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Hamiltonian (2.9) is not separable and the system is nonintegrable. 9 On the other hand, for a point particle all constant-curvature black holes have a full set of integrals of motion leading to the integrability of geodesics: for the sphere, the additional integrals (besides E) are L 2 and L z from SO(3), and for the ...	300	145856149	16
not separable, and dynamics is nonintegrable. One could change variables in the metric (2.1) as (φ1, φ2) → (φ 1 = φ1 cos φ2, φ 2 = φ1 sin φ2), and the string with the wrapping Φ 2 = nσ would provide an integrable system, with the separable Hamiltonian H = f But that is a different system from (2.9): even though a chang...	301	145856149	16
lines in the Poincare section in figure 1) and increasing areas covered with chaotic (area-filling) orbits. This is also obvious from the figure 2. 2. Orbits closer to the horizon are more chaotic than those further away; this will be quantified by the analysis of the Lyapunov exponents. This is logical, since the equa...	302	145856149	16
show the orbits in the vicinity of the spherical (A) and hyperbolic (B) horizon, at T = 0.01 (left) and T = 0.10 (right); obviously, hot horizons generate more chaos than cold ones. The light blue dot is the initial condition of the orbit (the position of the point on the string with Φ = 0 at τ = 0). Figure 3. Thermal ...	303	145856149	16
black hole. The phase space has invariant planes given by (R, P R , Φ, P Φ ) = (R 0 + Eτ, E/f 0 , N π, 0), with R 0 = const. and f 0 ≡ f (R 0 ) and N an integer. It is easy to verify this solution by first plugging inΦ = 0 into (2.8) to find Φ; eq. (2.7) and the constraint (2.9) then reduce to one and the same conditio...	304	145856149	16
with one undetermined constant, and we can match the constants to obtain a consistent solution: The value of r 0 is found from the need to satisfy also the Hamiltonian constraint. The constraint produces a Jacobi elliptic function with a different argument, and the matching to (2.10) reads 2f (r 0 ) + r 0 f (r 0 ) = 0....	305	145856149	16
f ∼ a(r − r 2 h ) ≡ a 2 , a smooth and finite limit is obtained by rescaling E → E 2 . Now expanding the sn function in produces simply a linear function at first order in : Therefore, a string can hover at the extremal horizon, at strict zero temperature, when its motion (angular rotation) becomes a simple linear wind...	306	145856149	16
H = 0. But eq. (2.7) implies exponential motion instead, D 1 sinh nτ + D 2 cosh nτ . Obviously, there is no way to make these two forms consistent. Accordingly, no hovering on the horizon (nor at any other fixed radial slice) is possible for a planar black hole. But the same logic that lead to (2.13) now predicts oscil...	307	145856149	16
δX(0) small enough in practice. This definition makes sense for classical systems; in quantum -10 - JHEP12(2019)150 mechanics, the linearity of the state vector evolution guarantees zero exponent but the intuition that initially small perturbations eventually grow large in a strongly coupled system remains when we look...	308	145856149	16
order. One might worry that the Lyapunov exponents are gauge-dependent, as we consider equations of motion in terms of the worldsheet coordinate τ , and for different worldsheet coordinates the variational equations would be manifestly different; in other words, the definition (3.1) depends on the choice of the time co...	309	145856149	16
, Φ(τ ) + ∆Φ (τ )). Then we expand in inverse powers of r 0 − r h , and express the angular combinationsΦ 2 ±sink 2 Φ making use of the constraint (2.9). When the dust settles, the leading-order equations simplify to: where C = C(k, E) is a subleading (at low temperature) correction whose form differs for spherical, pl...	310	145856149	16
by series expansion (with just the AdS term r 2 + k in f , without the leading black hole contribution A/r, we would trivially have integral motion and zero λ; but this approximation applies at large, not at intermediate distances). In this case the equations of motion yield R ∼ τ √ E 2 − 1, and the variational equatio...	311	145856149	16
