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Work on SARS Cov2

\n
\nChildren\n
    \n
  1. Analysis of the varient trend plots
    2. \n
  2. Appendix
    3. \n
  3. Glossary
    4. \n
  4. Work_documented
    5. \n
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Work on SARS Cov2

\n
\nChildren\n
    \n
  1. Analysis of the varient trend plots
    2. \n
  2. Appendix
    3. \n
  3. Glossary
    4. \n
  4. Work_documented
    5. \n
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Work on SARS Cov2

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\nChildren\n
    \n
  1. Analysis of the varient trend plots
    2. \n
  2. Appendix
    3. \n
  3. Glossary
    4. \n
  4. Work_documented
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BA.2.86","value":"10-ba286","line":34,"column":2,"depth":2},"interesting-plots-of-lineages-not-variant":{"type":"header","text":"Interesting plots of lineages not variant","value":"interesting-plots-of-lineages-not-variant","line":44,"column":0,"depth":2},"summary-for-variants":{"type":"header","text":"Summary for Variants","value":"summary-for-variants","line":67,"column":0,"depth":2},"b117alpha":{"type":"header","text":"B.1.1.7(alpha)","value":"b117alpha","line":69,"column":0,"depth":3},"ba275":{"type":"header","text":"BA.2.75","value":"ba275","line":74,"column":0,"depth":3},"ba286":{"type":"header","text":"BA.2.86","value":"ba286","line":83,"column":0,"depth":2},"b1351beta":{"type":"header","text":"B.1.351(Beta)","value":"b1351beta","line":89,"column":0,"depth":2},"b16172delta":{"type":"header","text":"B.1.617.2(Delta)","value":"b16172delta","line":95,"column":0,"depth":2},"p1gamma":{"type":"header","text":"P.1(Gamma)","value":"p1gamma","line":106,"column":0,"depth":2},"b11529omicron":{"type":"header","text":"B.1.1.529(Omicron)","value":"b11529omicron","line":110,"column":0,"depth":2},"b16171kappa":{"type":"header","text":"B.1.617.1(Kappa)","value":"b16171kappa","line":116,"column":0,"depth":2},"eg5":{"type":"header","text":"EG.5","value":"eg5","line":121,"column":0,"depth":2},"xbb116omicron":{"type":"header","text":"XBB.1.16(omicron)","value":"xbb116omicron","line":128,"column":0,"depth":2},"xbb15omicron":{"type":"header","text":"XBB.1.5(omicron)","value":"xbb15omicron","line":133,"column":0,"depth":2},"xbb-191":{"type":"header","text":"XBB 1.9.1","value":"xbb-191","line":140,"column":0,"depth":2},"xbb192":{"type":"header","text":"XBB.1.9.2","value":"xbb192","line":147,"column":0,"depth":2},"xbb23":{"type":"header","text":"XBB.2.3","value":"xbb23","line":153,"column":0,"depth":2},"ch11":{"type":"header","text":"CH.1.1","value":"ch11","line":158,"column":0,"depth":2},"xbbomicron":{"type":"header","text":"XBB(omicron)","value":"xbbomicron","line":163,"column":0,"depth":2}},"children":[],"parent":"paa0s59lp320n6q8rghycjw","data":{}},"body":"

Analysis of the varient trend plots

\n

Inference that are interesting

\n
    \n
  1. \n

    XBB.1.16(omicron):India sees the Spike earlier than the rest of the countries. The lowest frequency in india is higher than peaks of all other countries. \"xbb_1_16\" \"xbb_1_16_ci\"

    \n
    2. \n
  2. \n

    XBB : India and Germany records the high frequencies 70.92%,50% respectively, while other countries have frequnency less than 20% \"xbb\" \"xbb_ci\"

    \n
    3. \n
  3. \n

    Norway doesn't have occurances of XBB.1.9.2,XBB.1.16 while other countries has recorded occurances.

    \n
    4. \n
  4. \n

    EG.5 is more prevalent in Norway and India for two months straight than in other countries \"EG_5\" \"EG_5_CI\"

    \n
    5. \n
  5. \n

    XBB.1.9.1,EG.5 : Norway records occurances only for two months and it is highest than frequencies of other countries. No gradual increase or decrease recorded. \"xbb_1_9_1\" \"xbbb_1_9_1_ci\"

    \n
    6. \n
\n
\n

The CI would say how true are these sudden occurances.

