De novo protein design using geometric vector field networks

Innovations like protein diffusion have enabled significant progress in de novo protein design, which is a vital topic in life science. These methods typically depend on protein structure encoders to model residue backbone frames, where atoms do not exist. Most prior encoders rely on atom-wise features, such as angles and distances between atoms, which are not available in this context. Thus far, only several simple encoders, such as IPA, have been proposed for this scenario, exposing the frame modeling as a bottleneck. In this work, we proffer the Vector Field Network (VFN), which enables network layers to perform learnable vector computations between coordinates of frame-anchored virtual atoms, thus achieving a higher capability for modeling frames. The vector computation operates in a manner similar to a linear layer, with each input channel receiving 3D virtual atom coordinates instead of scalar values. The multiple feature vectors output by the vector computation are then used to update the residue representations and virtual atom coordinates via attention aggregation. Remarkably, VFN also excels in modeling both frames and atoms, as the real atoms can be treated as the virtual atoms for modeling, positioning VFN as a potential universal encoder. In protein diffusion (frame modeling), VFN exhibits an impressive performance advantage over IPA, excelling in terms of both designability (67.04% vs. 53.58%) and diversity (66.54% vs. 51.98%). In inverse folding (frame and atom modeling), VFN outperforms the previous SoTA model, PiFold (54.7% vs. 51.66%), on sequence recovery rate. We also propose a method of equipping VFN with the ESM model, which significantly surpasses the previous ESM-based SoTA (62.67% vs. 55.65%), LM-Design, by a substantial margin

Glycolysis mediates neuron specific histone acetylation in valproic acid-induced human excitatory neuron differentiation

Pregnancy exposure of valproic acid (VPA) is widely adopted as a model of environmental factor induced autism spectrum disorder (ASD). Increase of excitatory/inhibitory synaptic transmission ratio has been proposed as the mechanism of VPA induced ASD. How this happened, particularly at the level of excitatory neuron differentiation in human neural progenitor cells (NPCs) remains largely unclear. Here, we report that VPA exposure remarkably inhibited human NPC proliferation and induced excitatory neuronal differentiation without affecting inhibitory neurons. Following VPA treatment, mitochondrial dysfunction was observed before neuronal differentiation, as showed by ultrastructural changes, respiratory complex activity, mitochondrial membrane potential and oxidation levels. Meanwhile, extracellular acidification assay revealed an elevation of glycolysis by VPA stimulation. Interestingly, inhibiting glycolysis by 2-deoxy-d-glucose-6-phosphate (2-DG) efficiently blocked the excitatory neuronal differentiation of human NPCs induced by VPA. Furthermore, 2-DG treatment significantly compromised the VPA-induced expression of H3ac and H3K9ac, and the VPA-induced binding of H3K9ac on the promoter of Ngn2 and Mash1, two key transcription factors of excitatory neuron fate determination. These data, for the first time, demonstrated that VPA biased excitatory neuron differentiation by glycolysis-mediated histone acetylation of neuron specific transcription factors

Discretizing a backward stochastic differential equation

We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs

A representation formula for transition probability densities of diffusions and applications

We establish a representation formula for the transition probability density of a diffusion perturbed by a vector field, which takes a form of Cameron-Martin's formula for pinned diffusions. As an application, by carefully estimating the mixed moments of a Gaussian process, we deduce explicit, strong lower and upper estimates for the transition probability function of Brownian motion with drift of linear growth.Heat kernel estimates Diffusion

Falconius Bolivar 1898

Key t o the species of <i>Falconius</i> Bolivar, 1898 <p>1. Posterior angles of lateral lobes of pronotum stickle-like, apice of spine curved forward (Fig. 1).............................. 2</p> <p>- Posterior angles of lateral lobes of pronotum apices spine transverse (Fig. 2).......................................................... 10</p> <p> 2. Width of vertex equal to width of one eye; with one rounded concavity before posterior angles of lateral lobes of pronotum (Fig. 3) <i>................................................................................................. Falconius pseudoclavitarsis</i> Günther</p> <p>- Width of vertex wider than width of one eye; without rounded concavity before posterior angles of lateral lobes of pronotum....................................................................................................................................................................... 3</p> <p> 3. Spine of posterior angles slightly curved forward; upper margin of pronotum slightly straight in profile (Fig. 4)....... <i>..................................................................................................................................... Falconius palawanicus</i> Günther</p> <p>- Spine of posterior angles distinctly curved forward; upper margin of pronotum compresso-elevated in the form of hump between shoulders (Fig. 5) or undulated in profile (Fig. 6)................................................................................ 4</p> <p>4. Upper margin of pronotum compresso-elevated in the form of hump between shoulders in profile........................... 5</p> <p>- Upper margin of pronotum undulated, without compresso-elevated, not hump between shoulders in profile............ 6</p> <p> 5 Width of vertex 1.4 times the width of one eye; head not exserted above the pronotal surface; lower margins of mid- dle femur with two projections (Fig. 7) <i>...............................................................................</i> <i>Falconius bedoti</i> (Bolivar)</p> <p> - Width of vertex 2 times the width of one eye; head distinctly exserted above the pronotal surface; lower margins of middle femur nearly straight (Fig. 8) <i>.............................................................................</i> <i>Falconius clavitarsis</i> (Bolivar)</p> <p>6. Lower margins of middle femur nearly straight........................................................................................................... 7</p> <p>- Lower margins of middle femur undulated, with two projections............................................................................... 8</p> <p> 7. Width of vertex 1.5 times the width of one eye; width of tegmina 1.5 times the width of middle femur; first segment of hind tarsi expanded <i>........................................................................................................... Falconius dubius</i> Günther</p> <p> - Width of vertex 2 times the width of one eye; width of tegmina twice the width of middle femur; first segment of hind tarsi not expanded <i>..................................................................................... Falconius guangxiensis</i> Zheng et Jiang</p>Published as part of <i>Deng, Weian, Zheng, Zhemin & Wei, Shizhen, 2009, A review of the genus Falconius Bolivar (Orthoptera: Tetrigoidea: Scelimeninae), pp. 63-68 in Zootaxa 1976</i> on pages 64-65, DOI: <a href="http://zenodo.org/record/185173">10.5281/zenodo.185173</a&gt