Motecutar Microbiotogy (1992) 6(4), 555-562 A theoretical and experimental analysis of bacterial growth in the bladder David M. Gordon''' and Margaret A. Svanborg-Eden, 1978). There are severat different Department of Zoology, University of f\/lassachusetts. adhesin proteins expressed in E. coli. such as those Amherst. Massachusetts 01003, USA. encoded by the pap (eyetonephritis-associated Qiti), prs (eap-retated sequence), pilC, and afa/operons (Arthur et ai, 1989; Katlenius et ai,, 1982; Labigne-Roussett and Summary Falt^ow, 1988; O'tHantey etai. 1985; Ptos etai. 1989). A mathematical model of human micturition dyna- The potentiat rote of btadder hydrodynamics on the mics and bacterial growth predicts the population etimination of bacteria from the btadder has tong been growth rate required for a bladder infection to recognized (Boen and Sytwester, 1965; Cox and Hinman, become established in the absence of adhesin-medi- 1961; Dugdale, 1969; Hinman. 1968; Hinman and Cox. ated surface growth. Escherichia co//strains isolated 1966; Mact^intosh et ai, 1975a,b; O'Grady and Cattelt. from the urinary tract have significantly higher in 1966). tt has been suggested that without adhesin-medi- vitro growth rates in urine than strains isolated from ated surface growth E. co//coutd not overcome the tosses the intestinal flora. The results suggest that, for E. due to micturition, and hence could not estabtish poputa- coli isolated from the urinary tract, adhesin-mediated tions in the urinary tract (Arthur ef ai, 1989; Reid and surface growth may not be required for infections to Sobet. 1987; Svanborg-Eden, 1978). tmpticit in this become established and persist. The growth-rate dif- hypothesis is the suggestion that the growth rate of E. coti ferences observed between urinary tract and Intesti- in urine is insufficient to overcome these tosses. nal isolates suggests that the ability to survive and The purpose of this study was to determine if E. coii is efficiently utilize the resources available in urine is an abte to cotonize the human bladder in the absence of important adaptation for E. coli inhabiting the urinary adhesion. First, we present a mathematicat modet of tract. • - human micturition dynamics and bacteriat growth. The modet represents a 'worst-case scenario'; it assumes that there is no surface growth. The model predicts the growth Introduction rate required for the estabtishment and maintenance of Escherichia coii is the species responsible for most bacte- bacterial poputations in the btadder in the absence of rial urinary tract infections in humans (Svanborg-Eden, adhesion. We then determine the in vitro growth rates, in 1978). Atthougti the commensat intestinat flora have been urine, of E. coii isotated from the intestinal ftora and uri- impticated as the prinnary reservoir of infection (Boltgren nary tract infections. and Winberg. 1976; Caugant. 1983; Turck et ai, 1962; Vosti etai, 1964), certain properties are observed among Results urinary tract strains of E. co//that are not prevalent among intestinat isotates. tjrinary tract isotates have higher fre- A modei of bacterial grov\nh in the biadder quencies of O and K antigens, haemotysin production, The modet predicts the fate of a smatl number of bacteria aerobactin retease. serum resistance and adhesins that have succeeded in reaching the btadder. We assume (Arthur et ai., 1989; Doofson et ai, 1973; Glynn e^ ai, that the bladder fitis at a constant rate A, (mt h"^). fvlicturi- 1971; Kaijserefa/., 1977;Orsf<ov etai. 1971; Ptos etai. tion occurs when the amount of urine in the btadder 1989). Of these properties, adhesins are thought to be reaches a fixed volume, \/, (ml). Fottowing micturition critical, the possession of which enables E. coti fo colo- there is a residuat amount of urine remaining in the btad- nize the urinary tract (Arthur etai.. 1989; Plos etai, 1989; der, Vf, (ml). Thus the volume of urine in the btadder at time nhrough the period between micturitions is Received 17 June. 1991: revised 28 October, 1991; accepted 11 Novem V{t)=V,^U ber, 1991. Present addresses: t'nstitute of Parasitology. McGill Univer- sity. Macdofiald Campus, 21111 Lakeshore Road, St Anne de Bellevue, We assume that the bacteria in the urine exist as ran- Quebec. Canada H9X ICO; :^Osborn Memorial Laboratories. Yale Univer- sity, New Haven. Connecticut 06511, USA. *Fof correspondence. Tel domty distributed ptant<tonic cetIs; there is no surface (203) 432 3875: Fax (203) 432 3854. growth. We atso assume that the bacteriat population 556 D.M. Gordon and A/f. A. Riley The establishment condition states that the number of bacteria produced between micturition events must exceed the number that are tost due to micturition. The number of bacteria produced is a function of their