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From Principal Component to Direct Coupling Analysis of Coevolution in Proteins: Low-Eigenvalue Modes are Needed for Structure Prediction Simona Cocco , Remi Monasson , Martin Weigt1 2 3,4* 1Laboratoire de Physique Statistique de l’Ecole Normale Supe´rieure - UMR 8550, associe´ au CNRS et a` l’Universite´ Pierre et Marie Curie, Paris, France, 2Laboratoire de Direct-coupling analysis is a group of methods to harvest information about coevolving residues in a protein family by learning a generative model in an exponential family from data. Direct coupling analysis (DCA) infers coevolutionary couplings between pairs of residues indicating their spatial proximity, making such information a valuable input for subsequent structure prediction. stream A short reminder of covariation analysis %PDF-1.7 dva�^�!��M�X�x80���;�Kw�h��?Q��!�ܲ�q) ߄]U��Gi�O���YKBd����{�r����� @za��l�r ?���y��b��ib��d� �Q�������=�@��6a��$i�iƨ���Xzv���pA�P�Y�u2&2@l� <>/ProcSet[/PDF/Text]>>/Filter/FlateDecode/Length 3529>> In this paper we will use the latter term and its abbreviation DCA. Direct Coupling Analysis. inverse Potts/Ising problem [26, 30] and Direct Coupling Analysis [41]. E-mail address: ekeb@kth.se 1Joint rst authors Preprint submitted to Journal of Computational Physics January 21, 2014 arXiv:1401.4832v1 [q … D�[p;���\��:�:"��Pt$� ��a�"w噶�(�i��ȝ�+W�ꜞr�l`=娧��;��ꉗ�X[#1��XE���슜c/SQ>������6���,�_��[v������G�&B[5"|�u��0�l��v�cSi�W���zk?�a�d1B�ʛ���[Y{5@��9�}���~L�����m��;�#��Lb�_�ӱ��Pv��LW�(�/b����i]�1Y�~������G��vD%��O�K�r��@�A�x�ӏ��0�|:�mG�̆�&t+� 7���jIU�0�6�Й�V���(��ơ���l{v�:�%]�}s�0ሉ���z�f�힯��Sr�3J��s�O,!�Ɔr��`���.���ݡD\PI��x���>���q��lι"@8W��P���Z�}S^'Q���>!X_����a�S��VB����������c�*[�,�P}8�w������E���V�,��D��Dg�+�A���؏���6|�u�@r)0�ݱA��C�}Ĺɂ�2�b���y �G�ɲ5 R��~�(�{�>'I�N�x���^��s�+qm��@>|2XY���U�K�5���fc0p���П,=-\~�y��%�*QtD�@h=y:��[پ�*3����{:*��E�uRZ}MՈ�P�+00xٞ���j���>N\9rn_�Z���|��!�O�M'�-�WX"�3���N�#��y-�s��-�90�{�A��G\����b�3��c��Q�t7����!���Ay�}~�\���E��+�lGu&�'�a�{��צڛ�� �ʽ�s�EOwZ]�.��RuH �c=���=�c�M�DLZ�a8`�� �•�__�X�Y����)��u1�}r2u�W�2��3$�m4��Kw�^.�ܥ�f�j A�Ү��R��uH*(�mXd~���ސDa$�XQ�,�B�����֖��ه��KS�"�q8~���O��l�:���n �n��2�"q��$I�:��.A��I��/��w��M�!M�H���k*�$��4���H&�ǁ�4��۬o�=�p[CT~��=U`EO�$Vw 4�V���9E$g5B�}7.�K�2[�l�6 R6(D��l#g�B a"�L��V{�z!�H�e]{���Xa ڷ5gx�R�?��v� B���-v�p0�0���C����ѿe����pQ�����J"����w=�^��հJ�[�(s�̎|M� 2�� �Szu�I�08w[�҃f��!���$� g�l`}��0���yw�p7A0���<7�2(渦��b��;&=��R�m&II� ,���g� �f"N`z7�a.����ʾ6[�U\�����8qQ�G>1"�V(>�$��u�v�Sdt�Y��*����I��)0*B�d��D _�ѽu�*(ʁ��C��y@�;���dJk �e/��3k�s�.