LQE model allows us to form such estimates. Consistency between N and hematological considerations provides a plausibility check of the risk estimates. Within the group of estimates investigated, the most plausible lifetime excess risk estimates tend to lie near R _γ=0.01 Gy^–1, substantially higher than risk estimates based on the proportionality assumption. Received: 10 August 2000 / Accepted: 20 December 2000     

Galerkin-Ritz procedures for approximate solutions to systems of reaction-diffusion equations

For any essentially nonlinear system of reaction-diffusion equations of the generic form ∂c_i/∂t=D_i∇²c_i+Q_i(c,x,t) supplemented with Robin type boundary conditions over the surface of a closed bounded three-dimensional region, it is demonstrated that all solutions for the concentration distributionn-tuple function c=(c ₁(x,t),...,c _n (x,t)) satisfy a differential variational condition. Approximate solutions to the reaction-diffusion intial-value boundary-value problem are obtainable by employing this variational condition in conjunction with a Galerkin-Ritz procedure. It is shown that the dynamical evolution from a prescribed initial concentrationn-tuple function to a final steady-state solution can be determined to desired accuracy by such an approximation method. The variational condition also admits a systematic Galerkin-Ritz procedure for obtaining approximate solutions to the multi-equation elliptic boundary-value problem for steady-state distributions c=−c(x). Other systems of phenomenological (non-Lagrangian) field equations can be treated by Galerkin-Ritz procedures based on analogues of the differential variational condition presented here. The method is applied to derive approximate nonconstant steady-state solutions for ann-species symbiosis model.     

Biological nitrogen fixation: A key to world protein

Summary 1. Characteristics and methodology of the C₂H₂-C₂H₄ assay forin situ measurement of N₂ fixation are outlined. 2. Electron micrographic analysis of the developmental morphology of the natural soybean symbiosis and C₂H₂-C₂H₄ analysis indicate that increasing N₂-fixing activity from 12–35 days of age is accompanied by an increase in bacteroid number per cell, bacteroid number per vesicle and inclusions per bacteroid. The mole ratio of leghemoglobin to nitrogenase also increases from 50 to a relatively constant plateau of 500 to 1500 during this period. The quantitative validity of the C₂H₂-C₂H₄ assay as a measure of N₂ fixation during a complete growth cycle of soybeans on nitrogen-free medium is demonstrated by Σ (C₂H₂→C₂H₄)×28/3 values which are 75–95% of the values determined for N₂ fixed by Kjeldahl analyses. 3. A technique for the establishment of the first callus N₂-fixing symbiosis in mixed cultures ofRhizobium legume provides a defined experimental system for exploration of legume symbiosis. N₂-fixing activity is about 1% of the natural system and is influenced by exogenous auxins and cytokinins. Morphology, including infection threads and vesicle enclosed bacteroids, is similar to the nodule system. 4. N₂-fixing activity of field-grown soybeans, including varieties which differed in flowering characteristics and maturity dates, and of peanuts was determined biweekly with the C₂H₂-C₂H₄ assay. Activity extended from nodule initiation to senescence and correlated with the nitrogen demands of the plant and in most cases >90% of the N₂ fixed during the 60–70 day period of fruit formation and maturation. A logarithmic relationship between N₂-fixing activity and age, and N₂ fixed and age was demonstrated as a fundamental characteristic of these annual symbionts,i.e. log N₂ fixed =k(t−t ₀), wheret ₀ is age at activity initiation. The resultant parameters: 1) age at activity initiation, 2) calculated rate of daily increase (7–9% for soybeans and 7–10% for peanuts), 3) age at end of logarithmic phase (about 80 days for soybeans), and 4) total N₂ fixed (about 250 mg per soybean plant) are useful bases for evaluation of environmental, bacterial and host effects on N₂ fixation. Various N fertilizers applied at planting and flowering inhibited N₂ fixation of soybeans by decreasing the rate of daily increase. 5. Physical and chemical characteristics of nitrogenase, including those of crystalline Mo-Fe protein, reactions of nitrogenase, and model studies are consistent with a proposed mechanism. 6. Potential utilities of N₂ fixation research include increased food protein production via initially enhanced N₂ fixation of legumes such as soybeans and eventually extension of N₂-fixing symbioses to non-legumes and new chemistry of N₂, including the direct incorporation of aerial N₂ into important organic compounds. Contribution No. 1748.     

