R_free and the R_free ratio. Part I: derivation of expected values of cross-validation residuals used in macromolecular least-squares refinement

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Contents

Abstract

Introduction

Theory

• Error assumptions

• Definitions

  • Scalars

  • Column matrices

  • Rectangular matrices

• The expected value of the free residual

• Random exclusion of observations in unrestrained refinement

• The expected value of R_Gfree in unrestrained refinement

• The ratio of R_Gfree to R_G in unrestrained refinement

• R_Gfree and the R_Gfree ratio in restrained refinement

• Minimum variance weights minimise R_free

• The use of standard R-factors

Discussion

• Restrained and unrestrained R_Gfree ratios

• The meaning of the R_free ratio

• Observed R_free ratios from the Protein Data Bank

Conclusion

Appendix I - Statistical properties of free residuals

Appendix II - The ratio of R_free to R in unrestrained refinement

Appendix III - Minimum variance weights minimise the expected value of R_free

References

Figures

Table 1