�� q0��{�'v78_����a���r���*��Zm����L@iҍ����j2�[i��3G\ľ��77��_ 큟���8�F�� ���,�D 'R�|~�GY:ư%���`��&���l�ݕ��#v�SZ ����u];55�̲&����F�7���RW��;�PS��bl�ځ����LR�5U�$��zƧ�e�g]o�����ǧG�q�H���� e�v�'����(�7�K�N�9[i_�;;�&]&�7�j���gL� ��+22���bqcj�e؛ ��Cz��>5㩒C���X�s�!�B��~H@XY⥿���x��ㄕ��ԙ��,��Y~�-D��~6. These conclusions are established from theoretical arguments, and from the direct application of the Hop eld-Potts model to three sample protein families. x��˒ܶ�؛8U;4 ��K6�l)%�T��I�������>�Z���/p��q*�\�@��ht7�5��o�������W��7�_�*����$Q�gQr�����}u��7����Y {.�_}�7a�Gq���6�s?��h�i�4���׵��6���٦�']�l�'�^ۘf߁�C���v��x�m��nt��۞g�9��a�g�]�D�|D�m=�m�6��v0���l� �^����/c����My� ��`e�X��BcLe*��n�L���C7���v�:Sْ8�.pg��h�=���mQ�}��+�j�-�I�"�rܖ�~F7���s�-i�~����8�L�Gs�8��7pX�;��d���4f�՟?���;��M{ �a��� ��G�3�F!ȉ�����(M�z�' ��@� .T2��V)�3�A]�� =:(8�^�(����ZV{���w� �=�����(���l?��~��lk��m���I�O�*�$ �&�:�jFw�? the maximum entropy-based approach called mean field Direct Coupling Analysis (mfDCA) to infer a Potts model Hamiltonian governing the correlated mutations in a protein family. namely, an Ising model if the data are binary or a Potts model if the data have more than two types. DCA has been used to predict residue-residue contacts in a protein 3D structure from similar (homologous) protein sequences [4, … Keywords: protein structure prediction, contact map, direct-coupling analysis, Potts model, pseudolikelihood, inference Corresponding author. ,���j��uάP��:���R`�yrB���l1.�q�Ì��Y�2�����:`�ؽ����zb�}o({�ؒqI�%X�`Д.΁;'�u�!��3�G;xM 5 0 obj %���� Improved contact prediction in proteins: using pseudolikelihoods to infer Potts models. In protein families of realistic size, this learning can only be done approximately, and there is a trade-off between inference precision and computational speed. DCA (Weigt et al., 2009; Morcos et al., 2011) was performed using an in-house code of the asymmetric version of the Pseudo-likelihood method to infer the parameters of the Potts model (Balakrishnan et al., 2011; Ekeberg et al., 2013). ������$*Y���&��� From a statistical point of view these are inference problems in exponential families [1], while from a physical point of view the approach has been called the inverse Ising or Potts problem [2,3] and direct-coupling analysis (DCA) [4,5]. Sequences were reweighed using a maximum 90% identity threshold. 'x ���6�ƺ��b���R]�"��C�+�; 8�Rw�{�����c�{���Bl����n���I[!��%%�gyq��d�!��T"J�0�����n >��09�s���kis@��P�Nr�C�՛�ɸ_�4)��Es�F(eO��T �jC/��a 5�t K�)�Q��&�wI��9�a.��2����!`8t�l+�Z��)5�`k�v��:�]�� �B1)���L�q�q�H4@$��L�������+u�#�*�� J���ټ�G�/����}�x�x�&T��V��O�R�)%���$-�s���Q�[�S��w-E���ũ�D6���"leL�F���p�wo� ��C�i�M6X��~�Ƀ��f

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