Radiomics Can Distinguish Pediatric Supratentorial Embryonal Tumors, High-Grade Gliomas, and Ependymomas.

BACKGROUND AND PURPOSE: Pediatric supratentorial tumors such as embryonal tumors, high-grade gliomas, and ependymomas are difficult to distinguish by histopathology and imaging because of overlapping features. We applied machine learning to uncover MR imaging-based radiomics phenotypes that can differentiate these tumor types. MATERIALS AND METHODS: Our retrospective cohort of 231 patients from 7 participating institutions had 50 embryonal tumors, 127 high-grade gliomas, and 54 ependymomas. For each tumor volume, we extracted 900 Image Biomarker Standardization Initiative-based PyRadiomics features from T2-weighted and gadolinium-enhanced T1-weighted images. A reduced feature set was obtained by sparse regression analysis and was used as input for 6 candidate classifier models. Training and test sets were randomly allocated from the total cohort in a 75:25 ratio. RESULTS: The final classifier model for embryonal tumor-versus-high-grade gliomas identified 23 features with an area under the curve of 0.98; the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were 0.85, 0.91, 0.79, 0.94, and 0.89, respectively. The classifier for embryonal tumor-versus-ependymomas identified 4 features with an area under the curve of 0.82; the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were 0.93, 0.69, 0.76, 0.90, and 0.81, respectively. The classifier for high-grade gliomas-versus-ependymomas identified 35 features with an area under the curve of 0.96; the sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were 0.82, 0.94, 0.82, 0.94, and 0.91, respectively. CONCLUSIONS: In this multi-institutional study, we identified distinct radiomic phenotypes that distinguish pediatric supratentorial tumors, high-grade gliomas, and ependymomas with high accuracy. Incorporation of this technique in diagnostic algorithms can improve diagnosis, risk stratification, and treatment planning.

Radiomic Phenotypes Distinguish Atypical Teratoid/Rhabdoid Tumors from Medulloblastoma.

BACKGROUND AND PURPOSE: Atypical teratoid/rhabdoid tumors and medulloblastomas have similar imaging and histologic features but distinctly different outcomes. We hypothesized that they could be distinguished by MR imaging-based radiomic phenotypes. MATERIALS AND METHODS: We retrospectively assembled T2-weighted and gadolinium-enhanced T1-weighted images of 48 posterior fossa atypical teratoid/rhabdoid tumors and 96 match-paired medulloblastomas from 7 institutions. Using a holdout test set, we measured the performance of 6 candidate classifier models using 6 imaging features derived by sparse regression of 900 T2WI and 900 T1WI Imaging Biomarker Standardization Initiative-based radiomics features. RESULTS: From the originally extracted 1800 total Imaging Biomarker Standardization Initiative-based features, sparse regression consistently reduced the feature set to 1 from T1WI and 5 from T2WI. Among classifier models, logistic regression performed with the highest AUC of 0.86, with sensitivity, specificity, accuracy, and F1 scores of 0.80, 0.82, 0.81, and 0.85, respectively. The top 3 important Imaging Biomarker Standardization Initiative features, by decreasing order of relative contribution, included voxel intensity at the 90th percentile, inverse difference moment normalized, and kurtosis-all from T2WI. CONCLUSIONS: Six quantitative signatures of image intensity, texture, and morphology distinguish atypical teratoid/rhabdoid tumors from medulloblastomas with high prediction performance across different machine learning strategies. Use of this technique for preoperative diagnosis of atypical teratoid/rhabdoid tumors could significantly inform therapeutic strategies and patient care discussions.

Deep Learning for Pediatric Posterior Fossa Tumor Detection and Classification: A Multi-Institutional Study.