\n
\n
    \n
  1. \n

    XBB.1.9.1 : not present in Australia

    \n
    2. \n
  2. \n

    B.1.1.529(Omicron): The Final spike after a downhill trend during the last month of occurance(jun23) in Norway(66.66%) and Germany(16%) can be interesting. \"B_1_1_529\" \"B_1_1_529_CI\"

    \n
    3. \n
  3. \n

    CH.1.1: Norway records high frequencies (61%) compared to other countries. \"CH_1_1\" \"CH_1_1_CI\"

    \n
    4. \n
  4. \n

    XBB.2.3: Starts in Jan23 in India and is continuous till May23. There is a break of 3 months Jun23,Jul23,Aug23. Then there is a spike(highest frequency) in the month of Sept23-Oct23.(intereseting), while in other countries the trend is monotonous.\"XBB_2_3\" \"XBB_2_3_CI\"

    \n
    5. \n
\n
\n

10. BA.2.86

\n\n
\n

\"ba_2_86\"

\n
    \n
  1. No records of the following variants B.1.429(Epsilon), B.1.525(Eta), B.1.526(Iota), C.37(Lambda), B.1.621(Mu), P.3(Theta), P.2(Zeta), B.1.640 in the 10 chosen countries during Jan22-Oct23.
    2. \n
\n

Interesting plots of lineages not variant

\n
\n

All the following plots might change if the lineage mapping is done based on the characteristic mutations obtained from OutBreakInfo. Presently the mapping is based on mutations obtained from the GISAID database for each country.

\n
\n
    \n
  1. BF.7: Peaks of Denamrk around 30% and Germany 15% are notable because no other country has recorded such frequencies for this lineage - they are less than 5%. And Norway has no trace of this lineage. \"BF_7\"
    2. \n
  2. HW.1: Aaustralia has highest frequency of this lineage in the month of Sept23 - above 50%, while other countries have all their frequncies below 10%. South Koreaa and USA are the other two countries which have meager occurances of this ineage other 7 countries have no trace of this lineage. \"HW_1\"
    3. \n
  3. XBF: Australia and Canada records highest frequency - around 30%-35% while other countries have frequencies less than 20%. Australia records long period exposure this lineage. \"XBF\"
    4. \n
  4. XBK: Denmark records the highest occurance of this lineage in Jun23 - more than 30% while other countries record frequencies less than 10%. India has reported no cases from this lineage. \"XBK\"
    5. \n
  5. XBC.1.6: Australia records the highest frequency which is around 30% and the occurance in Australia is for a long period May23-Oct23. Minimal occurances are found in South korea, Canada, UK, USA. \"XBC_1_6\"
    6. \n
  6. XBC.1.3: Australia has long season (Nov22-Oct23) of this lineage and also records the highest frequency - more than 20%. \"XBC_1_3\"
    7. \n
  7. FL.10: Germany records the highest frequecy of 50% for a month in May23 while other countries have frequencies less than 5%. \"FL_10\"
    8. \n
  8. GE.1: India Records frequency of more than 30% in Jun23 while other countries have frequencies less than 10%. Uk has the prolonged season of this variant with minimal occurance.\"GE_1\"
    9. \n
  9. DV.x: Norway records the highest frequency of this lineage in Jun23 which is more than 30% while most countries record frequencies around 10%. Denmark has the longesst season of this lineage. Jan23-Oct23.\"DV_x\"
    10. \n
  10. BL.1: India records the longest season with this lineage - Jun22-Jun23 and has the hoghest frequency in Jun23 (more than 30%). It should be noted that there are no occurances in the months Jan23-May23. \"BL.1\"
    11. \n
  11. BQ.1.1: Spain has the longest season of this lineage with the highest frequency going upto more than 40%. \"BQ_1_1\"
    12. \n
  12. BR.2.1: Australia has the longest season(Jan22-Jun23) of this lineage with the highest frequency going around 40%. Feb22-Sep22 there are no occurances recorded. \"BR_2_1\"
    13. \n
  13. BY.1: Australia has the longest season with this lineage but with meager frequency. Canada has recorded the highest frequency in month Nov22 which is more than 30%. \"BY_1\"
    14. \n
  14. BR.1: Norway records highest frequency of this lineage which is more than 20% in the month of Sep22. \"BR_1\"
    15. \n
  15. GL.1: Australia records the highest frequency in Aug23 (more than 30%). \"GL_1\"
    16. \n
  16. EG.1.x: Germany has the highest frequency recorded 25% in Jul23. Frequencies in other countries are less than 5%. \"EG_1_x\"
    17. \n
  17. FK.1.x: Denmark records the highest frequency in May23 and South Korea has the longest season with htis lineage (May23-Oct23). \"FK_1_x\"
    18. \n
\n

Summary for Variants

\n

B.1.1.7(alpha)

\n\n

BA.2.75

\n\n

BA.2.86

\n\n

B.1.351(Beta)

\n\n

B.1.617.2(Delta)

\n\n

P.1(Gamma)

\n\n

B.1.1.529(Omicron)

\n\n

B.1.617.1(Kappa)

\n\n

EG.5

\n\n

XBB.1.16(omicron)

\n\n

XBB.1.5(omicron)

\n\n

XBB 1.9.1

\n\n

XBB.1.9.2

\n\n

XBB.2.3

\n\n

CH.1.1

\n\n

XBB(omicron)

\n\n

B.1.429(Epsilon), B.1.525(Eta), B.1.526(Iota), C.37(Lambda), B.1.621(Mu), P.3(Theta), P.2(Zeta), B.1.640 No data for these variants.