will likely appear, which we see also in the numerics. That the motion is chaotic on a pseudosphere (negative curvature) is of course no surprise; it is long known that both particles and waves have chaotic scattering dynamics on pseudospheres [46]. We dub this contribution the scattering contribution to the Lyapunov e...	312	145856149	16
bound is however multiplied by the winding number n of the ring string. The spirit of the bound is thus preserved but an extra factor -the winding numberenters the story. 3. Taking into account also the scattering chaos described by (3.9), the results are in striking accordance with the idea of [2]: there are two contr...	313	145856149	16
and the horizon, or to fall into the black hole. In other words, it is assumed that the Lyapunov time is much shorter than the "lifetime" of the string (let us call it event time t E ). Now we will show that this is indeed so. For the spherical black hole, upon averaging over the angle Φ, we are left with a one-dimensi...	314	145856149	16
λ ≤ 2πk B T / , and we have no in our system so far. The resolution is simple: the role of is played by the inverse string tension 2πα , which is obvious from the standard form JHEP12(2019)150 of the string action (2.3); the classical string dynamics is obtained for α → 0. Therefore, the dimensionful bound on chaos for...	315	145856149	16
n (B) are consistent with the analytical prediction. All calculations were done for the initial conditionṘ(0) = 0, and with energy E chosen to ensure a long period of hovering near the horizon. The temperatures are low enough that the scattering contribution is almost negligible. In figure 5 we look at the scattering t...	316	145856149	16
a forced nonlinear oscillator, it does not ring a bell on why to expect the systematic modification of the Maldacena-Shenker-Stanford bound and what the factor n means. Thus it makes sense to do two simple exercises: first, to estimate the energy and spin of the operators corresponding to (2.5) to understand if it has ...	317	145856149	16
the redshift function f (r) which depends on dimensionality. This, however, does not change the main story. We can redo the calculation of the radial fixed point from the second section, to find a similar result -a string can oscillate or run away/fall slowly in the vicinity of a horizon, and the variational equations ...	318	145856149	16
regimes: small amplitude φ 0 π which translates to E/T 1, and large amplitude φ 0 ∼ π, i.e., E/T ∼ 1. For these two extreme cases, we get: For the spin similar logic gives The bottom line is that in both extreme regimes (and then presumably also in the intermediate parameter range) we have E ∝ E/α n and S ∝ E 2 /α nT ;...	319	145856149	16
the OTOC never factorizes and the bound from [1] does not apply. Planetoid string In this subsubsection we consider so-called planetoid string configurations, also studied in [47] in the zero-temperature global AdS spacetime and shown to reproduce the leading Regge trajectory in gauge theory. This is again a closed str...	320	145856149	16
2 =Φ 1 2 − n 2 sin 2 Φ 1 is the adiabatic invariant on this submanifold. With two integrable submanifolds, a generic orbit will wander between them and exhibit chaos. The variational equations can be analyzed in a similar fashion as in the previous section. Here, the chaotic degree of freedom is Φ 1 (τ ), with the vari...	321	145856149	16
2πT ). In the vicinity of the other solution, with R = r 0 , things are different. Energy has the following behavior: For the spin, the outcome is so in this case there is no Regge trajectory at all, i.e., no simple relation for E 2 (S) because the scale r 0 and the quantity show up in the E 2 (S) dependence even at ze...	322	145856149	16
gives E ≥ 2πT n 2 α . On the other hand, we require that the spin S should be large in the classical regime: S 1. This implies E 2 4πT nα or, combining with the uncertainty relation, T n 3 α . Roughly speaking, we need to satisfy simultaneously T n 2 ≤ 1/α and T n 3 /α , which is perfectly possible: first, we need to h...	323	145856149	16
some boundary operator. In [17] this formalism was already applied to study the OTOC of field theory operators (heavy quarks) dual to an open string in BTZ black hole background, hanging from infinity to infinity through the horizon in eikonal approximation. That case has a clear interpretation: the endpoints of the st...	324	145856149	16
