Crowdsourcing digital health measures to predict Parkinson's disease severity: the Parkinson's Disease Digital Biomarker DREAM Challenge.

Consumer wearables and sensors are a rich source of data about patients' daily disease and symptom burden, particularly in the case of movement disorders like Parkinson's disease (PD). However, interpreting these complex data into so-called digital biomarkers requires complicated analytical approaches, and validating these biomarkers requires sufficient data and unbiased evaluation methods. Here we describe the use of crowdsourcing to specifically evaluate and benchmark features derived from accelerometer and gyroscope data in two different datasets to predict the presence of PD and severity of three PD symptoms: tremor, dyskinesia, and bradykinesia. Forty teams from around the world submitted features, and achieved drastically improved predictive performance for PD status (best AUROC = 0.87), as well as tremor- (best AUPR = 0.75), dyskinesia- (best AUPR = 0.48) and bradykinesia-severity (best AUPR = 0.95).

Assignment of Ferriheme Resonances for High- and Low-Spin Forms of Nitrophorin 3 by H and C NMR Spectroscopy and Comparison to Nitrophorin 2: Heme Pocket Structural Similarities and Differences.

Nitrophorin 3 (NP3) is the only one of the four major NO-binding heme proteins found in the saliva of the blood-sucking insect Rhodnius prolixus (also called the Kissing Bug) for which it has not been possible to obtain crystals of diffraction quality for structure determination by X-ray crystallography. Thus we have used NMR spectroscopy, mainly of the hyperfine-shifted ferriheme substituent resonances, to learn about the similarities and differences in the heme pocket and the iron active site of NP3 as compared to NP2, which has previously been well-characterized by both X-ray crystallography and NMR spectroscopy. Only one residue in the heme pocket differs between the two, F27 of NP2 is Y27 for NP3; in both cases this residue is expected to interact strongly with the 2-vinyl side chain of the B heme rotational isomer or the 4-vinyl of the A heme rotational isomer. Both the high-spin (S = 5/2) aquo complex, NP3-H(2)O, and the low-spin (S = 1/2) N-methylimidazole (NMeIm) complex of NP3 have been studied. It is found that the chemical shifts of the protons of both forms are similar to those of the corresponding NP2 complexes, but with minor differences that indicate a slightly different angle for the proximal histidine (H57) ligand plane. The B heme rotational isomer is preferred by both NP3 and NP2 in both spin states, but to a greater extent when phenylalanine is present at position 27 (A:B = 1:8 for NP2, 1:6 for NP3-Y27F, 1:4 for NP3, and 1:3 for NP2-F27Y). Careful analysis of the 5Me and 8Me shifts of the A and B isomers of the two high-spin nitrophorins leads to the conclusion that the heme environment for the two isomers differs in some way that cannot be explained at the present time. The kinetics of deprotonation of the high-spin complexes of NP2 and NP3 are very different, with NP2 giving well-resolved high-spin aquo and "low-spin" hydroxo proton NMR spectra until close to the end of the titration, while NP3 exhibits broadened (1)H NMR spectra indicative of an intermediate rate of exchange on the NMR timescale between the two forms throughout the titration. The heme methyl shifts of NP2-OH are similar in magnitude and spread to those of NP2-CN, while those of metmyoglobin-hydroxo complexes are much larger in magnitude but not spread. It is concluded that the hydroxo complex of NP2 is likely S = 1/2 with a mixed (d(XY))(2)(d(XZ),d(YZ))(3)/(d(xy))(1)(d(xz),d(yz))(4) electron configuration, while those of met-Mb-OH are likely S = 1/2,3/2 mixed spin systems.

NMR studies of nitrophorin distal pocket side chain effects on the heme orientation and seating of NP2 as compared to NP1.

The nitrophorins (NP) of the adult blood-sucking insect Rhodnius prolixus fall into two pairs based on sequence identity (NP1,4 (90%) and NP2,3 (79%)), which differ significantly in the size of side chains of residues which contact the heme. These residues include those in the distal pocket of NP2 (I120) and NP1 (T121) and the "belt" that surrounds the heme of NP2 (S40, F42), and NP1(A42, L44). To determine the importance of these residues and others conserved or very similar for the two pairs, including L122(123), L132(133), appropriate mutants of NP2 and NP1 have been prepared and studied by (1)H NMR spectroscopy. Wild-type NP2 has heme orientation ratio (A:B) of 1:8 at equilibrium, while wild-type NP1 has A:B ~1:1 at equilibrium. Another difference between NP2 and NP1 is in the heme seating with regard to His57(59). It is found that among the distal pocket residues investigated, the residue most responsible for heme orientation and seating is I120(T121). F42(L44) and L106(F107) may also be important, but must be investigated in greater detail.