BACKGROUND AND PURPOSE: Posterior fossa tumors are the most common pediatric brain tumors. MR imaging is key to tumor detection, diagnosis, and therapy guidance. We sought to develop an MR imaging-based deep learning model for posterior fossa tumor detection and tumor pathology classification. MATERIALS AND METHODS: The study cohort comprised 617 children (median age, 92 months; 56% males) from 5 pediatric institutions with posterior fossa tumors: diffuse midline glioma of the pons (n = 122), medulloblastoma (n = 272), pilocytic astrocytoma (n = 135), and ependymoma (n = 88). There were 199 controls. Tumor histology served as ground truth except for diffuse midline glioma of the pons, which was primarily diagnosed by MR imaging. A modified ResNeXt-50-32x4d architecture served as the backbone for a multitask classifier model, using T2-weighted MRIs as input to detect the presence of tumor and predict tumor class. Deep learning model performance was compared against that of 4 radiologists. RESULTS: Model tumor detection accuracy exceeded an AUROC of 0.99 and was similar to that of 4 radiologists. Model tumor classification accuracy was 92% with an F1 score of 0.80. The model was most accurate at predicting diffuse midline glioma of the pons, followed by pilocytic astrocytoma and medulloblastoma. Ependymoma prediction was the least accurate. Tumor type classification accuracy and F1 score were higher than those of 2 of the 4 radiologists. CONCLUSIONS: We present a multi-institutional deep learning model for pediatric posterior fossa tumor detection and classification with the potential to augment and improve the accuracy of radiologic diagnosis.

Variable Refocusing Flip Angle Single-Shot Imaging for Sedation-Free Fast Brain MRI.

BACKGROUND AND PURPOSE: Conventional single-shot FSE commonly used for fast MRI may be suboptimal for brain evaluation due to poor image contrast, SNR, or image blurring. We investigated the clinical performance of variable refocusing flip angle single-shot FSE, a variation of single-shot FSE with lower radiofrequency energy deposition and potentially faster acquisition time, as an alternative approach to fast brain MR imaging. MATERIALS AND METHODS: We retrospectively compared half-Fourier single-shot FSE with half- and full-Fourier variable refocusing flip angle single-shot FSE in 30 children. Three readers reviewed images for motion artifacts, image sharpness at the brain-fluid interface, and image sharpness/tissue contrast at gray-white differentiation on a modified 5-point Likert scale. Two readers also evaluated full-Fourier variable refocusing flip angle single-shot FSE against T2-FSE for brain lesion detectability in 38 children. RESULTS: Variable refocusing flip angle single-shot FSE sequences showed more motion artifacts (P < .001). Variable refocusing flip angle single-shot FSE sequences scored higher regarding image sharpness at brain-fluid interfaces (P < .001) and gray-white differentiation (P < .001). Acquisition times for half- and full-Fourier variable refocusing flip angle single-shot FSE were faster than for single-shot FSE (P < .001) with a 53% and 47% reduction, respectively. Intermodality agreement between full-Fourier variable refocusing flip angle single-shot FSE and T2-FSE findings was near-perfect (κ = 0.90, κ = 0.95), with an 8% discordance rate for ground truth lesion detection. CONCLUSIONS: Variable refocusing flip angle single-shot FSE achieved 2× faster scan times than single-shot FSE with improved image sharpness at brain-fluid interfaces and gray-white differentiation. Such improvements are likely attributed to a combination of improved contrast, spatial resolution, SNR, and reduced T2-decay associated with blurring. While variable refocusing flip angle single-shot FSE may be a useful alternative to single-shot FSE and, potentially, T2-FSE when faster scan times are desired, motion artifacts were more common in variable refocusing flip angle single-shot FSE, and, thus, they remain an important consideration before clinical implementation.

MR Imaging-Based Radiomic Signatures of Distinct Molecular Subgroups of Medulloblastoma.

BACKGROUND AND PURPOSE: Distinct molecular subgroups of pediatric medulloblastoma confer important differences in prognosis and therapy. Currently, tissue sampling is the only method to obtain information for classification. Our goal was to develop and validate radiomic and machine learning approaches for predicting molecular subgroups of pediatric medulloblastoma. MATERIALS AND METHODS: In this multi-institutional retrospective study, we evaluated MR imaging datasets of 109 pediatric patients with medulloblastoma from 3 children's hospitals from January 2001 to January 2014. A computational framework was developed to extract MR imaging-based radiomic features from tumor segmentations, and we tested 2 predictive models: a double 10-fold cross-validation using a combined dataset consisting of all 3 patient cohorts and a 3-dataset cross-validation, in which training was performed on 2 cohorts and testing was performed on the third independent cohort. We used the Wilcoxon rank sum test for feature selection with assessment of area under the receiver operating characteristic curve to evaluate model performance. RESULTS: Of 590 MR imaging-derived radiomic features, including intensity-based histograms, tumor edge-sharpness, Gabor features, and local area integral invariant features, extracted from imaging-derived tumor segmentations, tumor edge-sharpness was most useful for predicting sonic hedgehog and group 4 tumors. Receiver operating characteristic analysis revealed superior performance of the double 10-fold cross-validation model for predicting sonic hedgehog, group 3, and group 4 tumors when using combined T1- and T2-weighted images (area under the curve = 0.79, 0.70, and 0.83, respectively). With the independent 3-dataset cross-validation strategy, select radiomic features were predictive of sonic hedgehog (area under the curve = 0.70-0.73) and group 4 (area under the curve = 0.76-0.80) medulloblastoma. CONCLUSIONS: This study provides proof-of-concept results for the application of radiomic and machine learning approaches to a multi-institutional dataset for the prediction of medulloblastoma subgroups.