the horizon. In the Kruskal coordinates defined the usual way: the scattering amplitude becomes (4.18) The propagators are expressed in terms of the Kruskal momenta p i = (p U i , p V i ) and the coordinates x i = (x 1 i , x 2 i ) in the transverse directions. The in-state is defined by (p U 3 , x 3 ) at U = 0, and by ...	325	145856149	16
satisfied if the energy and thus the velocity is high enough) the coordinates are also roughly conserved, therefore the amplitude out\|in is diagonal and can be written as a phase shift exp(ıδ). The point of the eikonal approximation is that the JHEP12(2019)150 shift δ equals the classical action. The action of the ring...	326	145856149	16
obtain: with N ω containing the first two factors in (4.19) which only depend on ω and T . Introducing the change of variables p = Q sin γ, q = Q cos γ, we can reduce (4.28) to an exponential integral. With the usual contour choice for OTOC t i = − i , t 1 = t 3 = 0, t 2 = t 4 = t, we end up at leading order with There...	327	145856149	16
classical Lyapunov exponent, remains equal to 2πT ; it is only seen in the timescale on which the perturbation permeates the whole system. In conclusion, the violation of the Maldacena-Shenker-Stanford limit for the bulk Lyapunov exponent in AdS space in the eikonal approximation likely corresponds to a decrease of scr...	328	145856149	16
this is not the case, since it stretches along the radial direction and the scattering event -which is mostly limited to near-horizon dynamics because this is where the energy is boosted to the highest values -remains confined to a small segment of the string, whereas any oscillations propagate from end to end. However...	329	145856149	16
boosted pertrubation near the horizon, with \|z\| ∼ 1/s. At leading order in the expansion over T, X, the action (4.21) decouples the Gaussian functional integral over the (T, X) coordinates from the pendulum dynamics of the Φ coordinate. We can just as easily use the (U, V ) dynamics, with 1/2(Ṫ 2 −Ẋ 2 ) → −2UV ; this i...	330	145856149	16
n 2 Φ 2 . With the effective potential for the tachyon V eff (Φ) = n 2 Φ 2 , the worldsheet propagator takes the form For the plane wave states we take the ansatz ψ(Φ) = e ı Φ , where = l−ıν, with l ∈ Z being the angular momentum and 0 < ν 1 the correction from the interactions (fortunately we will not need the value o...	331	145856149	16
conclude that in the strong stringy regime the Lyapunov exponent in dual field theory behaves as 2π(1 + πα n 2 )T , differing from the expected chaos bound for nonzero winding numbers n. Thus, if the classical gravity eikonal approximation does not hold, the modification of the bulk Lyapunov exponent also has an effect...	332	145856149	16
-25 - JHEP12(2019)150 anyway, but the question remains why the bound is modified upwards instead of simply being unsaturated (in other words, we would simply expect to get λ < 2πT ). The twist is that the Lyapunov exponent in the bulk is related to but in general distinct from the Lyapunov exponent in field theory, usu...	333	145856149	16
an increased value for the field-theory Lyapunov rate, yielding some credit to the interpretation that complicated string configurations encode for strongly nonlocal operators, which might indeed violate the bound. But as we have explained, the approximations we took are rather drastic. We regard a more systematic stud...	334	145856149	16
the geometry deformed by N f additional D-branes in the bulk. In [50] it was found that the system becomes nonintegrable in the presence of the flavor branes (expectedly, as it becomes non-separable), but the Lyapunov exponent does not grow infinitely with the number of flavors, saturating instead when the number of co...	335	145856149	16
in turn be obtained as string excitations. Just how far can one go in making all this precise we do not know for now. In relation to [15,16] one more clarifying remark should be given. In these works, particles in the vicinity of the horizon are found to exhibit chaos (either saturating the bound or violating it, depen...	336	145856149	16
