Mouse Prion Protein Polymorphism Phe-108/Val-189 Affects the Kinetics of Fibril Formation and the Response to Seeding: EVIDENCE FOR A TWO-STEP NUCLEATION POLYMERIZATION MECHANISM*

Prion diseases are fatal neurodegenerative disorders associated with the polymerization of the cellular form of prion protein (PrP^C) into an amyloidogenic β-sheet infectious form (PrP^Sc). The sequence of host PrP is the major determinant of host prion disease susceptibility. In mice, the presence of allele a (Prnp^a, encoding the polymorphism Leu-108/Thr-189) or b (Prnp^b, Phe-108/Val-189) is associated with short or long incubation times, respectively, following infection with PrP^Sc. The molecular bases linking PrP sequence, infection susceptibility, and convertibility of PrP^C into PrP^Sc remain unclear. Here we show that recombinant PrP^a and PrP^b aggregate and respond to seeding differently in vitro. Our kinetic studies reveal differences during the nucleation phase of the aggregation process, where PrP^b exhibits a longer lag phase that cannot be completely eliminated by seeding the reaction with preformed fibrils. Additionally, PrP^b is more prone to propagate features of the seeds, as demonstrated by conformational stability and electron microscopy studies of the formed fibrils. We propose a model of polymerization to explain how the polymorphisms at positions 108 and 189 produce the phenotypes seen in vivo. This model also provides insight into phenomena such as species barrier and prion strain generation, two phenomena also influenced by the primary structure of PrP.     

Prion protein and susceptibility to kainate-induced seizures

Prion protein (PrP) is a cell surface glycoprotein which is required for susceptibility to prion infection and disease. However, PrP is expressed in many different cell types located in numerous organs. Therefore, in addition to its role in prion diseases, PrP may have a large variety of other biological functions involving the nervous system and other systems. We recently showed that susceptibility to kainate-induced seizures differed in Prnp^−/− and Prnp^+/+ mice on the C57BL/10SnJ background. However, in a genetic complementation experiment a PrP expressing transgene was not able to rescue the Prnp^+/+ phenotype. Thus the apparent effect of PrP on seizures was actually due to genes flanking the Prnp^−/− gene rather that the Prnp deletion itself. We discuss here several pitfalls in the use of Prnp^−/− genotypes expressed in various mouse genetic backgrounds to determine the functions of PrP. In particular, the use of Prnp^−/− mice with heterogeneous mixed genetic backgrounds may have weakened the conclusions of many previous experiments. Use of either co-isogenic mice or congenic mice with more homogeneous genetic backgrounds is now feasible. For congenic mice, the potential problem of flanking genes can be mitigated by the use of appropriate transgene rescue experiments to confirm the conclusions.     

Implications of prion polymorphisms

The sequence of a host’s prion protein (PrP) can affect that host’s susceptibility to prion disease and is the primary basis for the species barrier to transmission. Yet within many species, polymorphisms of the prion protein gene (Prnp) exist, each of which can further affect susceptibility or influence incubation period, pathology and phenotype. As strains are defined by these features (incubation period, pathology, phenotype), polymorphisms may also lead to the preferential propagation or generation of certain strains. In our recent study of the mouse Prnp^a and Prnp^b polymorphisms (which produced the proteins PrP^a and PrP^b, respectively), we found differences in aggregation tendency, strain adaptability and conformational variability. Comparing our in vitro data with that of in vivo studies, we found that differing incubation periods between Prnp^a and Prnp^b mice can primarily be explained on the basis of faster or more efficient aggregation of PrP^a. In addition, and more importantly, we found that the faithful propagation of strains in Prnp^b mice can be explained by the ability of PrP^b to adopt a wider range of conformations. This adaptability allows PrP^b to successfully propagate the structural features of a seed. In contrast, Prnp^a mice revert PrP^b strains into PrP^a -type strains, and overall they have a narrower distribution of incubation periods. This can be explained by PrP^a having fewer preferred conformations. We propose that Prnp polymorphisms are one route by which certain prion strains may preferentially propagate. This has significant implications for prion disease, chronic wasting disease (CWD) in particular, as it is spreading through North America. Deer which are susceptible to CWD also carry polymorphisms which influence their susceptibility. If these polymorphisms also preferentially allow strain diversification and propagation, this may accelerate the crossing of species barriers and propagation of the disease up the food chain.     