Dose-dependent expression of claudin-5 is a modifying factor in schizophrenia.

Schizophrenia is a neurodevelopmental disorder that affects up to 1% of the general population. Various genes show associations with schizophrenia and a very weak nominal association with the tight junction protein, claudin-5, has previously been identified. Claudin-5 is expressed in endothelial cells forming part of the blood-brain barrier (BBB). Furthermore, schizophrenia occurs in 30% of individuals with 22q11 deletion syndrome (22q11DS), a population who are haploinsufficient for the claudin-5 gene. Here, we show that a variant in the claudin-5 gene is weakly associated with schizophrenia in 22q11DS, leading to 75% less claudin-5 being expressed in endothelial cells. We also show that targeted adeno-associated virus-mediated suppression of claudin-5 in the mouse brain results in localized BBB disruption and behavioural changes. Using an inducible 'knockdown' mouse model, we further link claudin-5 suppression with psychosis through a distinct behavioural phenotype showing impairments in learning and memory, anxiety-like behaviour and sensorimotor gating. In addition, these animals develop seizures and die after 3-4 weeks of claudin-5 suppression, reinforcing the crucial role of claudin-5 in normal neurological function. Finally, we show that anti-psychotic medications dose-dependently increase claudin-5 expression in vitro and in vivo while aberrant, discontinuous expression of claudin-5 in the brains of schizophrenic patients post mortem was observed compared to age-matched controls. Together, these data suggest that BBB disruption may be a modifying factor in the development of schizophrenia and that drugs directly targeting the BBB may offer new therapeutic opportunities for treating this disorder.

Survivin as a therapeutic target in Sonic hedgehog-driven medulloblastoma.

Medulloblastoma (MB) is a highly malignant brain tumor that occurs primarily in children. Although surgery, radiation and high-dose chemotherapy have led to increased survival, many MB patients still die from their disease, and patients who survive suffer severe long-term side effects as a consequence of treatment. Thus, more effective and less toxic therapies for MB are critically important. Development of such therapies depends in part on identification of genes that are necessary for growth and survival of tumor cells. Survivin is an inhibitor of apoptosis protein that regulates cell cycle progression and resistance to apoptosis, is frequently expressed in human MB and when expressed at high levels predicts poor clinical outcome. Therefore, we hypothesized that Survivin may have a critical role in growth and survival of MB cells and that targeting it may enhance MB therapy. Here we show that Survivin is overexpressed in tumors from patched (Ptch) mutant mice, a model of Sonic hedgehog (SHH)-driven MB. Genetic deletion of survivin in Ptch mutant tumor cells significantly inhibits proliferation and causes cell cycle arrest. Treatment with small-molecule antagonists of Survivin impairs proliferation and survival of both murine and human MB cells. Finally, Survivin antagonists impede growth of MB cells in vivo. These studies highlight the importance of Survivin in SHH-driven MB, and suggest that it may represent a novel therapeutic target in patients with this disease.

Comparison of MALDI-TOF mass spectrometric to enzyme colorimetric quantification of glucose from enzyme-hydrolyzed starch.

Successful quantification of the glucose produced by enzyme hydrolysis of starch was achieved by a matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) protocol, using sorbitol as an internal standard. The starch contents measured by MALDI-TOF MS of corn starch, fiber-enriched oat flour derivatives, oat and barley flours, and barley flour/corn starch composites were evaluated in comparison to a widely accepted and validated method of starch determination, which relies on enzyme colorimetry (EC). The average starch content measured in a series of corn starch samples of different masses was 93 and 101% for EC and MALDI-TOF MS, respectively, values that represent the estimated purity of the sample. There was an agreement of 99% between the starch contents determined by the two analytical methods for complex flour-derived samples. Starch values estimated by MALDI-TOF MS consistently showed a greater degree of variability than those determined by EC, but this limitation was readily compensated by rapid acquisition of multiple mass spectra. This study is the first to report the quantification of glucose by MALDI-TOF MS, and it offers new perspectives into the potential utility of MALDI-TOF MS as a definitive tool for monosaccharide analysis and rapid starch determination in complex samples.