a string, along the lines of [7]. In this paper we have worked in the probe limit (no backreaction), whereas the true scrambling is really the relaxation time of the black hole (the time it needs to become hairless again), which cannot be read off solely from the Lyapunov time; this is the issue we also mentioned in th...	337	145856149	16
Discordant Amyloid Status Diagnosis in Alzheimer’s Disease Introduction: Early and accurate Alzheimer’s disease (AD) diagnosis has evolved in recent years by the use of specific methods for detecting its histopathological features in concrete cases. Currently, biomarkers in cerebrospinal fluid (CSF) and imaging techniq...	338	253458763	16
between amyloid PET and CSF biomarkers. Introduction Increasingly, middle-aged people suffer from memory loss, subjective complaints without any medical evidence, cognitive impairment derived from other disorders (e.g., anxiety and depression), and dementia, with Alzheimer's disease (AD) being the most common [1]. AD d...	339	253458763	16
between Aβ42, Tau, and neuroinflammation in AD and mild cognitive impairment (MCI), allowing us to differentiate among the changes associated with the normal aging process or the physiopathological processes of the disease. In fact, PET imaging enables preclinical AD detection [8], and it has some advantages, such as b...	340	253458763	16
additional tools, such as neuropsychological tests, in order to help in discrepant case diagnosis in clinical practice. Participants and Samples Collection The study involved patients from the neurology unit from the Hospital Universitari I Politècnic la Fe (Valencia, Spain) (n = 82), with ages between 48 and 80 years....	341	253458763	16
(severe dementia) [16]. The RBANS (repeatable battery for neuropsychological status assessment) test is a neuropsychological battery that evaluates 5 areas: immediate memory (IM), language (L), attention (A), delayed memory (DM), and visuospatial construction (VC). A resulting score lower than 85 in some areas would in...	342	253458763	16
groups, showing that around 18% of cases were discrepant. Additionally, it can be seen that discrepant results are mainly from intermediate CSF levels, which are close to the cut-off point (750 pg mL −1 ). In addition, Figure 2 shows that most of the discrepant cases correspond to patients with positive amyloid PET (1)...	343	253458763	16
to the cut-off point (750 pg mL −1 ). In addition, Figure 2 shows that most of the discrepant cases correspond to patients with positive amyloid PET (1) and negative CSF biomarkers (Aβ42 levels ≥ 750 pg mL −1 ). Similarly, a comparison between amyloid PET and the ratio between t-Tau and Aβ42 showed 18% of discrepant ca...	344	253458763	16
REVIEW 5 of 11 The diagnosis potential of the neuropsychological evaluation was evaluated with special attention to discordant cases; specifically, the scores obtained from CDR and RBANS. DM tests were assessed as complementary tools to the biochemical and imaging tests. For discrepant cases, patients with negative CSF...	345	253458763	16
reflect considerable variability in the classification of patients according to amyloid PET results, especially in cases with high levels of Aβ42 in CSF and high scores in RBANS.DM. Among the CDR results, there was no correlation between CSF biomarkers levels in the same way that happens in the other RBANS subsets. Bio...	346	253458763	16
for the diagnosis of AD is based on the evaluation of the amyloid status by means of CSF biomarker Aβ42 or amyloid PET imaging [18]. In this work, an assessment of the concordance between the results from CSF biomarker levels (Aβ42) and amyloid PET tests was carried out in order to compare their reliability in the diag...	347	253458763	16
Aβ42/Aβ40 ratio showed better concordance with amyloid PET results [24]. However, the t-Tau/Aβ42 ratio showed similar results to Aβ42 in our study. These differences among studies could be explained by the different cut-off points used, as well as by the differences in the selection of participants. In the present work...	348	253458763	16
analytical techniques considered the gold standard in AD diagnosis. Regarding the amyloid deposition, previous studies described the deposition of peptides Aβ37 or Aβ39 in extracellular plaques [21]. In addition, perivascular deposits in some amyloid plaques could contribute to high variability in amyloid PET results. ...	349	253458763	16