Molecular and transmission characteristics of primary-passaged ovine scrapie isolates in conventional and ovine PrP transgenic mice

A more complete assessment of ovine prion strain diversity will be achieved by complementing biological strain typing in conventional and ovine PrP transgenic mice with a biochemical analysis of the resultant PrPSc. This will provide a correlation between ovine prion strain phenotype and the molecular nature of different PrP conformers associated with particular prion strains. Here, we have compared the molecular and transmission characteristics of ovine ARQ/ARQ and VRQ/VRQ scrapie isolates following primary passage in tg338 (VRQ) and tg59 (ARQ) ovine PrP transgenic mice and the conventional mouse lines C57BL/6 (Prnp^a), RIII (Prnp^a), and VM (Prnp^b). Our data show that these different genotypes of scrapie isolates display similar incubation periods of >350 days in conventional and tg59 mice. Facilitated transmission of sheep scrapie isolates occurred in tg338 mice, with incubation times reduced to 64 days for VRQ/VRQ inocula and to ≤210 days for ARQ/ARQ samples. Distinct genotype-specific lesion profiles were seen in the brains of conventional and tg59 mice with prion disease, which was accompanied by the accumulation of more conformationally stable PrPSc, following inoculation with ARQ/ARQ compared to VRQ/VRQ scrapie isolates. In contrast, the lesion profiles, quantities, and stability of PrPSc induced by the same inocula in tg338 mice were more similar than in the other mouse lines. Our data show that primary transmission of different genotypes of ovine prions is associated with the formation of different conformers of PrPSc with distinct molecular properties and provide the basis of a molecular approach to identify the true diversity of ovine prion strains.     

Unexpected Rescue of Alpha-synuclein and Multimerin1 Deletion in C57BL/6JOlaHsd Mice by Beta-adducin Knockout

Uniform genetic background of inbred mouse strains is essential in experiments with genetically modified mice. In order to assess Add2 (beta-adducin) function, its null mutation was produced in embryonic stem cells derived from 129Sv mouse and the subsequently obtained mouse mutants were backcrossed for 6 generations with C57BL/6JOlaHsd strain. Comparison of brain proteins between mutated and control animals by two-dimensional gels linked to mass spectroscopy analysis showed expression of Snca (alpha-synuclein) in the mutated animals, but unexpectedly not in the control C57BL/6JOlaHsd mice. Comparison between C57BL/6JOlaHsd and C57BL/6NCrl mice confirmed the presence of a deletion encompassing Snca and in addition Mmrn1 (multimerin1) loci in C57BL/6JOlaHsd strain. The segregation of mutated Add2 together with an adjacent part of the chromosome 6 derived from 129Sv mice, rescued the loss of these two genes in knockout mice on C57BL/6JOlaHsd background. The fact that Add2 knockout was compared with the C57BL/6JOlaHsd mouse strain, which is actually a double knockout of Snca and Mmrn1 emphasizes a need for information provided by commercial suppliers and of exact denominations of substrains used in research.     

Age-Dependent Impairment of Eyeblink Conditioning in Prion Protein-Deficient Mice

Mice lacking the prion protein (PrP^C) gene (Prnp), Ngsk Prnp ^0/0 mice, show late-onset cerebellar Purkinje cell (PC) degeneration because of ectopic overexpression of PrP^C-like protein (PrPLP/Dpl). Because PrP^C is highly expressed in cerebellar neurons (including PCs and granule cells), it may be involved in cerebellar synaptic function and cerebellar cognitive function. However, no studies have been conducted to investigate the possible involvement of PrP^C and/or PrPLP/Dpl in cerebellum-dependent discrete motor learning. Therefore, the present cross-sectional study was designed to examine cerebellum-dependent delay eyeblink conditioning in Ngsk Prnp ^0/0 mice in adulthood (16, 40, and 60 weeks of age). The aims of the present study were two-fold: (1) to examine the role of PrP^C and/or PrPLP/Dpl in cerebellum-dependent motor learning and (2) to confirm the age-related deterioration of eyeblink conditioning in Ngsk Prnp ^0/0 mice as an animal model of progressive cerebellar degeneration. Ngsk Prnp ^0/0 mice aged 16 weeks exhibited intact acquisition of conditioned eyeblink responses (CRs), although the CR timing was altered. The same result was observed in another line of PrP^c-deficient mice, ZrchI PrnP ^0/0 mice. However, at 40 weeks of age, CR incidence impairment was observed in Ngsk Prnp ^0/0 mice. Furthermore, Ngsk Prnp ^0/0 mice aged 60 weeks showed more significantly impaired CR acquisition than Ngsk Prnp ^0/0 mice aged 40 weeks, indicating the temporal correlation between cerebellar PC degeneration and motor learning deficits. Our findings indicate the importance of the cerebellar cortex in delay eyeblink conditioning and suggest an important physiological role of prion protein in cerebellar motor learning.     

