Training with millions of crystal data to solve the crystallographic phase problem, the deep learning method PhAI is published in Science

Editor | KX

To this day, the structural detail and precision determined by crystallography, from simple metals to large membrane proteins, are unmatched by any other method. However, the biggest challenge, the so-called phase problem, remains retrieving phase information from experimentally determined amplitudes.

Researchers at the University of Copenhagen, Denmark, have developed a deep learning method called PhAI to solve crystal phase problems. A deep learning neural network trained using millions of artificial crystal structures and their corresponding synthetic diffraction data can generate accurate electron density maps. .

Research shows that this deep learning-based ab initio structure solution method can solve the phase problem at a resolution of only 2 Angstroms, which is equivalent to only 10% to 20% of the available data at atomic resolution, while traditional Ab initio methods typically require atomic resolution.

Relevant research was titled "PhAI: A deep-learning approach to solve the crystallographic phase problem" and was published in "Science" on August 1.

Paper link: https://www.science.org/doi/10.1126/science.adn2777

Crystallography is one of the core analytical techniques in natural sciences. X-ray crystallography provides a unique view into the three-dimensional structure of crystals.

In order to reconstruct the electron density map, enough complex structure factors $F$ of the diffraction reflections must be known. In a traditional experiment, only the amplitude $|F|$ is obtained, while the phase $phi$ is lost. This is a crystallographic phase problem.

Illustration: Standard crystal structure determination flow chart. (Source: Paper)

A major breakthrough came in the 1950s and 1960s, when Karle and Hauptmann** developed so-called direct methods for solving phase problems. But the direct method requires atomic resolution diffraction data. However, the requirement of atomic resolution is an empirical observation.

In recent years, traditional direct methods have been supplemented by dual space methods. The currently available ab initio methods appear to have reached their limits. A general solution to the phase problem remains unknown.

Mathematically speaking, any combination of structure factor amplitude and phase can be subjected to an inverse Fourier transform. However, physical and chemical requirements (such as having an atomically-like electron density distribution) impose rules on the possible combinations of phases consistent with a set of amplitudes. Advances in deep learning allow one to explore this relationship, perhaps in greater depth than current ab initio methods.

Here, researchers from the University of Copenhagen took a data-driven approach, using millions of artificial crystal structures and their corresponding diffraction data, aiming to solve phase problems in crystallography.

Study shows that this deep learning based ab initio structure solution method can be performed at a resolution of only minimum lattice plane distance (dmin) = 2.0 Å using only the data required by the direct method 10% to 20%.

Neural Network Design and Training

The artificial neural network constructed is called PhAI, which accepts the structure factor amplitude |F| and outputs the corresponding phase value ϕ. The architecture of PhAI is shown in the figure below.

Illustration: PhAI neural network method solves the phase problem. (Source: Paper) The number of structure factors in a crystal structure depends on the unit cell size. Depending on the computing resources, limits are placed on the size of the input data. The input structure factor amplitudes are chosen based on the Miller indices (h, k, l) obeying the

1. reflection.
That is, structures restricted to unit cell dimensions of about 10 Å at atomic resolution. Furthermore, the most common centrosymmetric space group P21/c was chosen. Central symmetry limits the possible phase values ​​to zero or π rad.

2. Penyelidikan mengenai melatih rangkaian saraf menggunakan struktur kristal buatan yang mengandungi terutamanya molekul organik. Kira-kira 49,000,000 struktur telah dicipta, di mana 94.29% adalah struktur kristal organik, 5.66% adalah struktur kristal logam-organik, dan 0.05% adalah struktur kristal bukan organik.
3. Input kepada rangkaian saraf terdiri daripada amplitud dan fasa, yang diproses oleh blok input konvolusi, ditambah dan dimasukkan ke dalam satu siri blok konvolusi (Conv3D), diikuti dengan satu siri blok multilayer perceptron (MLP). Fasa yang diramalkan daripada pengelas linear (pengelas fasa) dikitar melalui rangkaian masa Nc. Data latihan dijana dengan memasukkan atom logam dan molekul organik daripada pangkalan data GDB-13 ke dalam sel unit. Struktur yang terhasil disusun ke dalam data latihan yang daripadanya fasa sebenar dan amplitud faktor struktur pada faktor suhu sampel, resolusi dan integriti boleh dikira.
   Selesaikan masalah struktur sebenar
4. Rangkaian saraf terlatih dijalankan pada komputer standard dengan keperluan pengiraan sederhana. Ia menerima sebagai input senarai indeks hkl dan amplitud faktor struktur yang sepadan. Tiada maklumat input lain diperlukan, malah parameter sel unit struktur. Ini pada asasnya berbeza daripada semua kaedah ab initio moden yang lain. Rangkaian boleh meramalkan dan mengeluarkan nilai fasa dengan cepat.
5. Para penyelidik menguji prestasi rangkaian saraf menggunakan data pembelauan yang dikira daripada struktur kristal sebenar. Sebanyak 2387 kes ujian diperolehi. Untuk semua struktur yang dikumpul, berbilang nilai resolusi data antara 1.0 hingga 2.0 Å telah dipertimbangkan. Sebagai perbandingan, kaedah caj flip juga digunakan untuk mendapatkan maklumat fasa.

   

   Ilustrasi: Histogram pekali korelasi r antara fasa dan peta ketumpatan elektron sebenar.
   (Sumber: kertas)

Rangkaian saraf terlatih berfungsi dengan baik Ia boleh menyelesaikan semua struktur yang diuji (N = 2387) jika data pembelauan yang sepadan mempunyai resolusi yang baik, dan ia lebih baik dalam menyelesaikan struktur daripada resolusi rendah data Prestasi cemerlang. Walaupun rangkaian saraf jarang dilatih mengenai struktur bukan organik, ia boleh menyelesaikan struktur sedemikian dengan sempurna.

Kaedah cas flip berfungsi dengan baik semasa memproses data resolusi tinggi, tetapi keupayaannya untuk menghasilkan penyelesaian yang munasabah betul berkurangan secara beransur-ansur apabila resolusi data berkurangan, bagaimanapun, ia masih menyelesaikan kira-kira 32 piksel pada resolusi 1.6Å % Struktur. Bilangan struktur yang dikenal pasti dengan membalikkan cas boleh dipertingkatkan dengan percubaan selanjutnya dan menukar parameter input seperti ambang membalik.

Dalam pendekatan PhAI, Pengoptimuman meta ini dilakukan semasa latihan dan tidak perlu dilakukan oleh pengguna. Keputusan ini menunjukkan bahawa tanggapan umum dalam kristalografi bahawa data resolusi atom diperlukan untuk mengira fasa ab initio mungkin rosak. PhAI hanya memerlukan 10% hingga 20% data resolusi atom.

Hasil ini jelas menunjukkan bahawa resolusi atom tidak diperlukan untuk kaedah ab initio dan membuka jalan baharu untuk penentuan struktur berasaskan pembelajaran mendalam.

Cabaran pendekatan pembelajaran mendalam ini adalah untuk menskalakan rangkaian saraf, iaitu, data pembelauan untuk sel unit yang lebih besar akan memerlukan sejumlah besar data input dan output serta kos pengiraan semasa latihan. Pada masa hadapan, kajian lanjut diperlukan untuk melanjutkan kaedah ini kepada kes umum.

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