their higher risk levels for AD [25], as well as the higher number of female participants in this study. In addition, these could be explained by the influence of other factors, such as the ApoE genotype (not available in our data) [26]. Therefore, studies in other cohorts are necessary to confirm these results. Regard...	350	253458763	16
(positive) could be AD patients; however, if CSF Aβ42 levels are ≥the cut-off point (negative), the AD diagnosis was not corroborated. In these discrepant cases, the patients' cognitive impairment was evaluated according to the RBANS.DM domain, which constitutes an important tool in establishing diagnosis, much as it i...	351	253458763	16
most health systems. The main limitations of this study are the small sample size and the reduced number of discordant cases. In addition, the participants were patients from the Neurology Unit; therefore, the sample could be biased. Moreover, the specific cut-off point used according to clinical practice in this unit ...	352	253458763	16
Ministry of Economy and Competitiveness) and co-funded by European Union, ERDF "A way to make Europe". CCP acknowledges CPII21/00006. CPB acknowledges PFIS FI20/00022. LAS acknowledges Río Hortega CM20/00140. Institutional Review Board Statement: The study was conducted in accordance with the Declaration of Helsinki, a...	353	253458763	16
NEXGB: A Network Embedding Framework for Anticancer Drug Combination Prediction Compared to single-drug therapy, drug combinations have shown great potential in cancer treatment. Most of the current methods employ genomic data and chemical information to construct drug–cancer cell line features, but there is still a ne...	354	251998482	16
drug resistance [4]. For cancer patients, choosing the right combination of drugs to improve the efficiency of their treatment can greatly reduce their suffering. Traditional drug combination identification methods often consider clinical trials or high-throughput screening (HTS) [5], but they still have many problems....	355	251998482	16
vector machine) and employed four features based on drug-drug similarity to identify the drug combinations [14]. Yu et al. applied similarity networks to predict drug-target interactions and demonstrated the feasibility of predicting drug combinations through network embeddings [15,16]. Advances in biological technolog...	356	251998482	16
of considering potential drug-drug-disease relationships through a PPI network. Graph convolutional neural networks and self-attention mechanisms have been applied in the fields of predicting frequently occurring diseases and predicting compound-protein interactions [23,24]. Yang et al. proposed a method based on a gra...	357	251998482	16
we demonstrate the superiority of the NEXGB model and its predictive performance in specific tissues and specific cell lines. Parameter Relation In this study, struc2vec is used to generate feature vectors for proteins. We set the length of random walk sequences to 80, and each node generates 20 random walk sequences. ...	358	251998482	16
We compare the performance of NEXGB with other baselines. The compared methods include network proximity (NP [22]), matrix factorization (GraRep [30]), random walk (DeepWalk [31]), deep neural network (DeepSynergy [17]), and graph convolutional network (GraphSynergy [25]). NP quantifies the proximity between drug targe...	359	251998482	16
of the output node feature, and we output the 32-dimensional, 64-dimensional, and 128-dimensional node feature vectors through the PPI network. To illustrate the effect of feature dimension on the model, we train three different dimensions of features on the Oncology-Screen dataset. Through the ROC curve and AUC value,...	360	251998482	16
of the output node feature, and we output the 32−dimensional, 64−dimensional, and 128−dimensional node feature vectors through the PPI network. To illustrate the effect of feature dimension on the model, we train three different dimensions of features on the Oncology−Screen dataset. Through the ROC curve and AUC value,...	361	251998482	16
indexes were taken as the average value. We find that on the Oncology-Screen dataset, the recall value of XGBoost is not as good as that of SVM, but the other metrics are the best. Among the recall values, XGBoost is 0.827 and SVM is 0.829. Although the recall value of SVM is high, its performance on the other five met...	362	251998482	16
