### Abstract

Determining the three-dimensional (3D) structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using “single particle” cryo-electron microscopy (cryo-EM) for this purpose. In cryo-EM, hundreds of thousands of two-dimensional (2D) images are obtained of individual copies of the same particle, each held in a thin sheet of ice at some unknown orientation. Each image corresponds to the noisy projection of the particle’s electron-scattering density. The reconstruction of a high-resolution image from this data is typically formulated as a nonlinear, nonconvex optimization problem for unknowns which encode the angular pose and lateral offset of each particle. Since there are hundreds of thousands of such parameters, this leads to a very CPU-intensive task|limiting both the number of particle images which can be processed and the number of independent reconstructions which can be carried out for the purpose of statistical validation. Moreover, existing reconstruction methods typically require a good initial guess to converge. Here, we propose a deterministic method for high-resolution reconstruction that operates in an ab initio manner|that is, without the need for an initial guess. It requires a predictable and relatively modest amount of computational effort, by marching out radially in the Fourier domain from low to high frequency, increasing the resolution by a fixed increment at each step.

Original language | English (US) |
---|---|

Pages (from-to) | 1170-1195 |

Number of pages | 26 |

Journal | SIAM Journal on Imaging Sciences |

Volume | 10 |

Issue number | 3 |

DOIs | |

State | Published - 2017 |

### Fingerprint

### Keywords

- Cryo-EM
- Frequency marching
- Protein structure
- Recursive linearization
- Single particle reconstruction

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Imaging Sciences*,

*10*(3), 1170-1195. https://doi.org/10.1137/16M1097171

**Rapid solution of the cryo-EM reconstruction problem by frequency marching.** / Barnett, Alex; Greengard, Leslie; Pataki, Andras; Spivak, Marina.

Research output: Contribution to journal › Article

*SIAM Journal on Imaging Sciences*, vol. 10, no. 3, pp. 1170-1195. https://doi.org/10.1137/16M1097171

}

TY - JOUR

T1 - Rapid solution of the cryo-EM reconstruction problem by frequency marching

AU - Barnett, Alex

AU - Greengard, Leslie

AU - Pataki, Andras

AU - Spivak, Marina

PY - 2017

Y1 - 2017

N2 - Determining the three-dimensional (3D) structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using “single particle” cryo-electron microscopy (cryo-EM) for this purpose. In cryo-EM, hundreds of thousands of two-dimensional (2D) images are obtained of individual copies of the same particle, each held in a thin sheet of ice at some unknown orientation. Each image corresponds to the noisy projection of the particle’s electron-scattering density. The reconstruction of a high-resolution image from this data is typically formulated as a nonlinear, nonconvex optimization problem for unknowns which encode the angular pose and lateral offset of each particle. Since there are hundreds of thousands of such parameters, this leads to a very CPU-intensive task|limiting both the number of particle images which can be processed and the number of independent reconstructions which can be carried out for the purpose of statistical validation. Moreover, existing reconstruction methods typically require a good initial guess to converge. Here, we propose a deterministic method for high-resolution reconstruction that operates in an ab initio manner|that is, without the need for an initial guess. It requires a predictable and relatively modest amount of computational effort, by marching out radially in the Fourier domain from low to high frequency, increasing the resolution by a fixed increment at each step.

AB - Determining the three-dimensional (3D) structure of proteins and protein complexes at atomic resolution is a fundamental task in structural biology. Over the last decade, remarkable progress has been made using “single particle” cryo-electron microscopy (cryo-EM) for this purpose. In cryo-EM, hundreds of thousands of two-dimensional (2D) images are obtained of individual copies of the same particle, each held in a thin sheet of ice at some unknown orientation. Each image corresponds to the noisy projection of the particle’s electron-scattering density. The reconstruction of a high-resolution image from this data is typically formulated as a nonlinear, nonconvex optimization problem for unknowns which encode the angular pose and lateral offset of each particle. Since there are hundreds of thousands of such parameters, this leads to a very CPU-intensive task|limiting both the number of particle images which can be processed and the number of independent reconstructions which can be carried out for the purpose of statistical validation. Moreover, existing reconstruction methods typically require a good initial guess to converge. Here, we propose a deterministic method for high-resolution reconstruction that operates in an ab initio manner|that is, without the need for an initial guess. It requires a predictable and relatively modest amount of computational effort, by marching out radially in the Fourier domain from low to high frequency, increasing the resolution by a fixed increment at each step.

KW - Cryo-EM

KW - Frequency marching

KW - Protein structure

KW - Recursive linearization

KW - Single particle reconstruction

UR - http://www.scopus.com/inward/record.url?scp=85032954680&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032954680&partnerID=8YFLogxK

U2 - 10.1137/16M1097171

DO - 10.1137/16M1097171

M3 - Article

AN - SCOPUS:85032954680

VL - 10

SP - 1170

EP - 1195

JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

SN - 1936-4954

IS - 3

ER -