Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between $10^2$ and $10^3$). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. $10^{68}$ possible sequences, which nevertheless constitute only the astronomically small fraction $10^{-80}$ of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models.
Selection of sequence motifs and generative Hopfield-Potts models for protein familiesilies
进化相关蛋白质家族的统计模型最近引起了人们的兴趣：特别是成对Potts模型，如直接耦合分析所推断的那些，已经能够提取有关折叠蛋白质的三维结构的信息，以及蛋白质中氨基酸取代的影响。这些模型通常被要求再现蛋白质家族中氨基酸使用的单点和两点统计，{ \em，即}~以捕获所谓的残基保守和协变统计的共同进化起源的蛋白质。成对Potts模型是实现这一目标的最大熵模型。虽然是成功的，这些模型依赖于大量的{ \em ad hoc}引入的参数，这些参数必须从有限数量的数据中估计，并且其生物物理解释仍然不清楚。在这里，我们提出了一种方法来减少参数，这是基于选择集体序列基序。它自然导致制定的统计序列模型的Hopfield-Potts模型。这些模型可以准确地推断使用映射到限制玻尔兹曼机和持续的对比发散。我们发现，当应用于蛋白质数据时，即使是20-40个模式也足以获得统计上接近生成的模型。Hopfield模式形成可解释的序列基序，并可用于将氨基酸序列聚类为功能亚家族。然而，这些图案的分布式集体本质上限制了Hopfield-Potts模型在预测接触图的能力，显示出开发超越这里讨论的Hopfield-Potts模型的必要性。
Scoring-Assisted Generative Exploration for Proteins (SAGE-Prot): A Framework for Multi-Objective Protein Optimization via Iterative Sequence Generation and Evaluation
ProteinGuide: On-the-fly property guidance for protein sequence generative models
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley（电气工程与计算机科学系，加州大学伯克利分校）；Center for Computational Biology, University of California, Berkeley（计算生物学中心，加州大学伯克利分校）；Department of Molecular and Cell Biology, University of California, Berkeley（分子与细胞生物学系，加州大学伯克利分校）；Innovative Genomics Institute, University of California, Berkeley（创新基因组研究所，加州大学伯克利分校）；Howard Hughes Medical Institute, University of California, Berkeley（霍华德·休斯医学研究所，加州大学伯克利分校）
Molecular dynamics without molecules: searching the conformational space of proteins with generative neural networks
Wayne State University（韦恩州立大学）；Univ. of Bari Aldo Moro（巴里大学阿尔多·莫罗分校）；National Research Council (CONICET)（国家研究委员会（CONICET））；Daruma Institute for Applied Intelligence（达摩应用智能研究所）
Generative power of a protein language model trained on multiple sequence alignments
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Institute of Bioengineering（生物工程研究所）；School of Life Sciences（生命科学学院）；SIB Swiss Institute of Bioinformatics（瑞士生物信息学研究所）
Hotspot-Driven Peptide Design via Multi-Fragment Autoregressive Extension
Tsinghua University（清华大学）；University of Washington（华盛顿大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；ByteDance Inc.（字节跳动公司）；Helixon Inc.（Helixon公司）
Reinforcement-guided generative protein language models enable de novo design of highly diverse AAV capsids
LASIGE, Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院LASIGE实验室）；BioISI, Faculdade de Ciências da Universidade de Lisboa（里斯本大学科学学院BioISI实验室）；iBET – Instituto de Biologia Experimental e Tecnológica（生物实验与技术研究所）
Sparse generative modeling via parameter-reduction of Boltzmann machines: application to protein-sequence families
Universität Basel（巴塞尔大学）；Swiss Institute of Bioinformatics（瑞士生物信息学研究所）；Politecnico di Torino（都灵理工大学）；Italian Institute for Genomic Medicine（意大利基因组医学研究所）；Sorbonne Université（索邦大学）；Université PSL（巴黎文理研究大学）
Modeling Protein Evolution via Generative Inference From Monte Carlo Chains to Population Genetics
Politecnico di Torino（都灵理工大学）；Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Laboratory of Computational and Quantitative Biology（计算与定量生物学实验室）；École Normale Supérieure（巴黎高等师范学院）；PSL Université（巴黎文理研究大学）；Université de Paris（巴黎大学）；The James Franck Institute（詹姆斯·弗兰克研究所）；The University of Chicago（芝加哥大学）；Department of Physics, The University of Chicago（芝加哥大学物理系）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）；Italian Institute for Genomic Medicine, IRCCS Candiolo（意大利基因组医学研究所坎迪奥洛医院）；Dipartimento di Fisica, Sapienza Università di Roma（罗马大学物理系）
Generative Modeling of Full-Atom Protein Conformations using Latent Diffusion on Graph Embeddings
Signal Processing Laboratory (LTS2), EPFL, Lausanne, Switzerland（信号处理实验室（LTS2），瑞士洛桑联邦理工学院）；Institute of Bioengineering, EPFL, Lausanne, Switzerland（生物工程研究所，瑞士洛桑联邦理工学院）；Bioinformatics Group, University & Research Wageningen, The Netherlands（生物信息学组，荷兰瓦赫宁根大学及研究学院）；Ludwig Institute for Cancer Research, Lausanne, Switzerland（癌症研究路易斯研究所，瑞士洛桑）