is represented by the ROC−AUC value under cross−validation. Figure 3 shows the expression of NEXGB in different cell lines and tissues. NEXGB has strong predictive power (ROC−AUC greater than 0.7) for over 75% of cell lines (Figure 3a). The ROC−AUC values of different cell lines range from 0.587 to 0.835. Among all 29 ...	363	251998482	16
the lowest ROC-AUC value. The ES2 cell line has the fewest associated target proteins (56 associated target proteins), which may be one of the reasons for the poor performance of ES2 cell lines. However, the number of related target proteins is also less than 100, and DLD1 (75 related target proteins) belonging to colo...	364	251998482	16
reflecting the relationships between cell lines in 2D space. Figure 4 shows that all cell lines are divided into two clusters by the density-based spatial clustering of applications with noise (DBSCAN) clustering algorithm. We find that the ES2 cell line belongs to a separate category, and the rest of the cell lines be...	365	251998482	16
advances in network medicine [21,22]. To better learn the potential information between nodes in the PPI network, we use struc2vec to explore the synergy between anticancer drugs, drugs, and cell lines. The input features of XGBoost are the vector combinations of drugs and cell lines, and the output is the predicted pr...	366	251998482	16
and other existing methods. The increase in available information brings corresponding problems. Different measurement standards in the same drug combination leads to different results. How to balance these biological experimental data is also a critical problem. Nonetheless, we believe that further studies in pharmaco...	367	251998482	16
by GeneCards. Drug-Protein Associations. A total of 15,051 drug-protein associations are established based on FDA-approved or clinically investigated drugs [22]. The dataset contains 4428 drugs and 2256 unique human proteins (accessed on 17 September 2021). Cell-Protein Associations. The cell-protein association datase...	368	251998482	16
(label: 0). We concatenate the obtain drug features and cell line features according to the drug-drug-cell line combination data, input the combined features and labels into XGBoost for training, and output the prediction results. We further formulate the synergistic drug combination prediction problem as a binary clas...	369	251998482	16
nodes u and v can be denoted as: where f −1 = 0, R k (u) is the set of nodes with distance k(k ≥ 0) from node u, s(R k (u)) is the ordered degree sequence of node set R k (u), and g(s(R k (u)), s(R k (v))) > 0 is a measure of the distance between the ordered sequences s(R k (u)) and s(R k (v)). In general, s(R k (u)) a...	370	251998482	16
graph. When performing a random walk, staying at the current layer with the probability q, the probability from node u to node v in the k-th layer is: where z k (u) = ∑ v 1 u e − f k (u,v) is the normalization factor for vertex u in layer k. The random walk switches to other layers with probability 1 − q, and the proba...	371	251998482	16
cancer cell lines. In addition, the results on specific cell lines suggest that ES2 cell lines may have unique biological properties among ovarian cancer cell lines. Author Contributions: F.M. and F.L. jointly contributed to the design of the study. F.M. and Y.L. designed and implemented the method, performed the exper...	372	251998482	16
Light scattering by a vacuum-like sphere with magnetoelectric gyrotropy An exact transition matrix was formulated for electromagnetic scattering by a vacuum-like sphere with magnetoelectric gyrotropy. Both the total scattering and forward scattering efficiencies are lower when the magnetoelectric gyrotropy vector of th...	373	119259491	16
(2) is like free space with magnetoelectric properties. If an object made of a linear homogeneous material described by Eqs. (3) were to be placed in conventional free space, its scattering characteristics should depend on the magnitude and direction of w. We decided to theoretically examine this proposition by conside...	374	119259491	16