Cellular prion protein: implications in seizures and epilepsy

1. Cellular prion (PrP^c) is a plasma membrane protein involved with copper uptake, protection against oxidative stress, cell adhesion, differentiation, signaling, and survival in the central nervous system2. Deletion of PrP^c gene (Prnp) in mice enhances sensitivity to seizures in vivo and neuronal excitability in vitro which can be related to: (i) disrupted Ca⁺²-activated K⁺ currents, with loss of I _HAP conductance in hippocampus; (ii) abnormal GABA-A inhibition in the hippocampus; (iii) mossy fiber reorganization in the hippocampus; (iv) changes in ectonucleotidases in both hippocampus and neocortex; and (v) higher levels of neocortical and subcortical oxidative stress. Moreover, postnatal Prnp knockout mice showed a significant reduction of after hyperpolarization potentials in hippocampal CA1 cells.3. Taken together, these findings suggest that loss of PrP^c function contributes to the hyperexcitable and synchronized activities underlying epileptic seizures generated in neocortex and hippocampus. Hence, the role of PrP^c on human symptomatic, cryptogenic or idiopathic epileptic syndromes deserves further investigation.     

Regulation of GABAA and Glutamate Receptor Expression,Synaptic Facilitation and Long-Term Potentiation in the Hippocampus of Prion Mutant Mice

Background

Prionopathies are characterized by spongiform brain degeneration, myoclonia, dementia, and periodic electroencephalographic (EEG) disturbances. The hallmark of prioniopathies is the presence of an abnormal conformational isoform (PrP^sc) of the natural cellular prion protein (PrP^c) encoded by the Prnp gene. Although several roles have been attributed to PrP^c, its putative functions in neuronal excitability are unknown. Although early studies of the behavior of Prnp knockout mice described minor changes, later studies report altered behavior. To date, most functional PrP^c studies on synaptic plasticity have been performed in vitro. To our knowledge, only one electrophysiological study has been performed in vivo in anesthetized mice, by Curtis and coworkers. They reported no significant differences in paired-pulse facilitation or LTP in the CA1 region after Schaffer collateral/commissural pathway stimulation.

Methodology/Principal Findings

Here we explore the role of PrP^c expression in neurotransmission and neural excitability using wild-type, Prnp −/− and PrP^c-overexpressing mice (Tg20 strain). By correlating histopathology with electrophysiology in living behaving mice, we demonstrate that both Prnp −/− mice but, more relevantly Tg20 mice show increased susceptibility to KA, leading to significant cell death in the hippocampus. This finding correlates with enhanced synaptic facilitation in paired-pulse experiments and hippocampal LTP in living behaving mutant mice. Gene expression profiling using Illumina™ microarrays and Ingenuity pathways analysis showed that 129 genes involved in canonical pathways such as Ubiquitination or Neurotransmission were co-regulated in Prnp −/− and Tg20 mice. Lastly, RT-qPCR of neurotransmission-related genes indicated that subunits of GABA_A and AMPA-kainate receptors are co-regulated in both Prnp −/− and Tg20 mice.

Conclusions/Significance

Present results demonstrate that PrP^c is necessary for the proper homeostatic functioning of hippocampal circuits, because of its relationships with GABA_A and AMPA-Kainate neurotransmission. New PrP^c functions have recently been described, which point to PrP^c as a target for putative therapies in Alzheimer''s disease. However, our results indicate that a “gain of function” strategy in Alzheimer''s disease, or a “loss of function” in prionopathies, may impair PrP^c function, with devastating effects. In conclusion, we believe that present data should be taken into account in the development of future therapies.     

