Exact digital simulation of time-invariant linear systems with applications to neuronal modeling

An efficient new method for the exact digital simulation of time-invariant linear systems is presented. Such systems are frequently encountered as models for neuronal systems, or as submodules of such systems. The matrix exponential is used to construct a matrix iteration, which propagates the dynamic state of the system step by step on a regular time grid. A large and general class of dynamic inputs to the system, including trains of δ-pulses, can be incorporated into the exact simulation scheme. An extension of the proposed scheme presents an attractive alternative for the approximate simulation of networks of integrate-and-fire neurons with linear sub-threshold integration and non-linear spike generation. The performance of the proposed method is analyzed in comparison with a number of multi-purpose solvers. In simulations of integrate-and-fire neurons, Exact Integration systematically generates the smallest error with respect to both sub-threshold dynamics and spike timing. For the simulation of systems where precise spike timing is important, this results in a practical advantage in particular at moderate integration step sizes. Received: 3 October 1998 / Accepted in revised form: 19 March 1999     

On the comparative static properties of the expected population density in the presence of stochastic fluctuations

We consider the impact of increased stochastic fluctuations on the expected density of an unstructured population evolving according to a regular diffusion process subject to a concave expected growth rate. By relying on the flow nature of the solutions of stochastic differential equations and Girsanovs theorem, we demonstrate that typically increased volatility decreases the expected future population density. As a consequence, we are able to characterize the sensitivity of the expected population density with respect to changes in the diffusion coefficient measuring the size of the stochastic fluctuations. We provide both qualitative and quantitative information about the consequences of a mis-specified volatility structure and, especially, of a deterministic approximation to stochastic population growth. We also consider the effect of uncertainty in the initial density and demonstrate that the sign of the relationship between the expected population density and initial uncertainty is unambiguosly negative. Received: 15 February 1999 / Revised version: 29 September 1999 / Published online: 5 May 2000     

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.     

The Validity of Quasi-Steady-State Approximations in Discrete Stochastic Simulations

In biochemical networks, reactions often occur on disparate timescales and can be characterized as either fast or slow. The quasi-steady-state approximation (QSSA) utilizes timescale separation to project models of biochemical networks onto lower-dimensional slow manifolds. As a result, fast elementary reactions are not modeled explicitly, and their effect is captured by nonelementary reaction-rate functions (e.g., Hill functions). The accuracy of the QSSA applied to deterministic systems depends on how well timescales are separated. Recently, it has been proposed to use the nonelementary rate functions obtained via the deterministic QSSA to define propensity functions in stochastic simulations of biochemical networks. In this approach, termed the stochastic QSSA, fast reactions that are part of nonelementary reactions are not simulated, greatly reducing computation time. However, it is unclear when the stochastic QSSA provides an accurate approximation of the original stochastic simulation. We show that, unlike the deterministic QSSA, the validity of the stochastic QSSA does not follow from timescale separation alone, but also depends on the sensitivity of the nonelementary reaction rate functions to changes in the slow species. The stochastic QSSA becomes more accurate when this sensitivity is small. Different types of QSSAs result in nonelementary functions with different sensitivities, and the total QSSA results in less sensitive functions than the standard or the prefactor QSSA. We prove that, as a result, the stochastic QSSA becomes more accurate when nonelementary reaction functions are obtained using the total QSSA. Our work provides an apparently novel condition for the validity of the QSSA in stochastic simulations of biochemical reaction networks with disparate timescales.     

A Michaelis-Menten-style model for the autocatalytic enzyme prostaglandin H synthase

Prostaglandin H synthase (PGHS) is an autocatalytic enzyme which plays a key role in the arachidonic acid metabolic pathway. PGHS mediates the formation of prostaglandin H₂, the precursor for a number of prostaglandins which are important in a wide variety of biological processes, including inflammation, blood clotting, renal function, and tumorigenesis. Here we present a Michaelis-Menten-style model for PGHS. A stability analysis determines when the reaction becomes self-sustaining, and can help explain the regulation of PGHS activity in vivo. We also consider a quasi-steady-state approximation (QSSA) for the model, and present conditions under which the QSSA is expected to be a good approximation. Applying the QSSA for this model can be useful in computationally intensive modeling endeavors involving PGHS.     

Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth

In this paper we examine spatio-temporal pattern formation in reaction-diffusion systems on the surface of the unit sphere in 3D. We first generalise the usual linear stability analysis for a two-chemical system to this geometrical context. Noting the limitations of this approach (in terms of rigorous prediction of spatially heterogeneous steady-states) leads us to develop, as an alternative, a novel numerical method which can be applied to systems of any dimension with any reaction kinetics. This numerical method is based on the method of lines with spherical harmonics and uses fast Fourier transforms to expedite the computation of the reaction kinetics. Numerical experiments show that this method efficiently computes the evolution of spatial patterns and yields numerical results which coincide with those predicted by linear stability analysis when the latter is known. Using these tools, we then investigate the r?le that pre-pattern (Turing) theory may play in the growth and development of solid tumours. The theoretical steady-state distributions of two chemicals (one a growth activating factor, the other a growth inhibitory factor) are compared with the experimentally and clinically observed spatial heterogeneity of cancer cells in small, solid spherical tumours such as multicell spheroids and carcinomas. Moreover, we suggest a number of chemicals which are known to be produced by tumour cells (autocrine growth factors), and are also known to interact with one another, as possible growth promoting and growth inhibiting factors respectively. In order to connect more concretely the numerical method to this application, we compute spatially heterogeneous patterns on the surface of a growing spherical tumour, modelled as a moving-boundary problem. The numerical results strongly support the theoretical expectations in this case. Finally in an appendix we give a brief analysis of the numerical method. Received: 27 July 2000 / Revised version: 15 August 2000 / Published online: 16 February 2001     

How to predict diffusion of medium-sized molecules in polymer matrices. From atomistic to coarse grain simulations

The normal diffusion regime of many small and medium-sized molecules occurs on a time scale that is too long to be studied by atomistic simulations. Coarse-grained (CG) molecular simulations allow to investigate length and time scales that are orders of magnitude larger compared to classical molecular dynamics simulations, hence providing a valuable approach to span time and length scales where normal diffusion occurs. Here we develop a novel multi-scale method for the prediction of diffusivity in polymer matrices which combines classical and CG molecular simulations. We applied an atomistic-based method in order to parameterize the CG MARTINI force field, providing an extension for the study of diffusion behavior of penetrant molecules in polymer matrices. As a case study, we found the parameters for benzene (as medium sized penetrant molecule whose diffusivity cannot be determined through atomistic models) and Poly (vinyl alcohol) (PVA) as polymer matrix. We validated our extended MARTINI force field determining the self diffusion coefficient of benzene (2.27·10⁻⁹ m² s⁻¹) and the diffusion coefficient of benzene in PVA (0.263·10⁻¹² m² s⁻¹). The obtained diffusion coefficients are in remarkable agreement with experimental data (2.20·10⁻⁹ m² s⁻¹ and 0.25·10⁻¹² m² s⁻¹, respectively). We believe that this method can extend the application range of computational modeling, providing modeling tools to study the diffusion of larger molecules and complex polymeric materials.     

Subharmonic resonance and chaos in forced excitable systems

 Forced excitable systems arise in a number of biological and physiological applications and have been studied analytically and computationally by numerous authors. Existence and stability of harmonic and subharmonic solutions of a forced piecewise-linear Fitzhugh-Nagumo-like system were studied in Othmer ad Watanabe (1994) and in Xie et al. (1996). The results of those papers were for small and moderate amplitude forcing. In this paper we study the existence of subharmonic solutions of this system under large-amplitude forcing. As in the case of intermediate-amplitude forcing, bistability between 1 : 1 and 2 : 1 solutions is possible for some parameters. In the case of large-amplitude forcing, bistability between 2 : 2 and 2 : 1 solutions, which does not occur in the case of intermediate-amplitude forcing, is also possible for some parameters. We identify several new canonical return maps for a singular system, and we show that chaotic dynamics can occur in some regions of parameter space. We also prove that there is a direct transition from 2 : 2 phase-locking to chaos after the first period-doubling bifurcation, rather than via the infinite sequence of period doublings seen in a smooth quadratic interval map. Coexistence of chaotic dynamics and stable phase-locking can also occur. Received: 6 July 1998 / Revised version: 2 October 1998     