A sensitive method for detection of sulfamethazine and N4-acetylsulfamethazine residues in environmental samples using solid phase immunoextraction coupled with MALDI-TOF MS.

Sulfamethazine (SMT) and its major metabolite, N(4)-acetylsulfamethazine (NA-SMT), were each recovered from spiked water (0.1 ppb) and 10% (w/v) aqueous suspensions of soil (1 ppb) or composted manure (1 ppb), by using a three-stage solid phase immunoextraction (SPIE) system, followed by detection with matrix-assisted laser/desorption ionization time-of-flight mass spectrometry (MALDI-TOF MS). Sulfonamide recovery rates are reported for separate stages of the SPIE system and for trace-level sulfonamide SPIE extraction from the environmental samples. SPIE MALDI-TOF MS is a rapid and definitive technique with potentially better efficiency relative to other established trace-level sulfonamide analytical methods. SPIE MALDI-TOF MS required 1.5 h per batch (8-24 samples/batch) for sample enrichment, 5 min per batch for probe preparation, and 5 min per sample to acquire and process the spectrum. This is the first time MALDI-TOF MS has been reported as a potential means of detecting trace-level drug residues in complex environmental samples.

Treatment of recurrent peripheral nerve entrapment problems: role of scar formation and its possible treatment.

Surgical management of peripheral nerve entrapment syndromes is usually successful, but the recurrence of symptoms after initial improvement can and does occur. Extraneural fibrosis is one possible cause of recurrent peripheral nerve problems as a result of nerve compression or tethering. Several approaches to prevent extraneural scarring after surgery have been studied, including wrapping the involved nerve with a graft, the application of various chemical compounds, and radiation. ADCON-T/N, an antiscar bioabsorbable gel device was evaluated in a retrospective clinical review. Sixty-seven percent of patients treated with ADCON-T/N after reoperation of a peripheral nerve experienced prolonged clinical improvement compared with 50% of patients who did not receive ADCON-T/N. These preliminary results suggest that ADCON-T/N may prove to be clinically useful in the surgical treatment of peripheral nerve problems. Additional more rigorous clinical studies are necessary, however.

Amino acid residue mutations uncouple cooperative effects in Escherichia coli D-3-phosphoglycerate dehydrogenase.

d-3-Phosphoglycerate dehydrogenase from Escherichia coli contains two Gly-Gly sequences that occur at junctions between domains. A previous study (Grant, G. A., Xu, X. L., and Hu, Z. (2000) Biochemistry 39, 7316-7319) determined that the Gly-Gly sequence at the junction between the regulatory and substrate binding domain functions as a hinge between the domains. Mutations in this area significantly decrease the ability of serine to inhibit activity but have little effect on the K(m) and k(cat). Conversely, the present study shows that mutations to the Gly-Gly sequence at the junction of the substrate and nucleotide binding domains, which form the active site cleft, have a significant effect on the k(cat) of the enzyme without substantially altering the enzyme's sensitivity to serine. In addition, mutation of Gly-294, but not Gly-295, has a profound effect on the cooperativity of serine inhibition. Interestingly, even though cooperativity of inhibition can be reduced significantly, there is little apparent effect on the cooperativity of serine binding itself. An additional mutant, G336V,G337V, also reduces the cooperativity of inhibition, but in this case serine binding also is reduced to the point at which it cannot be measured by equilibrium dialysis. The double mutant G294V,G336V demonstrates that strain imposed by mutation at one hinge can be relieved partially by mutation at the other hinge, demonstrating linkage between the two hinge regions. These data show that the two cooperative processes, serine binding and catalytic inhibition, can be uncoupled. Consideration of the allowable torsional angles for the side chains introduced by the mutations yields a range of values for these angles that the glycine residues likely occupy in the native enzyme. A comparison of these values with the torsional angles found for the inhibited enzyme from crystal coordinates provides potential beginning and ending orientations for the transition from active to inhibited enzyme, which will allow modeling of the dynamics of domain movement.