Default risk modeling beyond the first-passage approximation: extended Black-Cox model.

We develop a generalization of the Black-Cox structural model of default risk. The extended model captures uncertainty related to firm's ability to avoid default even if company's liabilities momentarily exceeding its assets. Diffusion in a linear potential with the radiation boundary condition is used to mimic a company's default process. The exact solution of the corresponding Fokker-Planck equation allows for derivation of analytical expressions for the cumulative probability of default and the relevant hazard rate. Obtained closed formulas fit well the historical data on global corporate defaults and demonstrate the split behavior of credit spreads for bonds of companies in different categories of speculative-grade ratings with varying time to maturity. Introduction of the finite rate of default at the boundary improves valuation of credit risk for short time horizons, which is the key advantage of the proposed model. We also consider the influence of uncertainty in the initial distance to the default barrier on the outcome of the model and demonstrate that this additional source of incomplete information may be responsible for nonzero credit spreads for bonds with very short time to maturity.

Assignment of the ferriheme resonances of high- and low-spin forms of the symmetrical hemin-reconstituted nitrophorins 1-4 by 1H and 13C NMR spectroscopy: the dynamics of heme ruffling deformations.

The four major nitrophorins (NPs) of the adult blood-sucking insect Rhodnius prolixus have been reconstituted with the "symmetrical hemin" 2,4-dimethyldeuterohemin, and their NMR spectra have been investigated as the high-spin (S=5/2) aqua and low-spin (S=1/2) N-methylimidazole (NMeIm) and cyanide complexes. The NMeIm complexes allow assignment of the high-spin hemin resonances by saturation transfer difference spectroscopy. The cyanide complexes were investigated as paramagnetic analogues of the NO complexes. It is shown that the hemin ring is highly distorted from planarity, much more so for NP2 than for NP1 and NP4 (with ruffling being the major distortion mode), for both high- and low-spin forms. For the cyanide complexes, the conformation of the distorted ring changes on the NMR timescale to yield chemical exchange (exchange spectroscopy, EXSY) cross peaks for NP1sym(CN), NP3sym(CN) and NP4sym(CN) but not for NP2sym(CN). These changes in nonplanar conformation are visualized as a "rolling" of the ruffled macrocycle ridges through some number of degrees, the lowest-energy ruffling mode. This probably occurs in response to slow protein dynamics that cause the I120 and L132 side chains in the distal heme pocket to move in opposite directions (up and away vs. down and toward the hemin ring). This in turn changes the out-of-plane displacements of the 2M and 3M of the symmetrical hemin on the NMR timescale. Two other types of dynamics, i.e., changes in heme seating and NMeIm rotation, are also observed. The highly distorted heme and the dynamics it causes are unique to the NPs and a few other heme proteins with highly distorted macrocycles.

Assignment of the ferriheme resonances of the high-spin forms of nitrophorins 1 and 4 by 1H NMR spectroscopy: comparison to structural data obtained from X-ray crystallography.

In this work, we report the assignment of the majority of the ferriheme resonances of high-spin nitrophorins (NPs) 1 and 4 and compare them to those of NP2, published previously. It is found that the structures of the ferriheme complexes of NP1 and NP4, in terms of the orientation of the histidine imidazole ligand, can be described with good accuracy by NMR techniques and that the angle plot proposed previously for the high-spin form of the NPs (Shokhireva, T. Kh.; Shokhirev, N. V.; Walker, F. A. Biochemistry 2003, 42, 679-693) describes the angle of the effective nodal plane of the axial histidine imidazole in solution. There is an equilibrium between the two heme orientations (A and B), which depends on the heme cavity shape, which can be altered by mutation of amino acids with side chains (phenyl vs tyrosyl) near the potential position where a heme vinyl group would be in one of the isomers. The A:B ratio can be much more accurately measured by NMR spectroscopy than by X-ray crystallography.

Assignment of the ferriheme resonances of the low-spin complexes of nitrophorins 1 and 4 by (1)H and (13)C NMR spectroscopy: comparison to structural data obtained from X-ray crystallography.