\n
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Dendron (the tool used to generate this site) lets authors selective publish content. You will see this page whenever you click on a link to an unpublished page

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Expected_immunity

\n

Objective:

\n

Finding the expected immunity towards an amino acid substitution. This can hint the possibility of occurance of a mutation. When high number of people are immune to a aa_substitution over a time, then this substitution is more likely to undergo another substitution/change.

\n

Introduction:

\n
    \n
  1. All the mathematical models/equations used in the computation is taken from the lab's previous work.
    2. \n
  2. But in lab's work x,y denotes prevalent variants of SARS_Cov2
    3. \n
  3. In the present work x,y denote amino acid substitutions like \"Spike_A344T\", \"Spike_A344A\" - can be assumed like covid variant harbouring only one of the aa_substitutions at a time.
    4. \n
  4. Assumption of point 3 is followed throughout.
    5. \n
  5. Currently the work is studies the immunity against a single infection happended at the start of tthe time horizon.
    6. \n
\n

Calculation of probability of neutralisation:

\n
    \n
  1. To calculate the probability of neutralisation, the probability of antibodies(grouped by their epitope classes) binding to an variant harbouring an amino acid substituiton has to be found.
    2. \n
  2. This binding probability is: bv(t,x,y)=e−k∗[t−s]FRx,y(v)∗IC50(v)+e−k∗[t−s]b_v(t,x,y)=\\frac{e^{-k*[t-s]}}{FR_{x,y}(v)*IC50(v)+e^{-k*[t-s]}}bv​(t,x,y)=FRx,y​(v)∗IC50(v)+e−k∗[t−s]e−k∗[t−s]​. Where s is the start date.
    3. \n
  3. This equation is more like the pharmacokinetics equation - concentration of ligand_receptor complexconcentration of unbound receptor+concentration of ligand_receptor complex\\frac{concentration\\space of\\space ligand\\_receptor\\space complex}{concentration\\space of\\space unbound\\space receptor +concentration\\space of\\space ligand\\_receptor\\space complex}concentration of unbound receptor+concentration of ligand_receptor complexconcentration of ligand_receptor complex​. Here the IC50 adds weight to the fold resistance which is a way to denote the escape fraction(unbound).
    4. \n
  4. Based on x and y, the values plugged in for Fold resistance differs, that is, if x=Spike_A344T, y=Spike_A344T then FR=1; else if x=Spike_A344T,y=Spike_A344A(wt) the FR>1 (taken from the table).
    5. \n
  5. FR taken from a table is calculated for a position,epitope class combination. IC50 is fixed for an antibody antibody and doesn't change according to aa_substitution. Since IC50 and FR values considered here doesn't depend on the aa_substituition, bv(t,x,y)b_v(t,x,y)bv​(t,x,y) can possibly have only 2 values for a position.
    6. \n
  6. In detail: In accordance to the previous point, for a position 344, on t the bv(t,x,y)b_v(t,x,y)bv​(t,x,y) for x,y combinations:- 1: x≠y, FRx,y(v)>1bv(t,s_a344t,s_a344a)==bv(t,s_a344t,s_a344e)==bv(t,s_a344t,s_a344del)2: x==y, FRx,y(v)=1bv(t,s_a344t,s_a344t)==bv(t,s_a344e,s_a344e)==bv(t,s_a344a,s_a344a)\\\\1: \\space x\\neq y,\\space FR_{x,y}(v)>1\\\\ b_v(t,s\\_a344t, s\\_a344a)==b_v(t,s\\_a344t, s\\_a344e)==b_v(t,s\\_a344t, s\\_a344del)\\\\2: \\space x==y,\\space FR_{x,y}(v)=1\\\\ b_v(t,s\\_a344t, s\\_a344t)==b_v(t,s\\_a344e, s\\_a344e)==b_v(t,s\\_a344a, s\\_a344a)1: x=y, FRx,y​(v)>1bv​(t,s_a344t,s_a344a)==bv​(t,s_a344t,s_a344e)==bv​(t,s_a344t,s_a344del)2: x==y, FRx,y​(v)=1bv​(t,s_a344t,s_a344t)==bv​(t,s_a344e,s_a344e)==bv​(t,s_a344a,s_a344a)
    7. \n
  7. So for each position, bvb_vbv​ was found with FR>1 and with FR=1
    8. \n
  8. Eventually for each position 2 probability of neutralisation values were computed.
    9. \n
\n

calculating the expected immunity against a variant/aa_substitution:

\n
    \n
  1. E[Immuney(t)]=∑x∈X∑s<t πx(s)∗I(s)∗PNeut(t−s,x,y)E[Immune_y(t)]=\\sum_{x\\in X}\\sum_{s<t}\\space \\pi_x(s)*I(s)*P_{Neut}(t-s,x,y)E[Immuney​(t)]=∑x∈X​∑s<t​ πx​(s)∗I(s)∗PNeut​(t−s,x,y)
    2. \n
  2. here πx(s)\\pi_x(s)πx​(s) is the frequency of variant with aa_sub x on day s.
    3. \n
  3. I(s)I(s)I(s) the incidence (calculated using GInPipe in the lab's work) is obtained by computiing the number of sequences collected on each day. This data is got from GISAID
    4. \n
  4. Probability of neutralisation values are plugged in according to the x,y combination. If x==y the PNeut for the position, calculated using FR=1 is used else the other one is used.
    5. \n
\n
\n

y=Spike_F140IX={Spike_F140I,Spike_F140F}t=03−01−2022E[S_f140iimmune(03−01−2022)]={[πS_f140i(01−01−2022)∗P1Neut(pos=140,t=01−01−2022)]+[πS_f140i(02−01−2022)∗P1Neut(pos=140,t=02−01−2022)]}+{[πS_f140f(01−01−2022)∗P2Neut(pos=140,t=01−01−2022)]+[πS_f140f(02−01−2022)∗P2Neut(pos=140,t=02−01−2022)]}\\\\y=Spike\\_F140I\\\\ X=\\{Spike\\_F140I,Spike\\_F140F\\}\\\\t=03-01-2022\\\\E[S\\_f140i_{immune}(03-01-2022)]\\\\=\\{[\\pi_{S\\_f140i}(01-01-2022)*P1_{Neut}(pos=140,t=01-01-2022)]+[\\pi_{S\\_f140i}(02-01-2022)*P1_{Neut}(pos=140,t=02-01-2022)]\\}+\\\\\\{[\\pi_{S\\_f140f}(01-01-2022)*P2_{Neut}(pos=140,t=01-01-2022)]+[\\pi_{S\\_f140f}(02-01-2022)*P2_{Neut}(pos=140,t=02-01-2022)]\\}y=Spike_F140IX={Spike_F140I,Spike_F140F}t=03−01−2022E[S_f140iimmune​(03−01−2022)]={[πS_f140i​(01−01−2022)∗P1Neut​(pos=140,t=01−01−2022)]+[πS_f140i​(02−01−2022)∗P1Neut​(pos=140,t=02−01−2022)]}+{[πS_f140f​(01−01−2022)∗P2Neut​(pos=140,t=01−01−2022)]+[πS_f140f​(02−01−2022)∗P2Neut​(pos=140,t=02−01−2022)]}

\n
\n

This way for each variant/aa_substitution the expected immunity is calculated for everyday in the period of observation.

\n

Algorithm of computation of expected immunity:

\n
Function get_dis_fact:\n   Pass In: start_date,end_date\n   num_day=end_date-start_date\n   k - is the half life\n   For i=0 to num_day\n     discount_factor_vector.append(round(exp(-k*i),3))\n   return(discount_factor_vector)\n\nFunction get_bv:\n   Pass In: fr,IC50\n   Constants: start_date, End_date\n   calling get_dis_fact function\n   time_iter=start_date\n   while(time_iter<End_date):\n      days_dif=time_iter-start_date\n      bv_vec.append(discount_factor_vector[days_dif]/\n      (fr*IC50+discount_factor_vector[days_diff]))\n      increment time_iter\n   return(bv_vec)\n\nFunction Exp_immune:\n   Pass In: Frequency_df,P1_neut,P2_neut, incidence\n   Constant: Start_day\n   For y in variants:\n      For d in observation_dates:\n         initialise data_frames freq_df,pneut_df,incidence_df\n         dates=[start_date:d) (d not included s<t)\n         dates_diff=[start_date-dates]\n         For x in variants with mutation on same position as y:\n            freq_df.append(Frequency_df[dates,x])\n            incidence_df.append(incidence[dates])\n            if y==x:\n               pneut_df.append(p1[pos,dates_diff])\n            elif y!=x:\n               pneut_df.append(p2[pos,dates_diff])\n         double_sum.sum(freq_df*pneut_df*incidence_df)\n      immune_df.append(double_sum)\n   return(immune_df)       \n
\n

All the scripts are present in \"/Users/vishnushirishyamsaisundar/Documents/Master_Thesis_work/Work/Data_Analysis/Expected_immunity_computation\"

\n

Observations and modifications:

\n\n

Visualisation and analysis:

\n\n

Further questions:

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Finding_surface_residues

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DSSP server

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DSSP server

\n\n
dssp 6xlu.pdb 6xlu.dssp\n
\n\n

Get Area server

\n

GETAREA

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NetSurfP 3.0

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NetSurfP 3.0

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Note:\nA pariwise sequence alignment was done with the uniprot spike sequence and the sequence obtained from the 6xlu structure. \"The The sequences align fairly well.