located at the origin of a Cartesian coordinate system (x, y, z). The ambient medium is free space. The sphere is illuminated by a plane wave with field phasors Without any loss of generality, we fix k inc = k 0ẑ , e inc x, and h inc = (ωµ 0 ) −1 (k inc × e inc ) ŷ. Incident-field representation In order to formulate t...	375	119259491	16
given by and total scattering efficiency is given as Internal-field representation The electric and magnetic field phasors excited inside the vacuum-like sphere with magnetoelectric gyrotropy are represented by [13,17] the coefficients b smn and c smn being unknown. Equations (28) and (29) lead to the relation is the T...	376	119259491	16
left Q ext , Q sca , Q f , and Q b unchanged. When w ẑ, both w and the direction of propagation of the incident plane wave had to be reversed together for Q ext , Q sca , Q f , and Q b to remain unchanged. Regardless of the choice of w, we found that Q ext = Q sca , implying that the absorption efficiency Q abs = 0. Th...	377	119259491	16
the size parameter increases. Efficiencies The plots of Q sca , Q f , and Q b as functions of the size parameter k 0 a when w h inc are identical to those when w e inc . Thus, the effect of magnetoelectric gyrotropy is independent of its orientation when w ⊥ k inc . Figure 2 shows plots of Q sca , Q f , and Q b as func...	378	119259491	16
and Q f , as is clear from comparing Figs. 2 and 3. Both Q sca and Q f are higher when w is coparallel, than when w is antiparallel, to the propagation vector k inc of the incident plane wave. Given the foregoing trends, for arbitrarily directed w it is reasonable to expect that the effects of the component of w that i...	379	119259491	16
maximum magnitude of the former is smaller than that of the latter, when w e inc . When w is co/anti-parallel to k inc , the differential scattering appears identical in the φ = 0 • and φ = 90 • planes, as shown in Figs. 4(c) and 4(d). However, more lobes exist when w is co-parallel than when it is anti-parallel to k i...	380	119259491	16
the radius of the sphere is less than a tenth of the free-space wavelength. As an example, Fig. 5 depicts plots of Q Rayleigh sca and Q sca versus k 0 a ∈ (0, 0.6] for \|w\| = 0.25. Clearly, the long-wavelength approximation agrees well for entire range of k 0 a when w is coparallel to k inc . When w is parallel to the i...	381	119259491	16
be monotonic but undulatory. Both the total scattering and forward scattering efficiencies are generally lower when the magnetoelectric gyrotropy vector of the sphere is perpendicular to the propagation vector of the incident plane wave than when it is anti-parallel to the propagation vector. Further enhancements occur...	382	119259491	16
Genetic variations in GBA1 and LRRK2 genes: Biochemical and clinical consequences in Parkinson disease Variants in the GBA1 and LRRK2 genes are the most common genetic risk factors associated with Parkinson disease (PD). Both genes are associated with lysosomal and autophagic pathways, with the GBA1 gene encoding for t...	383	251518480	16
of alpha-synuclein protein aggregates (1,2). PD patients exhibit a classic triad of motor symptoms including bradykinesia, rigidity and resting tremor. A spectrum of non-motor symptoms has also been described, including cognitive decline, sleep disturbances, hyposmia and psychiatric symptoms (3). Approximately 10-15% o...	384	251518480	16
kDa lysosomal hydrolase enzyme, glucocerebrosidase (GCase). The mature GCase peptide consists of 497 residues and is comprised of three noncontinuous domains (as shown in Figure 1). The active site is located in Domain III, which is a (β/α) 8 triosephosphate isomerase (TIM). Domain I consists of an antiparallel βsheet,...	385	251518480	16
RecNcil) are shown with spheres. The color of the spheres corresponds with the odds ratio associated with the variant: green (< ); yellow ( -) and red (> ) ( , ). This figure was created using The PyMOL Molecular Graphics System, Version . Schrödinger, LLC. Common GBA variants Almost 300 unique variants have been repor...	386	251518480	16
of N370S GBA1 is the only X-ray structure resolved. The N370S mutation occurs at the interface of domains II and III (9) and prevents stabilization of loop 3 at an acidic pH, impairing the ability of GCase to bind its substrate (12, 24). Within PD, GBA1 gene variants are stratified into complex, severe, mild and risk v...	387	251518480	16
