Although deep learning approaches have had tremendous success in image, video and audio processing, computer vision, and speech recognition, their applications to three-dimensional (3D) biomolecular structural data sets have been hindered by the geometric and biological complexity. To address this problem we introduce the element-specific persistent homology (ESPH) method. ESPH represents 3D complex geometry by one-dimensional (1D) topological invariants and retains important biological information via a multichannel image-like representation. This representation reveals hidden structure-function relationships in biomolecules. We further integrate ESPH and deep convolutional neural networks to construct a multichannel topological neural network (TopologyNet) for the predictions of protein-ligand binding affinities and protein stability changes upon mutation. To overcome the deep learning limitations from small and noisy training sets, we propose a multi-task multichannel topological convolutional neural network (MM-TCNN). We demonstrate that TopologyNet outperforms the latest methods in the prediction of protein-ligand binding affinities, mutation induced globular protein folding free energy changes, and mutation induced membrane protein folding free energy changes. Availability: weilab.math.msu.edu/TDL/

Complex dendrites in general present formidable challenges to understanding neuronal information processing. To circumvent the difficulty, a prevalent viewpoint simplifies the neuronal morphology as a point representing the soma, and the excitatory and inhibitory synaptic currents originated from the dendrites are treated as linearly summed at the soma. Despite its extensive applications, the validity of the synaptic current description remains unclear, and the existing point neuron framework fails to characterize the spatiotemporal aspects of dendritic integration supporting specific computations. Using electrophysiological experiments, realistic neuronal simulations, and theoretical analyses, we demonstrate that the traditional assumption of linear summation of synaptic currents is oversimplified and underestimates the inhibition effect. We then derive a form of synaptic integration current within the point neuron framework to capture dendritic effects. In the derived form, the interaction between each pair of synaptic inputs on the dendrites can be reliably parameterized by a single coefficient, suggesting the inherent low-dimensional structure of dendritic integration. We further generalize the form of synaptic integration current to capture the spatiotemporal interactions among multiple synaptic inputs and show that a point neuron model with the synaptic integration current incorporated possesses the computational ability of a spatial neuron with dendrites, including direction selectivity, coincidence detection, logical operation, and a bilinear dendritic integration rule discovered in experiment. Our work amends the modeling of synaptic inputs and improves the computational power of a modeling neuron within the point neuron framework.

Budding yeast, which undergoes polarized growth during budding and mating, has been a useful model system to study cell polarization. Bud sites are selected differently in haploid and diploid yeast cells: haploid cells bud in an axial manner, while diploid cells bud in a bipolar manner. While previous studies have been focused on the molecular details of the bud site selection and polarity establishment, not much is known about how different budding patterns give rise to different functions at the population level. In this paper, we develop a two-dimensional agent-based model to study budding yeast colonies with cell-type specific biological processes, such as budding, mating, mating type switch, consumption of nutrients, and cell death. The model demonstrates that the axial budding pattern enhances mating probability at an early stage and the bipolar budding pattern improves colony development under nutrient limitation. Our results suggest that the frequency of mating type switch might control the trade-off between diploidization and inbreeding. The effect of cellular aging is also studied through our model. Based on the simulations, colonies initiated by an aged haploid cell show declined mating probability at an early stage and recover as the rejuvenated offsprings become the majority. Colonies initiated with aged diploid cells do not show disadvantage in colony expansion possibly due to the fact that young cells contribute the most to colony expansion.