\n
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Appendix

\n

Deep Mutational scanning data:

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checking inconsistencies

\n\n
month_numbers<-list()\nfor(i in names(ten_country_mut_data)){\n  month_numbers[[i]]<-data.frame(ten_country_mut_data[[i]] %>% \\\n  group_by(format(Collected_date,\"%Y-%m\")) %>% count())\n  colnames(month_numbers[[i]])<-c(\"Month\",\"number\")\n}\n
\n\n
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trend","value":"comparison-of-pressure-trend-with-the-variant-trend","line":274,"column":0,"depth":2},"repeating-the-process-with-mutations":{"type":"header","text":"Repeating the process with Mutations","value":"repeating-the-process-with-mutations","line":281,"column":0,"depth":2}},"children":["drw8w7u2kcr0z6nl2ekgoea","g9181ia6dhnmpqfklf2mwit","vhn93xdheb909udqychwrcl","o7n9flqgbqf3xbm437bc0ih","xhw6w5ghbjhkzbo7huxzhwg"],"parent":"paa0s59lp320n6q8rghycjw","data":{}},"body":"

Work_documented

\n

Objective

\n

Is it possible to predict the positions that are vulnerable for forth coming mutations.

\n

Steps in the workflow

\n
\n graph TD;\n1[start]--Based on data quantity-->A[Choosing countries for the study]--checking for extreme low value outliers-->B[Downloading sequence and meta data from these countries for 22 months]--Mapping lineages to parental lineage-->C[Finding the difference in the trend of variant frequencies in these countries]\n
\n\n

Data acquisition

\n\n
\n

There were some inconsistencies in the Date entries (only year no month or year and month an no date) such entries were removed.\nOn the course of doing this it was identified that the number of entries that was downloaded for each countries do not exactly match the numbers in Work/Data_Analysis/chosen_ten_country_submission.csv excluding few countries.\nAfter removing the inconsistent date entries the numbers(downloaded and number in file) for India match.\nThe inconsistencies are reported in the file Work/Data_Analysis/inconsistencies_in_data.numbers.\nThe number of downloaded entries are more than then numbers in file.\nAfter looking into it, it was observed that there were few more entries added to these countries in the time gap(around a week) between the compiling Work/Data_Analysis/chosen_ten_country_submission.csv and downloading data. checking inconsistencies

\n

Summary

\n

Summary of the downloaded data

\n
\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
CountryTotal number of entries downloaded (Jan22-Oct23)Entries after removing the date inconsistenciesNumber of unassignedPercentage of unassigned
Asia / India181061578300 %
Asia / South Korea138081380800 %
Europe / Denmark16390016390070,004 %
Europe / Germany663746623600 %
Europe / Norway122641226400 %
Europe / Spain179911792100 %
Europe / United Kingdom3283530597740,242 %
North America / Canada207912079100 %
North America / USA754877497150,007 %
Oceania / Australia132671325750,038 %
\n

Note on the unassigned

\n

Mapping lineages

\n\n
awk -F\";\" '{gsub(/[()]/,\"\",$6);print $5\";\"$6}' \nten_country_mut_data/* \\\n>ten_country_mut_data/ten_country_lineage_mut.csv\n
\n
\n

gsub is used to remove the brackets in the AA_mutations column.
\nColumns of the CSV files are separated by a semicolon ';'

\n
\n\n

Frequency computation

\n\n

Dealing with the unassigned

\n\n

\"pangolin_assignment\"

\n

\"pangolin_assignemt_details\"

\n\n

Finding positions under pressure (BIG GOAL)

\n

The big goal is to find the positions under pressure. To obtain this, firstly the frequency of mutation on each position of Spike RBD and NTD Epitopes are calculated. (RBD spike mutations in position 330-530, NTD(14-20,140-158,245-264) mutations)(Question on the position) For this the aa_substitution data obtained from GISAID was used.\n\"frequency

\n

STEPS:

\n\n

Question on interpolation

\n

Computing the pressure on the position

\n

With the formula (given by Prof.Max) the pressure on each position from t0 to t was computed\nP(pos,t)=∑s=t0texp⁡−k[t−s]×f(pos,s)\\\\ P(pos,t)=\\sum_{s=t_0}^{t}\\exp^{-k[t-s]}\\times f(pos,s) \\\\P(pos,t)=∑s=t0​t​exp−k[t−s]×f(pos,s)

\n\n

Masking

\n\n
\n

The categorising treshold is set as 25% similar to Netsurf3.0. This would need advice.