15N-determined dinitrogen fixation potential of genetically diverse bean lines (Phaseolus vulgaris L.)

Improvement of dinitrogen fixation in beans (Phaseolus vulgaris L.) will depend on the selection of superior plant genotypes and the presence of efficient rhizobial strains. This study was conducted to evaluate diverse bean lines for N₂ fixation potential using the¹⁵N-depleted dilution technique under field conditions in Wisconsin, USA. Plants of 21 bean lines and three non-nodulating isolines of soybean received appliin Wisconsin, USA. Plants of 21 bean lines and three non-nodulating isolines of soybean received applications of¹⁵N-depleted ammonium sulphate. Shoots harvested at the V₆, R₃ and R₇ stages and dry seeds were analyzed for total N using the Kjeldahl procedure, and the ratio of¹⁵N to¹⁴N was determind on a MAT 250 mass spectrometer. Nodule occupancy of the applied strain ofR. leguminosarum biovarphaseoli, CIAT 899, was determined in five of the bean lines. Total shoot N content showed a pattern of accumulation similar to shoot dry weight and fixed N₂ in the shoot. Based on shoot total N, N₂ fixed in the shoot and shoot dry weight Riz 30 and Preto Cariri were identified as being as good fixers as Puebla 152 and Cargamanto appear to begin N₂ fixation early. Furthermore, some bean lines that fixed considerable N₂ did not translocate a large amount of N to the grains. Preto Cariri accumulated 21.2 kg N ha⁻¹ in the seeds compared to Puebla 152 which accumulated 43.8 kg N ha⁻¹ of the fixed N₂ into the grains. At the early sampling, Puebla 152 and 22–27 had a considerable higher percentage of their crown nodules formed by the inoculant strain CIAT 899, than did Rio Tibagi which has been considered a poor N₂ fixer.     

Trade-off relationships between some reproductive characteristics in plants with special reference to life history stragegy

Several reproductive triats in plants were studied in more than 200 populations of 61 wild species from diverse ecological conditions. As a result, it was found that there occur three distinct types of plants in the energy allocation patterns to reproductive structures (RA) and the propagule output per plant (P_N), i.e. (1) the number of propagules per plant increases in response to the increase in RA (Type I), (2) the number of propagules decreases in response to the increase in RA (Type II), and (3) the RA remains constant despite the great differences in the propagule number per plant. A conspicuous trade-off relationship was also discovered to occur between the RA to a single propagule (R_A) and the propagule output per plant (P_N), such that log R_A=logC−blot P_N, or R_A=C/P_N ^b =CP_N ^−b , where C is a constant. The three different ranges ofb-values were recognized, i.e.b<1.0,b>1.0, andb=1.0, which correspond to Type I, Type II, and Type III, respectively. Related problems to the concept ofr- andK-strategy are also discussed.     

Kinetic processes initiated by a nanosecond high-current discharge in hot air

Results from numerical investigations of kinetic processes initiated by a pulsed nanosecond discharge in hot (T ₀ ≥ 1000 K) air at atmospheric pressure are presented. The calculated results on the dynamics of the electron density, the population of the N₂(B³Π _g ) and N₂(C³Π _u ) states, and the atomic oxygen density in the axial discharge region agree with experiment. The method for determining the gas temperature by measuring the rotational structure of the transitions N₂(C³Π _u , ν) → N₂(B³Π _g , ν′) of the 2⁺ nitrogen system is analyzed. It is shown that, in relatively weak reduced electric fields typical of secondary discharge pulses, the electron impact excitation of the N₂(C³Π _u ) state from the ground state N₂(X¹Σ _g ⁺) can be accompanied by its additional step population from the N₂(B³Π _g ), N₂(a′Σ _u ⁻), and other electronic states. This effect substantially influences the rotational distribution of nitrogen molecules in the N₂(C³Π _u , ν) state; moreover, the temperature determined from this distribution can be substantially higher than the true gas temperature.     