Specific interactions at the regulatory domain-substrate binding domain interface influence the cooperativity of inhibition and effector binding in Escherichia coli D-3-phosphoglycerate dehydrogenase.

The crystal structure of d-3-phosphoglycerate dehydrogenase reveals a limited number of contacts between the regulatory and substrate binding domains of each subunit in the tetrameric enzyme. These occur between the side chains of Arg-339, Arg-405, and Arg-407 in the regulatory domain and main chain carbonyls in the substrate binding domain. In addition, Arg-339 participates in a hydrogen bonding network within the regulatory domain involving Arg-338 and Tyr-410, the C-terminal residue of the enzyme subunit. Mutagenic analysis of these residues produce profound effects on the enzyme's sensitivity to serine, the cooperativity of serine inhibition, and in some cases, the apparent overall conformation of the enzyme. Mutations of Arg-405 and Arg-407, which span the interface where the two domains come together, reduce the cooperativity of inhibition and increase the sensitivity of the enzyme to serine concentration. Serine binding studies with Arg-407 converted to Ala demonstrate that cooperativity of serine binding is also significantly reduced in a manner similar to the reduction in the cooperativity of inhibition. Mutations of Tyr-410 and Arg-338 decrease the sensitivity to serine without an appreciable effect on the cooperativity of inhibition. In the case of Tyr-410, a deletion mutant demonstrates that this effect is due to the loss of the C-terminal carboxyl group rather than the tyrosine side chain. All mutations of Arg-339, with the exception of its conversion to Lys, had profound effects on the stability of the enzyme. In general, those mutants that decrease sensitivity to serine are those that participate mainly in intradomain interactions and may also directly affect the serine binding sites themselves. Those mutants that decrease cooperativity are those that participate in interdomain interaction within the subunit. The observation that the mutants that decrease cooperativity also increase sensitivity to serine suggests a potential separation of pathways between how the simple act of serine binding results in noncooperative active site inhibition in the first place and how serine binding also leads to cooperativity between sites in the native enzyme.

Modification of cysteine.

This unit describes a number of methods for modifying cysteine residues of proteins and peptides by reduction and alkylation procedures. A general procedure for alkylation of cysteine residues in a protein of known size and composition with haloacyl reagents or N-ethylmaleimide (NEM) is presented, and alternate protocols describe similar procedures for use when the size and composition are not known and when only very small amounts of protein are available. Alkylations that introduce amino groups using bromopropylamine and N-(iodoethyl)-trifluoroacetamide are also presented. Two procedures that are often used for subsequent sequence analysis of the protein, alkylation with 4-vinylpyridine and acrylamide, are described, and a specialized procedure for 4-vinylpyridine alkylation of protein that has been adsorbed onto a sequencing membrane is also presented. Reversible modification of cysteine residues by way of sulfitolysis is described, and a protocol for oxidation with performic acid for amino acid compositional analysis is also provided. Gentle oxidation of cysteine residues to disulfides by exposure to air is detailed. Support protocols are included for recrystallization of iodoacetic acid, colorimetric detection of free sulfhydryls, and desalting of modified samples.

Development of an in vitro blood-brain barrier.

The blood-brain barrier represents a significant protective barrier for the passage of pathogens and toxicants, but it is difficult to study in vivo. This unit describes an in vitro system that can be used as a model for the blood-brain barrier to study its functions in an accessible format.

Role of an interdomain Gly-Gly sequence at the regulatory-substrate domain interface in the regulation of Escherichia coli. D-3-phosphoglycerate dehydrogenase.

The regulatory and substrate binding domains of D-3-phosphoglycerate dehydrogenase (PGDH, EC 1.1.1.95) from Escherichia coli are connected by a single polypeptide strand that contains a Gly-Gly sequence approximately midway between the domains. The potential flexibility of this sequence and its strategic location between major domain structures suggests that it may function in the conformational change leading from effector binding to inhibition of the active site. Site-directed mutagenesis of this region (Gly-336-Gly-337) supports this hypothesis. When bulky side chains were substituted for the glycines at these positions, substantial changes in the ability of serine to inhibit the enzyme were seen with little effect on the activity of the enzyme. The effect of these substitutions could be alleviated by placing a new glycine residue at position 335, immediately flanking the original glycine pair. On the other hand, substituting a glycine at position 338 revealed a critical role for the side chain of Arg-338. This residue may function in stabilizing the conformation about the Gly-Gly turn, resulting in a specific orientation of the adjacent domains relative to each other. Rotation about the phi or psi bonds of either Gly-336 or Gly-337 would have a profound effect on this orientation. The data are consistent with this as a role for the Gly-Gly sequence between the regulatory and substrate binding domains of PGDH.