\n
\n\n

The positions being picked by each of the tools are compared with the positions given by Prof.Max(screenshot). The tabulation is available in Work/Data_Analysis/Positions_being_picked.numbers

\n

Visualization of the positions under pressure

\n

Like previous variant trend visualization, the pressure trend was also visualised using geom_line in two ways, positionwise and countrywise. These plots are present in Work/Data_Analysis/pressure_plots. There are 6 plots - 3 countrywise, 3 positionsise. The 3 denotes the 3 masking tool outputs that were used to generate the plots.

\n

Entropy for each positions:

\n

The amino acid substitution on a position is not constant. Example: on position 14 mutations found in india include Spike_Q14H,Spike_Q14del,Spike_Q14R. So calculating the number of such prevailing mutations on a position is the entropy. This was calculated to weigh down the pressure on a postiion .... Not processed further yet

\n

Neutralisation probability:

\n

For knowing how impactful would a mutation on a site be, the probaility of neutralisation is being calculated. The Probability of neutralisation of a variant y by the antibodies elicited by variant x at time t.

\n
PNeut(t,x,y)=1−∏v∈Ax/y(1−bv(t,x,y))\\\\ P_{Neut}(t,x,y)=1-\\prod_{v\\in A_{x/y}}(1-b_v(t,x,y))PNeut​(t,x,y)=1−v∈Ax/y​∏​(1−bv​(t,x,y))
\n

To compute this probability the binding probability bv(t,x,y)b_v(t,x,y)bv​(t,x,y) of an antibody of a particular epitope class with the variant is needed.

\n
bv(t,x,y)=exp−k[t−s]FRx,y(v).IC50x(v)+exp−k[t−s]\\\\ b_v(t,x,y)=\\frac{exp^{-k[t-s]}}{FR_{x,y}(v).IC50_x(v)+exp^{-k[t-s]}}bv​(t,x,y)=FRx,y​(v).IC50x​(v)+exp−k[t−s]exp−k[t−s]​
\n\n
\n

Another method: binding probability for all the time steps for all the antibodies were computed first and then averaging these binding probability of antibodies across an antibody class was done and used to find the probability of neutralisation. The weight values did not differ drasitically to be precise there are only 116 values that differ. Just sticking to the earlier method.\nDefinition Reference

\n
\n

Analysis of the weighted plot

\n\n

Comparison of pressure trend with the variant trend

\n\n

Repeating the process with Mutations

\n\n
\nChildren\n
    \n
  1. Expected_immunity
    2. \n
  2. Finding_surface_residues
    3. \n
  3. Mapping_lineages
    4. \n
  4. Possible_questions
    5. \n
  5. checking inconsistencies
    6. \n
\n
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used","updated":1708937317211,"created":1700240802023,"custom":{},"fname":"Glossary","type":"note","vault":{"fsPath":".","selfContained":true,"name":"Literature"},"contentHash":"dcf3970a38bb355f7f76468c17bad4eb","links":[{"from":{"fname":"Work_documented","id":"r423m96u71ix4pb458fk8u2","vaultName":"Literature"},"type":"backlink","position":{"start":{"line":23,"column":135,"offset":1908},"end":{"line":23,"column":177,"offset":1950},"indent":[]},"value":"Glossary"},{"from":{"fname":"Work_documented","id":"r423m96u71ix4pb458fk8u2","vaultName":"Literature"},"type":"backlink","position":{"start":{"line":23,"column":190,"offset":1963},"end":{"line":23,"column":264,"offset":2037},"indent":[]},"value":"Glossary"},{"from":{"fname":"Work_documented","id":"r423m96u71ix4pb458fk8u2","vaultName":"Literature"},"type":"backlink","position":{"start":{"line":94,"column":375,"offset":10252},"end":{"line":94,"column":427,"offset":10304},"indent":[]},"value":"Glossary"},{"from":{"fname":"Work_documented","id":"r423m96u71ix4pb458fk8u2","vaultName":"Literature"},"type":"backlink","position":{"start":{"line":135,"column":81,"offset":15564},"end":{"line":135,"column":121,"offset":15604},"indent":[]},"value":"Glossary"}],"anchors":{"outliers":{"type":"header","text":"Outliers","value":"outliers","line":7,"column":0,"depth":2},"point-outlier":{"type":"header","text":"Point outlier:","value":"point-outlier","line":9,"column":0,"depth":3},"subsequences":{"type":"header","text":"Subsequences:","value":"subsequences","line":13,"column":0,"depth":3},"outlier-estimation-and-methods":{"type":"header","text":"Outlier Estimation and methods:","value":"outlier-estimation-and-methods","line":17,"column":0,"depth":3},"hampler-filter":{"type":"header","text":"Hampler Filter","value":"hampler-filter","line":33,"column":0,"depth":4},"confidence-interval":{"type":"header","text":"Confidence interval","value":"confidence-interval","line":37,"column":0,"depth":2},"interpolation":{"type":"header","text":"Interpolation","value":"interpolation","line":50,"column":0,"depth":2}},"children":[],"parent":"paa0s59lp320n6q8rghycjw","data":{}},"body":"