Efficient production of medium-chain-length poly(3-hydroxyalkanoates) from octane by Pseudomonas oleovorans: economic considerations

Poly(3-hydroxyalkanoates) (PHA) have the potential to become a biodegradable alternative for conventional plastics. In order to produce PHA at competitive costs in comparison with commonly used plastics, efficient PHA production systems will have to be developed. Poly(3-hydroxybutyrate) fermentations are well developed and in actual use on an industrial scale; medium-chain-length PHA (mcl-PHA) production is less well described, although the vast majority of all PHA known today are mcl-PHA. This paper compares and describes mcl-PHA production systems with respect to the volumetric productivity, the cellular PHA content and the polymer yield on carbon substrates. Nitrogen was shown to be the most effective limitation to trigger PHA formation in P. oleovorans after different nutrient limitations had been compared. By using an economic model for the calculation of PHA production costs, we show that it should be possible to produce octane-based mcl-PHA on a large scale (more than 1000 tonnes/year) at costs below U.S. $ 10 kg⁻¹. Received: 4 April 1997 / Accepted: 20 May 1997     

Mathematical modeling of the onset of capillary formation initiating angiogenesis

It is well accepted that neo-vascular formation can be divided into three main stages (which may be overlapping): (1) changes within the existing vessel, (2) formation of a new channel, (3) maturation of the new vessel. In this paper we present a new approach to angiogenesis, based on the theory of reinforced random walks, coupled with a Michaelis-Menten type mechanism which views the endothelial cell receptors as the catalyst for transforming angiogenic factor into proteolytic enzyme in order to model the first stage. In this model, a single layer of endothelial cells is separated by a vascular wall from an extracellular tissue matrix. A coupled system of ordinary and partial differential equations is derived which, in the presence of an angiogenic agent, predicts the aggregation of the endothelial cells and the collapse of the vascular lamina, opening a passage into the extracellular matrix. We refer to this as the onset of vascular sprouting. Some biological evidence for the correctness of our model is indicated by the formation of teats in utero. Further evidence for the correctness of the model is given by its prediction that endothelial cells will line the nascent capillary at the onset of capillary angiogenesis. Received: 27 May 1999 / Revised version: 28 December 1999 / Published online: 16 February 2001     

Scaling food chains in aquatic mesocosms: do the effects of depth override the effects of planktivory?

To assess the effects of physical dimension and planktivorous fish on phytoplankton standing crop, we repeated an experiment at different scales in plastic enclosures during summer 1995 in Lake Créteil, France. Enclosures were scaled for a constant surface (1.5 × 1.5 m) as depth was increased from 2.5 to 4.5 m. Even-link (zooplankton and phytoplankton) and odd-link (planktivorous fish, zooplankton and phytoplankton) food webs were established in both shallow and deep enclosures. Fish densities in the deep enclosures were scaled to allow comparisons with shallow ones for both in individuals m⁻² or individuals m⁻³. We explicitly designed this experiment to examine the scale-dependent behavior of the top-down mechanism of algal biomass control in lakes, and in particular to test the hypothesis of stronger cascading effects of fish on lower trophic levels at reduced depth. Both fish and enclosure size had highly significant effects on phytoplankton biomass over the duration of the experiment. No depth × fish interaction effects were observed. The presence of planktivorous fish enhanced phytoplankton biomass in both shallow and deep enclosures, although the reduction in depth generally produced a stronger effect. The mean concentration of chlorophyll a in the deep odd-link systems (ca 5 mg m⁻³) was lower than in the shallow even-link systems (ca 17 mg m⁻³). Statistical interpretation did not change when data were expressed as phytoplankton biomass per unit of surface area. Light limitation and zooplankton grazing are the most probable mechanisms explaining our results in these nutrient-enriched systems. Moreover, we found that the strength of the cascading effect of fish on plankton was not a function of depth. We believe that further studies on scaling effects should be conducted in order to improve our understanding of ecological patterns and to extrapolate results from micro/mesocosms to natural ecosystems. Received: 18 January 1999 / Accepted: 7 June 1999     