Mouse-Hamster Chimeric Prion Protein (PrP) Devoid of N-Terminal Residues 23-88 Restores Susceptibility to 22L Prions,but Not to RML Prions in PrP-Knockout Mice

Prion infection induces conformational conversion of the normal prion protein PrP^C, into the pathogenic isoform PrP^Sc, in prion diseases. It has been shown that PrP-knockout (Prnp^0/0) mice transgenically reconstituted with a mouse-hamster chimeric PrP lacking N-terminal residues 23-88, or Tg(MHM2Δ23-88)/Prnp^0/0 mice, neither developed the disease nor accumulated MHM2^ScΔ23-88 in their brains after inoculation with RML prions. In contrast, RML-inoculated Tg(MHM2Δ23-88)/Prnp^0/+ mice developed the disease with abundant accumulation of MHM2^ScΔ23-88 in their brains. These results indicate that MHM2Δ23-88 itself might either lose or greatly reduce the converting capacity to MHM2^ScΔ23-88, and that the co-expressing wild-type PrP^C can stimulate the conversion of MHM2Δ23-88 to MHM2^ScΔ23-88 in trans. In the present study, we confirmed that Tg(MHM2Δ23-88)/Prnp^0/0 mice remained resistant to RML prions for up to 730 days after inoculation. However, we found that Tg(MHM2Δ23-88)/Prnp^0/0 mice were susceptible to 22L prions, developing the disease with prolonged incubation times and accumulating MHM2^ScΔ23-88 in their brains. We also found accelerated conversion of MHM2Δ23-88 into MHM2^ScΔ23-88 in the brains of RML- and 22L-inoculated Tg(MHM2Δ23-88)/Prnp^0/+ mice. However, wild-type PrP^Sc accumulated less in the brains of these inoculated Tg(MHM2Δ23-88)/Prnp^0/+ mice, compared with RML- and 22L-inoculated Prnp^0/+ mice. These results show that MHM2Δ23-88 itself can convert into MHM2^ScΔ23-88 without the help of the trans-acting PrP^C, and that, irrespective of prion strains inoculated, the co-expressing wild-type PrP^C stimulates the conversion of MHM2Δ23-88 into MHM2^ScΔ23-88, but to the contrary, the co-expressing MHM2Δ23-88 disturbs the conversion of wild-type PrP^C into PrP^Sc.     

Effect of mouse genotype on interferon production. I. Lines congenic at theIf-1 locus

The level of circulating Interferon induced in mice by Newcastle disease virus is controlled by a single codominant locus,If-1, with two alleles,If-1 ^l for low andIf-1 ^h for high production. This locus is linked to the histocompatibility locusH-28. Of three C57BL/6By lines congenic for the BALB/cBy allele atH-28, two are carrying the BALB/cBy allele and one, the C57BL/6By allele atIf-1. Thus, mouse strains that are genetically very similar but different in their production of NDV-induced circulating Interferon now are available.A preliminary report of these studies was presented at the ASM meeting at Miami Beach in May 1973.     

Prion Replication in the Hematopoietic Compartment Is Not Required for Neuroinvasion in Scrapie Mouse Model

Fatal neurodegenerative prion diseases are caused by the transmissible PrP^Sc prion agent whose initial replication after peripheral inoculation takes place in follicular dendritic cells present in germinal centers of lymphoid organs. However, prion replication also occurs in lymphoid cells. To assess the role of the hematopoietic compartment in neuroinvasion and prion replication, we generated chimeric mice, on a uniform congenic C57/BL6J background, by bone marrow replacement with hematopoietic cells expressing different levels of PrP protein. Nine different types of chimeric mice were inoculated intraperitoneally either with the lymphotropic Rocky Mountain Laboratory (RML) strain or the non lymphotropic ME-7 scrapie strain, at different doses. Here, we clearly demonstrate that overexpression of PrP by the hematopoietic system, or the lack of PrP expression by the bone marrow derived cells, does not change the incubation time period of the disease, even when the mice are infected at limiting doses. We conclude that the hematopoietic compartment is more or less permissive to prion replication, both for RML and ME-7, but does not play a role in neuroinvasion.     