Glossary

\n

Outliers

\n

Point outlier:

\n\n

Subsequences:

\n\n

Outlier Estimation and methods:

\n\n

Hampler Filter

\n

This is also part of descriptive statistics. Considers values outside the interval I=[median−3∗MAD,median+3∗MAD]I=[median-3*MAD,median+3*MAD]I=[median−3∗MAD,median+3∗MAD] as outliers. To understand MAD(median absolute deviation) \"MAD\"

\n

Confidence interval

\n

In general a 95% confidence interval means there is 95% probability that the confidence interval contains the mean.2 To understand what is CI of a sample proportion, the term population proportion is defined first.

\n
\n

A population proportion is the proportion of individuals in a population sharing a certain trait, denoted as p. The sample proportion is the proportion of individuals in a sample sharing a certain trait, denoted ˆp.3

\n
\n

Just like the estimating the CI of mean the CI of proportion is estimated by adding and subtracting margin of error from ^p to get the limits of CI.

\n
Margin of Error =z×p^×(1−p^)n\\\\ Margin\\space of\\space Error\\space =z\\times\\sqrt{\\frac{\\hat p\\times(1-\\hat p)}{n}}Margin of Error =z×np^​×(1−p^​)​​
\n

Where z is the z-score for 95% confidence level.4\nFor multinomial sample prortions the confidence intervals are often approximated by single binomial confidence interval, I assume the trait of iterest is considered as p^\\hat pp^​ while others become (1−p^)(1-\\hat p)(1−p^​). There are also methods to to calculate confidence interval simultaneously. One such method sisonglaz was used in the work through function MultinomCI from DescTools package.

\n

Interpolation

\n

Finding a new datapoint based on the preexisting data point is called the interpolation. Common methods of interpolation includes linear,polynomial, spline interpolation. Linear interpolation fits a stright line between known points and uses the slope off the line to interpolate the missing data points. In both polynomial and spline interpolation polynomials are used to do the interpolation. The difference is that spline fits multiple piecewise polynomials to the subset of data to do the interpolation, on the other hand polynomial interpolation fits one polynomial to the entire data to do the interpolation.5