Third-order reverse correlation analysis of muscle spindle primary afferent fiber responses to random muscle stretch

 The response of primary muscle spindle afferent fibers to muscle stretch is nonlinear. Now spindle responses (trains of action potentials) to band-limited Gaussian white noise length perturbations of the gastrocnemius muscles (input signal) are described in cats. The input noise upper cutoff frequency was clearly above the frequency range of physiological length changes in cat hindleg muscles. The input–output relation was analyzed by means of peri-spike averages (PSAs), which could be shown to correspond to the kernels of Wiener’s white noise approach to systems identification. The present approach (the reverse correlation analysis) was applied up to the third order. An experiment consisted of two recordings: one (the source recording) to determine PSAs and the other (the test recording) to provide an input signal for predicting responses. The predictions of different orders were compared with the actual neuronal response (the observation) of the test recording. Four different approximation procedures were developed to adapt prediction and observation and to determine weighting factors for the predictions of different orders. The approximations also yielded the value of the power density P of the input noise signal: at a variety of stimulus parameters, P from approximations had the same magnitude as P determined directly from the input signal amplitude spectrum. The prediction of a sequence of action potentials improved the higher the order of components. 37 of 42 action potentials of a test recording (the observation) could be confidently predicted from PSAs or kernels. Compared with the size of the linear first-order prediction curve, the relative sizes of the second and third-order prediction curves were: 1.0 : 0.47 : 0.26. Received: 15 November 1994/Accepted in revised form: 23 May 1995     

Influence of long-latency reflex modulation on the performance of quick adjustment movements

The effect of long-latency reflex modulation on the performance of a quick adjustment movement following a muscle stretch was studied in 26 healthy male subjects. When the subjects felt a sudden angle displacement in the direction of a wrist extension they were required to make an adjustment movement by moving a handlebar, held in the hand, to align with a target position as quickly and as accurately as possible. The index of performance (adjustment time) was the time taken to move the handle to the target position from stretch onset. A DC torque motor was used to evoke electromyographic (EMG) reflex responses on a wrist flexor. Averaging of the rectified EMG, recorded from surface electrodes placed over the flexor, showed short- and long-latency reflexes (M1 and M2 components). For all subjects, the amplitudes of the reflex components decreased during the adjustment movement because the target position for this study was fixed to the extension side of the wrist joint. The decrease in the M2 component, which is considered to be a transcortical reflex, was significantly larger than the decrease in the M1 component, which is spinal reflex. The main finding was of a positive correlation between the length of adjustment time and the degree of reduction of M1 and M2 with the adjustment movement (r = 0.602 for M1, P < 0.01; r = 0.850 for M2, P < 0.001). Moreover, there were correlations between the consistency of the voluntary response onset and the degree of M2 decrease (r = 0.577, P < 0.01), and between the consistency of the voluntary response onset and the length of the adjustment time (r = 0.603, P < 0.01). Therefore, we have concluded that the subjects who were able to perform adjustment movements within a short time could modulate the long-latency reflex of the muscle involved in such movements in order to make the function of their voluntary muscle activity more effective, and thus were able to respond appropriately. Accepted: 19 February 1997     

Process development for high-level secretory production of carboxypeptidase Y by Saccharomyces cerevisiae