Establishment of a new glial cell line from hippocampus of prion protein gene-deficient mice

Cellular prion protein (PrP^C) is expressed not only in neuronal cells but also in non-neuronal cells such as astroglial cells. In the present study, the prion protein (PrP) gene (Prnp)-deficient astroglial cell line GpL1 from hippocampal cells of ZrchI Prnp^−/− mice were established. Transfection of Prnp suppressed cell death in GpL1 cells under serum-free conditions. The PrP-expressing GpL1 cells showed increased superoxide dismutase activity compared to control GpL1 cells. These results suggest that the anti-oxidative activity of PrP^C functions in not only neuronal cells but also astroglial cells possibly due to the increased anti-oxidative activity of astroglial cells.     

Involvement of Cellular Prion Protein in α-Synuclein Transport in Neurons

The cellular prion protein, encoded by the gene Prnp, has been reported to be a receptor of β-amyloid. Their interaction is mandatory for neurotoxic effects of β-amyloid oligomers. In this study, we aimed to explore whether the cellular prion protein participates in the spreading of α-synuclein. Results demonstrate that Prnp expression is not mandatory for α-synuclein spreading. However, although the pathological spreading of α-synuclein can take place in the absence of Prnp, α-synuclein expanded faster in PrP^C-overexpressing mice. In addition, α-synuclein binds strongly on PrP^C-expressing cells, suggesting a role in modulating the effect of α-synuclein fibrils.     

“Agouti NOD”: identification of a CBA-derived Idd locus on Chromosome 7 and its use for chimera production with NOD embryonic stem cells

Penetrance of the complex of genes predisposing the nonobese diabetic (NOD) mouse to autoimmune diabetes is affected by the maternal environment. NOD.CBALs-Tyr⁺/Lt is an agouti-pigmented Chromosome 7 congenic stock of NOD/Lt mice produced as a resource for embryo transfer experiments to provide the necessary maternal factors and allow the easy identification of NOD (albino) embryo donor phenotype. CBcNO6/Lt, a recombinant congenic agouti stock already containing approximately 50% NOD genome, was used as the donor source of a wild-type CBA tyrosinase allele. When the incidence of diabetes was assessed after nine generations of backcrossing and one generation of sib-sib mating, significant reduction in diabetes development was observed. No difference in diabetes development was observed in Tyr/Tyr^c heterozygotes, showing that protection was recessive. Analysis of diabetes progression in another NOD stock congenic for C57BL/6 alleles on Chromosome 7 linked to the glucose phosphate isomerase (Gpi1^b) locus provided no protection, indicating that the diabetes resistance (Idd) gene was distal to 34 cM (D7Mit346). Approximately 5 cM of the distal congenic region overlaps a region from C57L previously associated with protection when homozygous. The delayed onset and reduced frequency of diabetes in the NOD.CBALs-Tyr⁺/Lt stock is an advantage when females of this stock are used as surrogate mothers in studies involving hysterectomy or embryo transfers. Indeed, a newly developed NOD embryonic stem (ES) cell line injected into NOD.CBALs- Tyr⁺/Lt blastocysts produced approximately 50% live-born mice, of which approximately 11% were chimeric. Presumably because of high genomic instability, no germline transmission was observed.     

Skin graft rejection in mice repopulated with marrow of the skin donor type: A SKn gene in a congenic line

Genetically anemic W/W ^c mice and lethally irradiated wild-type mice were cured and populated by grafted marrow cells from donor mice of three congenic lines that differed at non-H-2 histocompatibility loci. Tail skin from mice of the same congenic lines was grafted 3–4 weeks later. In two cases, the recipients behaved as expected, no longer rejecting skin syngeneic with the marrow graft that had repopulated them. However, B6-H-24 ^c skin was rejected by WBB6F₁-W/W mice that were cured with B6-H-24 ^c marrow showing a mean survival time of 9.9 weeks. It was rejected somewhat faster, with a mean survival time of 5.9 weeks, by W/W mice cured with marrow from other types of donors. Results were more variable in lethally irradiated WBB6F₁-+/+ recipients of B6-H-24 ^c marrow, but they also rejected B6-H-24 ^c skin. Both types of recipients remained chimeras after the skin was rejected, showing more than 90% of the B6-H-24 ^c hemoglobin type. This is the first report of a Skn gene in a congenic line.     