In this work we report the assignment of the majority of the ferriheme resonances of low-spin nitrophorins (NP) 1 and 4 and compare them to those of NP2, published previously. It is found that the structure of the ferriheme complexes of NP1 and NP4, in terms of the orientation of the ligand(s), can be determined with good accuracy by NMR techniques in the low-spin forms and that angle plots proposed previously (Shokhirev, N. V.; Walker, F. A. J. Biol. Inorg. Chem. 1998, 3, 581-594) describe the angle of the effective nodal plane of the axial ligands in solution. The effective nodal plane of low-spin NP1, NP4, and NP2 complexes is in all cases of imidazole and histamine complexes quite similar to the average of the His-59 or -57 and the exogenous ligand angles seen in the X-ray crystal structures. For the cyanide complexes of the nitrophorins, however, the effective nodal plane of the axial ligand does not coincide with the actual histidine-imidazole plane orientation. This appears to be a result of the contribution of an additional source of asymmetry, the orientation of one of the zero-ruffling lines of the heme. Probably this effect exists for the imidazole and histamine complexes as well, but because the effect of asymmetry that occurs from planar exogenous axial ligands is much larger than the effect of heme ruffling the effect of the zero-ruffling line can only be detected for the cyanide complexes, where the only ligand plane is that of the proximal histidine. The three-dimensional structures of the three NP-CN complexes, including that of NP2-CN reported herein, confirm the high degree of ruffling of these complexes. There is an equilibrium between the two heme orientations (A and B) that depends on the heme cavity shape and changes somewhat with exogenous axial ligand. The A:B ratio can be much more accurately measured by NMR spectroscopy than by X-ray crystallography.

Magnetic resonance spectroscopic investigations of the electronic ground and excited states in strongly nonplanar iron(III) dodecasubstituted porphyrins.

A series of axially ligated complexes of iron(III) octamethyltetraphenylporphyrin, (OMTPP)Fe(III), octaethyltetraphenylporphyrin, (OETPP)Fe(III), its perfluorinated phenyl analogue, (F(20)OETPP)Fe(III), and tetra-(beta,beta'-tetramethylene)tetraphenylporphyrin, (TC(6)TPP)Fe(III), have been prepared and characterized by (1)H NMR spectroscopy: chloride, perchlorate, bis-4-(dimethylamino)pyridine, bis-1-methylimidazole, and bis-cyanide. Complete spectral assignments have been made using 1D and 2D techniques. The temperature dependences of the proton resonances of the complexes show significant deviations from simple Curie behavior and evidence of ligand exchange, ligand rotation, and porphyrin ring inversion at ambient temperatures. At temperatures below the point where dynamics effects contribute, the temperature dependences of the proton chemical shifts of the complexes could be fit to an expanded version of the Curie law using a temperature-dependent fitting program developed in our laboratory that includes consideration of a thermally accessible excited state. The results show that, although the ground state differs for various axial ligand complexes and is usually fully consistent with that observed by EPR spectroscopy at 4.2 K, the excited state often has S = (3)/(2) (or S = (5)/(2) in the cases where the ground state has S = (3)/(2)). The EPR spectra (4.2 K) of bis-4-(dimethylamino)pyridine and bis-1-methylimidazole complexes show "large-g(max)" signals with g(max) = 3.20 and 3.12, respectively, and the latter also shows a normal rhombic EPR signal, indicating the presence of low-spin (LS) (d(xy))(2)(d(xz),d(yz))(3) ground states for both. The bis-cyanide complex also yields a large-g(max) EPR spectrum with g = 3.49 and other features that could suggest that some molecules have the (d(xz),d(yz))(4)(d(xy))(1) ground state. The EPR spectra of all five-coordinate chloride complexes have characteristic features of predominantly S = (5)/(2) ground-state systems with admixture of 1-10% of S = (3)/(2) character.

NMR and EPR studies of low-spin Fe(III) complexes of meso-tetra-(2,6-disubstituted phenyl)porphyrinates complexed to imidazoles and pyridines of widely differing basicities.