However, more recent longitudinal studies suggest that GBA1 status does not influence the risk of developing motor complications, even where different types of variants were considered separately (52)(53)(54). Evaluating the biochemical consequences of GBA1 variants and their relationship with clinical features may aid...	388	251518480	16
often lead to a loss of GCase function. Analysis of GCase activity in the blood of PD patients has demonstrated that patients with severe GBA1 mutations exhibit a greater reduction in GCase activity when compared to those with mild GBA1 mutations and risk variants (56). This is supported by functional analysis of recom...	389	251518480	16
cell-derived midbrain dopamine neurons, heterozygous N370S mutations cause a loss of GCase function, impaired macroautophagy and alpha-synuclein pathology. This was rescued by the small molecular chaperone, ambroxol, suggesting these arose due to improper trafficking and activity of N370S GCase protein (68). In cells h...	390	251518480	16
L444P and N370S fibroblasts exhibited an increase in the release of extracellular vesicles compared to control lines. However, alpha-synuclein pathology in SH-SY5Y cells was only promoted when incubated with vesicles isolated from L444P lines, and not N370S lines (76). In addition, a recent study showed that the E326K ...	391	251518480	16
demonstrated, which correlated with decreased GCase activity. When these lipids were extracted and incubated with recombinant alpha-synuclein, an increase in the pathogenic aggregation of alpha-synuclein was observed, due to a higher content of short-chain lipids in the L444P cells (81). This may occur as lipid membran...	392	251518480	16
may correlate with disease severity, perhaps due to more pronounced conformational changes. However, another fibroblast study has demonstrated heterogeneity in ER retention and degradation across lines with the N370S genotype (86), weakening the genotype-phenotype correlation argument. Overall, current evidence suggest...	393	251518480	16
can cross the BBB and enter the CSF where it can alter GCase activity and protein level (ClinicalTrials.gov Identifier: NCT02941822) (98). Ambroxol also increased the alpha-synuclein concentration in the CSF and, importantly, improved motor function. A phase III clinical trial of ambroxol in treating PD is expected to ...	394	251518480	16
protein, to the GCase enzyme (106). Denali Therapeutics have recently developed the transport-vehiclemodified recombinant GCase enzyme (ETV:GBA1) compound, using their transport vehicle platform technology which has the potential to actively transport enzymes across the BBB (107). Preclinical research is underway with ...	395	251518480	16
decline in motor function in PD (ClinicalTrials.gov Identifier: NCT02906020). LRRK2 is expressed ubiquitously in the brain, including neurons and glial cells, as well as in the kidneys, lungs, liver, heart and immune cells (118)(119)(120)(121). The LRRK2 protein is thought to be primarily cytosolic but can also localiz...	396	251518480	16
ROC domain contains motifs that are conserved amongst GTP-binding proteins, suggesting that LRRK2 is a functioning GTPase that can regulate LRRK2 kinase activity (132)(133)(134)). An in vitro study showed that the R144C/G/H/S mutations located in the ROC domain, increases kinase activity while decreasing GTP hydrolysis...	397	251518480	16
10% of cases, respectively), whereas the variant is rarely found in Asians (only 0.1%) (145). The penetrance of PD in subjects carrying a LRRK2 mutation is not fully elucidated and varies with age, which may explain both the high prevalence of mutations in sporadic PD cases and the detection of mutations in unaffected ...	398	251518480	16
Although data comparing different genotypes is limited, there may be genotype-phenotype associations within LRRK2-PD, with risk variants showing a more rapid progression and G2019S a more benign course. Higher incidence of postural instability gait difficulty (PIGD) sub-type has been reported in PD patients of both AJ ...	399	251518480	16

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