Regulation of resistance to leprosy by chromosome 1 locus in the mouse

Mice of different inbred strains vary in their resistance to intravenous infection with Mycobacterium lepraemurium (MLM). The mean survival time of MLM-infected A/J and DBA/2 mice is significantly longer than that of similarly infected C57BL/6 and BALB/c mice. The typing of AXB/BXA recombinant inbred strains (A = A/J, B = C57BL/6) for the trait of relative resistance/susceptibility to MLM revealed a perfect match with the strain distribution pattern of resistance/susceptibility to Mycobacterium bovis (BCG), the trait which is controlled by the Bcg (Ity, Lsh) locus on chromosome 1. The control, by this gene, of response to MLM was further confirmed by the demonstration that BALB/c-Bcg ^r congenic mice,which carry the DBA/2-derived Bcg ^r (resistant) allele on chromosome 1, are significantly more resistant to MLM infection than their BALB/c (Bcg ^s , susceptible) counterparts.     

High prevalence of prion protein genotype associated with resistance to chronic wasting disease in one Alberta woodland caribou population

Chronic wasting disease (CWD) is a prion disease found in deer, elk and moose in North America and since recently, wild reindeer in Norway. Caribou are at-risk to encounter CWD in areas such as Alberta, Canada, where the disease spreads toward caribou habitats. CWD susceptibility is modulated by species-specific polymorphisms in the prion protein gene (Prnp). We sequenced Prnp of woodland caribou from 9 Albertan populations. In one population (Chinchaga) a significantly higher frequency of the 138N allele linked to reduced CWD susceptibility was observed. These data are relevant for developing CWD management strategies including conservation of threatened caribou populations.     

Oxidative stress impairs autophagic flux in prion protein-deficient hippocampal cells

We previously reported that autophagy is upregulated in Prnp-deficient (Prnp^0/0) hippocampal neuronal cells in comparison to cellular prion protein (PrP^C)-expressing (Prnp^+/+) control cells under conditions of serum deprivation. In this study, we determined whether a protective mechanism of PrP^C is associated with autophagy using Prnp^0/0 hippocampal neuronal cells under hydrogen peroxide (H₂O₂)-induced oxidative stress. We found that Prnp^0/0 cells were more susceptible to oxidative stress than Prnp^+/+ cells in a dose- and time-dependent manner. In addition, we observed enhanced autophagy by immunoblotting, which detected the conversion of microtubule-associated protein 1 light chain 3 β (LC3B)-I to LC3B-II, and we observed increased punctate LC3B immunostaining in H₂O₂-treated Prnp^0/0 cells compared with H₂O₂-treated control cells. Interestingly, this enhanced autophagy was due to impaired autophagic flux in the H₂O₂-treated Prnp^0/0 cells, while the H₂O₂-treated Prnp^+/+ cells showed enhanced autophagic flux. Furthermore, caspase-dependent and independent apoptosis was observed when both cell lines were exposed to H₂O₂. Moreover, the inhibition of autophagosome formation by Atg7 siRNA revealed that increased autophagic flux in Prnp^+/+ cells contributes to the prosurvival effect of autophagy against H₂O₂ cytotoxicity. Taken together, our results provide the first experimental evidence that the deficiency of PrP^C may impair autophagic flux via H₂O₂-induced oxidative stress.     

Biochemical genetics of a new glucosephosphate isomerase allele (Gpi-1 c) from wild mice

We have found a new allele at the structural locus for glucosephosphate isomerase (called Gpi-1 ^c ) in a population of wild mice. The Gpi-1 ^c allele codes for an enzyme of greater cathodal electrophoretic mobility than either the Gpi-1 ^a or Gpi-1 ^b alleles found in the wild and in the SM/J and C57BL/6J inbred strains. Mice homozygous for Gpi-1 ^c have erythrocyte enzyme activity reduced to 33% of normal levels, altered pH profile, lowered heat stability, and normal K _m 's when compared with SM/J and C57BL/6J mice. The activity of the enzyme in brain, liver, and kidney is not so markedly lowered, although the electrophoretic mobility, pH profile, and heat stability are altered in these tissues. Deficiencies of erythrocyte glucosephosphate isomerase in man, to this level, can cause severe hemolytic anemia. Homozygotes for Gpi-1 ^c show only mild hematological symptoms. The frequency of Gpi-1 ^c in wild populations of mice is discussed and the occurrence of a further rare allele Gpi-1 ^d is reported.This work was supported by M.R.C. grants to Professor R. J. Berry and Dr. H. Kacser, whom we should also like to thank for much help and useful discussion.