A series of bis-axially ligated complexes of iron(III) tetramesitylporphyrin, TMPFe(III), tetra-(2,6-dibromophenyl)porphyrin, (2,6-Br2)4TPPFe(III), tetra-(2,6-dichlorophenyl)porphyrin, (2,6-Cl2)4TPPFe(III), tetra-(2,6-difluorophenyl)porphyrin, (2,6-F2)4TPPFe(III), and tetra-(2,6-dimethoxyphenyl)porphyrin, (2,6-(OMe)2)4TPPFe(III), where the axial ligands are 1-methylimidazole, 2-methylimidazole, and a series of nine substituted pyridines ranging in basicity from 4-(dimethylamino)pyridine (pK(a)(PyH(+)) = 9.70) to 3- and 4-cyanopyridine (pKa(PyH+) = 1.45 and 1.1, respectively), have been prepared and characterized by EPR and 1H NMR spectroscopy. The EPR spectra, recorded at 4.2 K, show "large g(max)", rhombic, or axial signals, depending on the iron porphyrinate and axial ligand, with the g(max) value decreasing as the basicity of the pyridine decreases, thus indicating a change in electron configuration from (d(xy))2(d(xz),d(yz)3 to (d(xz),d(yz))4(d(xy))1 through each series at this low temperature. Over the temperature range of the NMR investigations (183-313 K), most of the high-basicity pyridine complexes of all five iron(III) porphyrinates exhibit simple Curie temperature dependence of their pyrrole-H paramagnetic shifts and beta-pyrrole spin densities, rho(C) approximately 0.015-0.017, that are indicative of the S = 1/2 (d(xy))(2)(d(xz),d(yz))(3) electron configuration, while the temperature dependences of the pyrrole-H resonances of the lower-basicity pyridine complexes (pK(a)(PyH(+)) < 6.00) show significant deviations from simple Curie behavior which could be fit to an expanded version of the Curie law using a temperature-dependent fitting program developed in this laboratory that includes consideration of a thermally accessible excited state. In most cases, the ground state of the lower-basicity pyridine complexes is an S = 1/2 state with a mixed (d(xy))2(d(xz),d(yz))3/(d(xz),d(yz))4(d(xy))1 electron configuration, indicating that these two are so close in energy that they cannot be separated by analysis of the NMR shifts; however, for the TMPFe(III) complexes with 3- and 4-CNPy, the ground states were found to be fairly pure (d(xz),d(yz))4(d(xy))1 electron configurations. In all but one case of the intermediate- to low-basicity pyridine complexes of the five iron(III) porphyrinates, the excited state is found to be S = 3/2, with a (d(xz),d(yz))3(d(xy))1(d(z)2)1 electron configuration, lying some 120-680 cm(-1) higher in energy, depending on the particular porphyrinate and axial ligand. Full analysis of the paramagnetic shifts to allow separation of the contact and pseudocontact contributions could be achieved only for the [TMPFe(L)2]+ series of complexes.

Assignment of heme resonances and determination of the electronic structures of high- and low-spin nitrophorin 2 by 1H and 13C NMR spectroscopy: an explanation of the order of heme methyl resonances in high-spin ferriheme proteins.

The (1)H NMR resonances of the heme substituents of the low-spin Fe(III) form of nitrophorin 2, as its complexes with N-methylimidazole (NP2-NMeIm) and imidazole (NP2-ImH), have been assigned by a combination of (1)H homonuclear two-dimensional NMR techniques and (1)H-(13)C HMQC. Complete assignment of the proton and partial assignment of the (13)C resonances of the heme of these complexes has been achieved. Due to favorable rates of ligand exchange, it was also possible to assign part of the (1)H resonances of the high-spin heme via saturation transfer between high- and low-spin protein forms in a partially liganded NP2-NMeIm sample; additional resonances (vinyl and propionate) were assigned by NOESY techniques. The order of heme methyl resonances in the high-spin form of the protein over the temperature range of 10-37 degrees C is 8 = 5 > 1 > 3; the NMeIm complex has 5 > 1 > 3 > 8 as the order of heme methyl resonances at <30 degrees C, while above that temperature, the order is 5 > 3 > 1 > 8, due to crossover of the closely spaced 3- and 1-methyl resonances of the low-spin complex at higher temperatures. This crossover defines the nodal plane of the heme orbital used for spin delocalization as being oriented 162 +/- 2 degrees clockwise from the heme N(II)-Fe-N(IV) axis for the heme in the B orientation. For the NP2-ImH complex, the order of heme methyl resonances is 3 > 5 > 1 > 8, which defines the orientation of the nodal plane of the heme orbital used for spin delocalization as being oriented approximately 150-155 degrees clockwise from the heme N(II)-Fe-N(IV) axis. In both low-spin complexes, the results are most consistent with the exogenous planar ligand controlling the orientation of the nodal plane of the heme orbital. In the high-spin form of NP2, the proximal histidine plane is shown to be oriented 135 degrees clockwise from the heme N(II)-Fe-N(IV) axis, again for the B heme orientation. A correlation between the order of heme methyl resonances in the high-spin form of NP2 and several other ferriheme proteins and an apparent 90 degrees shift in the nodal plane of the orbital involved in spin delocalization from that expected on the basis of the orientation of the axial histidine imidazole nodal plane have been explained in terms of bonding interactions between Fe(III), the axial histidine imidazole nitrogen, and the porphyrin pi orbitals of the high-spin protein.