Synthetic DNA molecules encoding the HPV31 L1 protein are provided. Specifically, the present invention provides polynucleotides encoding HPV31 L1 protein, wherein said polynucleotides are free from internal transcription termination signals that are recognized by yeast. Also provided are synthetic polynucleotides encoding HPV31 L1 wherein the polynucleotides have been codon-optimized for high level expression in a yeast cell. The synthetic molecules may be used to produce HPV31 virus-like particles (VLPs), and to produce vaccines and pharmaceutical compositions comprising the HPV31 VLPs. The vaccines of the present invention provide effective immunoprophylaxis against papillomavirus infection through neutralizing antibody and cell-mediated immunity TABLE-US-00001 HPV31 L1 total rebuild nucleotide and amino acid sequence: M S L W R P S 1 ATGTCTTTGT GGAGACCATC E A T V Y L P P V P TGAAGCTACC GTCTACTTGC CACCAGTCCC V S K V V S T 51 AGTCTCTAAG GTCGTCTCTA D E Y V T R T N I Y CCGACGAATA CGTCACCAGA ACCAACATCT Y H A G S A 101 ACTACCACGC TGGTTCTGCT R L L T V G H P Y Y AGATTGTTGA CCGTCGGTCA CCCATACTAC S I P K S D N 151 TCTATCCCAA AGTCTGACAA P K K I V V P K V S CCCAAAGAAG ATCGTCGTCC CAAAGGTCTC G L Q Y R V F 201 TGGTTTGCAA TACAGAGTCT R V R L P D P N K F TCAGAGTCAG ATTGCCAGAC CCAAACAAGT G F P D T S 251 TCGGTTTCCC AGACACCTCT F Y N P E T Q R L V TTCTACAACC CAGAAACCCA AAGATTGGTC W A C V G L E 301 TGGGCTTGTG TCGGTTTGGA V G R G Q P L G V G AGTCGGTAGA GGTCAACCAT TGGGTGTCGG I S G H P L L 351 TATCTCTGGT CACCCATTGT N K F D D T E N S N TGAACAAGTT CGACGACACC GAAAACTCTA R Y A G G P 401 ACAGATACGC TGGTGGTCCA G T D N R E C I S M GGTACCGACA ACAGAGAATG TATCTCTATG D Y K Q T Q L 451 GACTACAAGC AAACCCAATT C L L G C K P P I G GTGTTTGTTG GGTTGTAAGC CACCAATCGG E H W G K G S 501 TGAACACTGG GGTAAGGGTT P C S N N A I T P G CTCCATGTTC TAACAACGCT ATCACCCCAG D C P P L E 551 GTGACTGTCC ACCATTGGAA L K N S V I Q D G D TTGAAGAACT CTGTCATCCA AGACGGTGAC N V D T G F G 601 ATGGTCGACA CCGGTTTCGG A N D F T A L Q D T TGCTATGGAC TTCACCGCTT TGCAAGACAC K S W V P L D 651 CAAGTCTAAC GTCCCATTGG I C N S I C K Y P D ACATCTGTAA CTCTATCTGT AAGTACCCAG Y L K M V A 701 ACTACTTGAA GATGGTCGCT E P Y G D T L F F Y GAACCATACG GCGACACCTT GTTCTTCTAC L R R E Q M F 751 TTGCGTAGAG AACAGATGTT V R H F F N R S G T CGTAAGGCAC TTCTTCAACA GATCCGGCAC V G E S V P T 801 CGTAGGTGAA TCTGTCCCAA D L Y I K G S G S T CCGACCTGTA CATCAAGGGC TCCGGTTCCA A T L A N S 851 CCGCTACCCT GGCTAACTCC T Y F P T P S G S N ACCTACTTCC CAACTCCATC TGGCTCCATG V T S D A Q I 901 GTCACCTCCG ACGCTCAGAT F N K P Y W M Q R A CTTCAACAAG CCATACTGGA TGCAGCGTGC Q G H N N G I 951 ACAGGGTCAC AACAACGGTA C W G N Q L F V T V TCTGTTGGGG TAACCAGCTG TTCGTGACTG V D T T R S 1001 TGGTCGATAC CACGCGTTCT T N N S V C A A I A ACCAACATGT CTGTCTGTGC TGCAATCGCT N S D T T F K 1051 AACTCTGACA CTACCTTCAA S S N F K E Y L R H GTCCTCTAAC TTCAAGGAGT ACCTGAGACA G E E F D L Q 1101 TGGTGAGGAA TTCGATCTGC F I F Q L C K I T L AATTCATCTT CCAGTTGTGC AAGATCACCC S A D I N T 1151 TGTCTGCTGA CATCATGACC Y I H S M N P A I L TACATCCACA GTATGAACCC TGCCATCCTG E D W N F G L 1201 GAGGACTGGA ACTTCGGTCT T T P P S G S L E D GACCACTCCA CCTTCCGGTT CTTTGGAAGA.