Mathematical biology of social behavior: III

A society composed of individuals each of whom can perform one of two mutually exclusive activitiesR ₁ andR ₂ is considered. The tendency toward the performance of those activities is measured by the intensities ε₁ and ε₂ of excitation of two corresponding neural centers, which cross-inhibit each other. It follows from the theory developed by H. D. Landahl that an individual with ε₁ − ε₂ = 0, that is one who has no preference for either one of the two activities, will on the average performR ₁ andR ₂ with equal probability. As ε₁ − ε₂ increases, the probabilityP ₁ ofR ₁ increases, tending to 1. As ε₂ − ε₁ increases, the probabilityP ₂ ofR ₂ increases, tending to 1. We haveP ₁+P ₂=1. The effect of imitation is now studied. The total number of individuals in the society which exhibits an activityR ₁ at a given time is considered as constituting a stimulus which increases ε₁. Similarly, the total number of individuals which exhibits activityR ₂ at a given time constitutes a stimulus which increases ε₂. Using the standard equations of the mathematical biophysics of the central nervous system, equations are established which govern the behavior of such a society and the following conclusions are reached. It the quantity ε₁ − ε₂ is distributed in the society in such a way that the distribution function is symmetric with respect to ε₁ − ε₂ = 0, then on the average one-half of the population exhibitsR ₁, the other halfR ₂. This social configuration may, however, be unstable. The slightest accidental excess of individuals exhibiting, for example,R ₁, may bring it into a stable configuration, in which most individuals exhibitR ₁, and only a smaller fraction exhibitR ₂. A slight initial deviation in favor ofR ₂ brings it into a stable configuration, in which most individuals exhibitR ₂. Thus in this case there may be two stable configurations. If the population is in one of those stable configurations, and the distribution function of ε₁ − ε₂ is made asymmetric, favoring the other activity, the population will pass into a stable configuration, in which that other activity is predominant, if the asymmetry of the distribution exceeds a threshold value. By making some drastic simplifications the equations derived here may be reduced to a form which waspostulated by the author previously in his mathematical theory of human relations.     

Hückel framework study on the superconducting vibronic interaction in (AB) N chains

Superconducting vibronic interaction in the vibronic superconductivity motif has been studied in the Hückel framework for (AB) _N chain systems. Within the on-site and nearest-neighbor approximation a new vibronic constant, /L, has been introduced, of which the importance has been discussed. The effect of the vibronic operator, , has also been studied. It is also concluded that the size-dependence of the superconducting vibronic interaction also exists in the (AB) _N chain systems.On leave from the Changchun Institute of Applied Chemistry, Academia Sinica, Changchun, P. R. China, as an STA fellowship awardee hosted by the Institute of Physical and Chemical Research of Japan.     

Measurement of N2 fixation in maize (Zea mays L.)—ricebean (Vigna umbellata [Thunb.] Ohwi and Ohashi) intercrops

The yield of N in maize (Zea mays L.) and ricebean (Vigna umbellata [Thumb.] Ohwi and Ohashi) were compared on a Tropoqualf soil in North Thailand in 1984 and 1985. Both species were grown in field plots in monoculture or as intercrops at a constant planting density equivalent to 8 maize or 16 ricebean plants per m². The contribution of symbiotic N₂ fixation to ricebean growth was estimated from measurements of the natural abundance of¹⁵N (δ¹⁵N) in shoot nitrogen and from analysis of ureides in xylem sap vacuumextracted from detached stems. The natural abundance of¹⁵N in the intercropped ricebean was found to be considerably less than that in monoculture in both growing seasons. Using maize and a weed (Ageratum conyzoides L.) as non-fixing¹⁵N reference plants the proportions (P ¹⁵N) of ricebean shoot N derived from N₂ fixation ranged from 0.27 to 0.36 in monoculture ricebean up to 0.86 when grown in a 75% maize: 25% ricebean intercrop. When glasshouse-derived calibration curves were used to calculate plant proportional N₂ fixation (Pur) from the relative ureide contents of field collected xylem exudates, the contribution of N₂ fixation to ricebean N yields throughout the 1985 growing season were greater in intercrop than in monocrop even at the lowest maize:legume ratio (25∶75). Seasonal patterns of sap ureide abundance indicated that N₂ fixation was greatest at the time of ricebean podset. The averagePur andP ¹⁵N in ricebean during the first 90 days of growth showed identical rankings of monocrop and intercrop treatments in terms of N₂ fixation, although the two sets ofP values were different. Nonetheless, seasonal estimates of N₂ fixation during the entire 147 days of legume growth determined from ureide analyses indicated that equivalent amounts of N could be fixed by ricebean in a 75∶25 intercrop and in monoculture despite the former being planted at one-quarter the density.