In order to develop a production process for carboxypeptidase Y (CPY, yeast vacuolar protease) secreted by Saccharomyces cerevisiae KS58-2D, medium composition, culture conditions, and expression systems were investigated. We found that the addition of histidine to thiamine-free medium, in which CPY production was almost negligible, raised the intracellular thiamine level, resulting in the increase of CPY production. On the basis of the choice of an expression system that uses an inducible GAL10 promoter, reassessment of histidine concentration in the medium, and optimization of the pH level during cultivation (pH 6.5), active CPY was secreted in a quantity of over 400 mg/l, which was more than tenfold that higher than that previously reported. The process developed could be easily scaled-up to industrial-scale fermentation. Received: 16 January 1998 / Received revision: 16 February 1998 / Accepted: 27 February 1998     

Fracture mechanics of the cell wall of Chara corallina

Previous mechanical studies using algae have concentrated on cell extension and growth using creep-type experiments, but there appears to be no published study of their failure properties. The mechanical strength of single large internode cell walls (up to 2 mm diameter and 100 mm in length) of the charophyte (giant alga) Chara corallina was determined by dissecting cells to give sheets of cell wall, which were then notched and fractured under tension. Tensile tests, using a range of notch sizes, were conducted on cell walls of varying age and maturity to establish their notch sensitivity and to investigate the propagation of cracks in plant cell walls. The thickness and stiffness of the walls increased with age whereas their strength was little affected. The strength of unnotched walls was estimated as 47 ± 13 MPa, comparable to that of some grasses but an order of magnitude higher than that published for model bacterial cellulose composite walls. The strength was notch-sensitive and the critical stress intensity factor K _1c was estimated to be 0.63 ± 0.19 MNm^−3/2, comparable to published values for grasses. Received: 4 April 2000 / Accepted: 21 July 2000     

Analysis of recurrent cortico-basal ganglia-thalamic loops for working memory

 We analyse a simplified form of the frontal lobe architecture of cortico-basal ganglia-thalamo-cortical loops to determine the manner in which they can learn temporal sequences as part of working memory activity. In particular, we consider how the temporal duration of activity can arise in this setting. We start from a hard-wired version in which temporally extended activity is created by the `long' loop of cortex → basal ganglia → thalamus → cortex, and show it arises from a near saddle-node bifurcation. The manner in which the transition between patterns occurs is also considered. This is then extended to analyse the temporal sequence storage and regeneration abilities of trained networks with a similar architecture. The temporal dynamics of this activity is also analysed. Implications of this for other working memory activities and for understanding the architecture of the frontal lobes are discussed in conclusion. Received: 12 April 1999 / Accepted in revised form: 5 November 1999     

Turing instabilities in general systems

We present necessary and sufficient conditions on the stability matrix of a general n(≥2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing bifurcation. The necessary (kinetic) condition, requiring that the system be composed of an unstable (or activator) and a stable (or inhibitor) subsystem, and the sufficient condition of sufficiently rapid inhibitor diffusion relative to the activator subsystem are established in three theorems which form the core of our results. Given the possibility that the unstable (activator) subsystem involves several species (dimensions), we present a classification of the analytically deduced Turing bifurcations into p (1 ≤p≤ (n− 1)) different classes. For n = 3 dimensions we illustrate numerically that two types of steady Turing pattern arise in one spatial dimension in a generic reaction-diffusion system. The results confirm the validity of an earlier conjecture [12] and they also characterise the class of so-called strongly stable matrices for which only necessary conditions have been known before [23, 24]. One of the main consequences of the present work is that biological morphogens, which have so far been expected to be single chemical species [1–9], may instead be composed of two or more interacting species forming an unstable subsystem. Received: 21 September 1999 / Revised version: 21 June 2000 / Published online: 24 November 2000     