Removal of the tryptophan 139 side chain in Escherichia coli D-3-phosphoglycerate dehydrogenase produces a dimeric enzyme without cooperative effects.

Escherichia coli d-3-phosphoglycerate dehydrogenase (PGDH) is a homotetrameric enzyme whose activity is allosterically regulated by l-serine, the end-product of its metabolic pathway. Previous studies have shown that PGDH displays two modes of cooperative interaction. One is between the l-serine binding sites and the other is between the l-serine binding sites and the active sites. Tryptophan 139 participates in an intersubunit contact near the active site catalytic residues. Site-specific mutagenesis of tryptophan 139 to glycine results in the dissociation of the tetramer to a pair of dimers and in the loss of cooperativity in serine binding and between serine binding and inhibition. The results suggest that the magnitude of inhibition of activity at a particular active site is primarily dependent on serine binding to that subunit but that activity can be modulated in a cooperative manner by interaction with adjacent subunits. The disruption of the nucleotide domain interface in PGDH by mutating Trp-139 suggests the potential for a critical role of this interface in the cooperative allosteric processes in the native tetrameric enzyme.

The relationship between effector binding and inhibition of activity in D-3-phosphoglycerate dehydrogenase.

The binding of L-serine to phosphoglycerate dehydrogenase from Escherichia coli displays elements of both positive and negative cooperativity. At pH 7.5, approximately 2 mol of serine are bound per mole of tetrameric enzyme. A substantial degree of positive cooperativity is seen for the binding of the second ligand, but the binding of the third and fourth ligand display substantial negative cooperativity. The data indicate a state of approximately 50% inhibition when only one serine is bound and approximately 80-90% inhibition when two serines are bound. This is consistent with the tethered domain hypothesis that has been presented previously. Comparison of the data derived directly from binding stoichiometry to the binding constants determined from the best fit to the Adair equation, produce a close agreement, and reinforce the general validity of the derived binding constants. The data also support the conclusion that the positive cooperativity between the binding to the first and second site involves binding sites at opposite interfaces over 110 A apart. Thus, an order of binding can be envisioned where the binding of the first ligand initiates a conformational transition that allows the second ligand to bind with much higher affinity at the opposite interface. This is followed by the third ligand, which binds with lesser affinity to one of the two already occupied interfaces, and in so doing, completes a global conformational transition that produces maximum inhibition of activity and an even lower affinity for the fourth ligand, excluding it completely. Thus, maximal inhibition is accomplished with less than maximal occupancy of effector sites through a mechanism that displays strong elements of both positive and negative cooperativity.

Phosphate ion partially relieves the cooperativity of effector binding in D-3-phosphoglycerate dehydrogenase without altering the cooperativity of inhibition.

The binding of L-serine to phosphoglycerate dehydrogenase from E. coli displays elements of both positive and negative cooperativity. In addition, the inhibition of enzymatic activity by L-serine is also cooperative with Hill coefficients greater than 1. However, phosphate buffer significantly reduces the cooperative effects in serine binding without affecting the cooperativity of inhibition of activity. The maximal degree of inhibition and fluorescence quenching in Tris buffer occurs when an average of two serine binding sites out of four are occupied. This value increases to three out of the four sites at maximal levels of inhibition and quenching in phosphate buffer. The increase from two to three sites appears to be due to the ability of phosphate to reduce the site to site cooperative effects and render each ligand binding site less dependent on each other. The correlation between the level of inhibition and the fractional site occupancy indicates that in Tris buffer, one serine is bound to each interface at maximal effect. In the presence of phosphate, the order of binding appears to change so that both sites at one interface fill before the first site at the opposite interface is occupied. In each case, there is a good correlation between serine binding, conformational change at the regulatory site interfaces, and inhibition of enzyme activity. The observation that phosphate does not appear to have a similar effect on the cooperativity of inhibition of enzymatic activity suggests that there are two distinct cooperative pathways at work: one path between the four serine binding sites, and one path between the serine binding sites and the active sites.