\n
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Mapping_lineages

\n
Function mapping_lineages (lineage_cmut,alias_df)\n\n    Function chunk_lineage(lineage_cmut,alias_df)\n        \n        1.Chunks lineages and sublineages by the first character of Pangolin string. \n        One element of the input data frame is considered at an instance and all the \n        members of the clade to which it belongs are chunked and passed to the downstream \n        processing.\n\n        2. If there are no lineages having the same first \n        character but there are entries in the input df, the lineage is \n        mapped to it's own and is stored in alias_df.\n\n        3. else If the there are no more entries in the \n        lineage_cmut then the lineage is mapped to itself and  return is called.\n\n        4. else the chunk stored in temp_df is passed to\n        long_sublineage\n\n    End\n\n    Function long_sublineage(temp_df,lineage_cmut,\n    alias_df,alias_df_temp)\n\n        1. Finds the sublineage with longest character string\n        and stores it in longlineage_df\n\n        2. If multiple lineages have long character string\n        both the lineages are stored in longlineage_df\n\n        3. If linegaes length is just one then it is the\n        parental lineage and it is mapped to it's own and is\n        removed from temp_df amd is stored in alias_df\n\n    END\n\n    Function match_merge(longlineage_df,temp_df\n    lineage_cmut,alias_df,alias_df_temp)\n\n    1. Iterates through the longlineage_df, forms pattern\n    from the first element taken and tries to find\n    neighbours in longlineage_df based on jaccard value\n    using function find_jaccard\n\n        1. If neighbours are found their mutations are\n        combined (union).\n\n        2. Checks if these neighbors are paretnal lineage to\n        some other lineage in the alias_temp_df\n\n        3. Checking if there is a parental lineage to the\n        neighbours in the temp_df\n\n        4. If parental lineage is found and if the length of the parental \n        lineage string is more than one, the mutations of the\n        neighbours and the parernal lineages are again\n        combined (union) and stored in the place of \n        mutations of the parental lineage in temp_df. Neighbours are \n        mapped to their found parent and are stored in alias_df_temp, \n        since there is potential for surther mapping. This parental \n        lineage also becomes the parental lineage for the \n        sublineages that had these neighbours as parental \n        lineage in alias_df_temp.These neighbors are removed from \n        longlineage_df and the loop is iterated for the next round.\n        \n        5. Else if the length of the parental lineage is \n        equal to 1 then everything in the previous point \n        that was written in the alias_df_temp is written to\n        alias_df. Mutations are not meddled with, since it is \n        the ultimate paretnal lineage and there is no go further.\n\n        6. If no parental lineage was found then the the\n        Neighbours are mapped to the pattern which is the\n        name of the neigbors without the last character. This\n        pattern concatinated with x becomes the parental \n        lineage of the neighbors. This also becomes the \n        parental lineage for those sublineages for which the \n        nighbors were parental lineage.\n\n    2. If there are no neighbors found\n\n        1. Code directly starts finding the parental \n        lineage for the element being considered.\n\n        2. If paretnal lineage is found and the length of \n        the lineage is more than 1, the element in hand \n        is mapped to the found paretnal lineage and jaccard \n        value is stored in the alias_df_temp.  Mutations of \n        the element and the found parental lineage is combined and \n        stored in the place of the parental mutations in temp_df\n\n        3. Sublineages for which the lineage in hand is the parental\n        lineage in alias_df_temp gets mapped to the newly found parental lineage.\n\n        4. If the length of the parental lineage being \n        found is equal to one then point 2,3 is repeated \n        but difference would be that instaed of \n        alias_temp_df, alias_df is used and mutations are not meddeled with.\n\n    3. If no parerntal and neighbors were found\n\n        1. The lineage being considered is mapped to \n        itself.\n\n        2. For sublineages in the alias_df_temp that has \n        the lineage being considered as parental lineage is \n        remains the same. It is just transfered to \n        alias_df with no changes.\n\n    \n    Once the longlineage_df has been fully processed if \n    there are entries in temp_df long_sublineage is called else chunk lineage is called.\n    \n\n\n\n    END\n\nEnd\n
\n
Function find_jaccard(pat,search_df,pat_mutations=0)\n\n    search_lineage_loc<-grep(pat,search_df$lineage)\n\n    1. If pat_mutations==0 means the function is finding the\n    neighbours. Else the function is overloaded\n    to find the parental lineage.\n\n    2. If pat_mutations==0 the length(search_lineage_loc) should be\n    more than 1 - neighbours other than the lineage in hand.\n\n    3. If no neighbours were found then function returns \n    neighbours=\"0\", jaccard_value=-1,neighbour_loc=0\n\n    4. Other than point 2 the overloaded function does the\n    same functionality for both the overloaded purposes\n    and returns jaccard value, neighbours, neighbour_loc \nEnd\n
\n
Function Find_parental(pat,parental_df)\n\n    1. Recursively searches with the pattern \n    until it finds the parental lineage satisfying \n    the conditions \n    2. The pattern is shortened every iteration.\nEnd\n
\n

\"Flowchart\nquestion on the treshold

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Possible_questions

\n

1. Why/How was this particular time period (Jan22-Oct23) chosen, while pandemic has been prevelant 2020 onwards?

\n\n

2. There are continuous deposition of sequences to GISAID even for the earlier dates, the following tables shows the difference in numbers. Will calculating CI account these changes ?

\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
CountryNumber of downloaded(18-20 Nov 23)Number in GISAID at later date(8 Dec 2023)
India1578315809
South_korea1380813826
Denmark163900163905
Germany6623666244
Norway1226412264
Spain1792118039
UK3059730606
Canada2079120802
USA7497175165
australia1325713261
\n\n

3. The jaccard index treshold chosen to decide a parent or a neighbour is 50%. Is this okay?

\n\n

4. Why do we do linear interpolation, why not spline interpolation?

\n

-ANS: In a sparse data using a spline interpolation might give unexpected results which might not be right.

\n

5. Aaccording to Uniprot the RBD region in spike is 319-541aa \"spike

\n

ANS: There are no interesting epitopes before position 330 and after position 530 so it's fine.

\n

6. If a RBD spike position in the wildtype is occupied by a hydrophobic residue and it is replaced by hydrophilic residue, the solvent accessibility might change probably due to the difference in the fold. In that case should we study these positions in each of the VOI?

\n

ANS: The Mutation doesnt alter the fold to a great extent, if that happens it will affect the function of the protein, so using the wildtype to compute the solvent accessibility is not so bad idea.

\n

7. The computed pressure trend for a position is obtained by calculating pressure at multiple time points. For now pressure is computed every 180 days. The time horizon is not exactly divisible into bins of 180 days. There will be difference in the final bin. Will this be a problem?

\n
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