Specificity of resistance training responses in neck muscle size and strength

This study examined hypertrophy after head extension resistance training to assess which muscles of the complicated cervical neuromuscular system were used in this activity. We also determined if conventional resistance exercises, which are likely to evoke isometric action of the neck, induce generalized hypertrophy of the cervical muscle. Twenty-two active college students were studied. [mean (SE) age, weight and height: 21 (1) years, 71 (4) kg and 173 (3) cm, respectively]. Subjects were assigned to one of three groups: RESX (head extension exercise and other resistance exercises), RES (resistance exercises without specific neck exercise), or CON (no training). Groups RESX (n = 8) and RES (n = 6) trained 3 days/week for 12 weeks with large-muscle mass exercises (squat, deadlift, push press, bent row and mid-thigh pull). Group RESX also performed three sets of ten repetitions of a head extension exercise 3 days/week with a load equal to the 3 × 10 repetition maximum (RM). Group CON (n = 8) was a control group. The cross-sectional area (CSA) of nine individual muscles or muscle groups was determined by magnetic resonance imaging (MRI) of the cervical region. The CSA data were averaged over four contiguous transaxial slices in which all muscles of interest were visible. The 3 × 10 RM for the head extension exercise increased for RESX after training [from 17.9 (1.0) to 23.9 (1.4) kg, P < 0.05] but not for RES [from 17.6 (1.4) to 17.7 (1.9)␣kg] or CON [from 10.1 (2.2) to 10.3 (2.1) kg]. RESX showed an increase in total neck muscle CSA after training [from 19.5 (3.0) to 22.0 (3.6) cm², P < 0.05], but RES and CON did not [from 19.6 (2.9) to 19.7 (2.9)␣cm² and 17.0 (2.5) to 17.0 (2.4) cm², respectively]. This hypertrophy for RESX was due mainly to increases in CSA of 23.9 (3.2), 24.0 (5.8), and 24.9 (5.3)% for the splenius capitis, and semispinalis capitis and cervicis muscles, respectively. The lack of generalized neck muscle hypertrophy in RES was not due to insufficient training. For example, the CSA of their quadriceps femoris muscle group, as assessed by MRI, increased by 7 (1)% after this short-term training (P < 0.05). The results suggest that: (1) the splenius capitis, and semispinalis capitis and cervicis muscles are mainly responsible for head extension; (2) short-term resistance training does not provide a sufficient stimulus to evoke neck muscle hypertrophy unless specific neck exercises are performed; and (3) the postural role of head extensors provides modest loading in bipeds. Accepted: 15 October 1996     

A bispecific single-chain antibody directed against EpCAM/CD3 in combination with the cytokines interferon α and interleukin-2 efficiently retargets T and CD3+CD56+ natural-killer-like T lymphocytes to EpCAM-expressing tumor cells

 Cytokine-induced killer cells (CIK), generated in vitro from peripheral blood mononuclear cells (PBMC) by addition of interferon γ (IFNγ), interleukin-2 (IL-2), IL-1 and a monoclonal antibody (mAb) against CD3, are highly efficient cytotoxic effector cells with the CD3⁺CD56⁺ phenotype. In this study, we evaluated whether the cytotoxicity of these natural-killer-like T lymphocytes against the colorectal tumor cell line HT29 can be enhanced by the addition of a bispecific single-chain antibody (bsAb) directed against EpCAM/CD3. For determination of bsAb-redirected cellular cytotoxicity we used a new flow-cytometric assay, which directly counts viable tumor cells and can assess long-term cytotoxicity. We found that this bsAb induced distinct cytotoxicity at a concentration above 100 ng/ml with both PBMC and CIK at an effector-to-target cell ratio as low as 1:1. CIK cells revealed higher bsAb-redirected cytotoxicity than PBMC. Cellular cytotoxicity appeared after 24 h whereas PBMC showed the highest bsAb-redirected cytotoxicity after 72 h. The addition of the cytokines IL-2 and IFNα but not granulocyte/macrophage-colony-stimulating factor enhanced bsAb-redirected cytotoxicity of both PBMC and CIK. When the bsAb was combined with the murine mAb BR55-2, which recognizes the Lewis^y antigen, bsAb-redirected cytotoxicity was partly augmented, whereas murine mAb 17-1A, which binds to EpCAM as well, slightly suppressed bsAb-redirected cytotoxicity induced by the bsAb. We conclude that CIK generated in vitro or in vivo combined with this new EpCAM/CD3 bsAb and the cytokine IL-2 should be evaluated for the treatment of EpCAM-expressing tumors. Received: 9 December 1999 / Accepted: 18 May 2000