growth rate and the time availabte for growth to occur. The dura- tion of the growth period is determined by the rate of urine production and the amount of urine that accumulates in the btadder between micturitions. Figure 1 presents growth rate (y) extinction-establish- ment boundaries as a function of ftow rate {X), and maxi- 0 15 30 45 60 75 90 105 128 135 IS Urine Flow Rate (mt/h) mum (V^) and residuat (VJ btadder votumes. If ttie bacte- riat poputation has a growth rate which ties above a boundary it witt estabtish a poputation. When the poputa- tion growth rate ties betow a boundary the bacterial popu- tation witt not increase its numbers and witt eventuatty be 03 wastied out of the btadder. To infer the growtti rate B Establishment required for estabtishment of an E. coii poputation in ttie IT human btadder requires a t^nowtedge of typicat micturition dynamics in humans. IO tn heatthy adutts, normat urine production ranges from Extinction 1-2 titres per day, resulting in ftow rates (X.) that span "0 0.0025 0005 00075 O01 00125 0015 00175 0 OS" 40-80 mt h"^ (Mundy etai., 1984). tWicturition resutts in tVlinimum / Maximum Btadder Votume the retease of 200-400 mt of urine (V^) (tVlundy et ai., Fig. 1. The growth rate extinction-establishment boundary for bacterial 1984). The votume (V^) of urine remaining in the bladder populations as a function of human micturition dynamics. If the bacterial foltowing micturition is about 1 mt (Shand etal, 1968). growth rate lies below the boundary the baderia will fail to establish; if Figure la presents ttie growth-rate boundary for a above, the population will estabtish and be maintained. A, Effect of the rate of urine production (/,) on the boundary. Residual range of ftow rates white assuming that 300 mt of urine is bladder volume (V,,) was 1 ml and maximum btadder volume (I/,) was released at micturition (V,) and 1 mt remains (V^). This 300 ml. figure ittustrates that the growth rate required for estab- B. Effect of the ratio of residual :maximum bladder volume on the boundary. The flow rate (X) was 60 ml h~'. tishment is a tinear function of the rate of urine production (k). Figure 1b demonstrates the effect of residuat votume (expressed as ttie fraction V^fV^) on the growth-rate grows at a constant rate \\> (h ^). The vatidity of this boundary. The ftow rate was 60 ml h^' and V^ was 300 ml. assumption in ttie context of the modet is demonstrated in This figure shows that, except for very smalt vatues of V^. a tater section of this paper, tn the time between micturi- a change in residuat volume has tess effect on the growth tions, ttie number of bacteria in the btadder is given by rate required for establishment than an equivatent per cent change in the urine ftow rate (X). Rates of urine production (X) and the amount of urine where NQ is the number of bacteria present in the residuat produced at micturition (V^) normatty vary for a number of urine. Ttiese two equations specify our modet. and with reasons. To investigate the effect of this variation on the these we can determine the condition for estabtishment. estabtishment condition, modifications were made to the That is, given the dynamics of urine ftow through the blad- basic modet. The modifications consisted of atlowing vari- der, we can ast^ what growth rate the bacteriat poputation ation in either the amount of urine voided at micturition must exhibit in order to estabtish and persist in the blad- (V^), or ttie rate of urine production (X) during the intervals der, assuming no adhesion. between micturitions. Vatues of I/, or X were setected ran- The intervat T(h) between micturition events is domly from a normat distribution with a given mean and T={V,-V,)/X. standard deviation. The simutations were initiated witti Let Nh be the number of bacteria remaining in the btadder 100 cetts present in the btadder. Estabtishment occurred after the k[U micturition. Then if the number of bacteria grew to exceed 10'' cetls. and extinction occurred if the poputation dectined to less ttian 10 celts. Ttie parameter vatues used were: Vn=^ mt, The bacterial poputation is growing if, and onty if, l/;,= 300 mt and ?. = 60 ml h"V In simulations examining ^^;>Nh. that is when the effect of variation in X, 60 mt h"' represented ttie or mean ftow rate, while V^ was hetd constant at 300 mt. The Bacteriat growth in the bladder 557 or 120 mt, a growth rate of 1.2 h '' was required for more than 50% of the simulations to result in estabtishment. The resutts show that random variation in X or I/, can resutt in estabtishment even when the growth rate is tess than required and that this occurs more often as the varia- tion in X or V^ increases. tHowever, in att cases the proba- bitity of estabtishment increases as the growth rate increases.