Double-CRISPR Knockout Simulation (DKOsim): A Monte-Carlo Randomization System to Model Cell Growth Behavior and Infer the Optimal Library Design for Growth-Based Double Knockout Screens

Double-CRISPR Knockout Simulation (DKOsim): A Monte-Carlo Randomization System to Model Cell Growth Behavior and Infer the Optimal Library Design for Growth-Based Double Knockout Screens | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Double-CRISPR Knockout Simulation (DKOsim): A Monte-Carlo Randomization System to Model Cell Growth Behavior and Infer the Optimal Library Design for Growth-Based Double Knockout Screens View ORCID Profile Yue Gu , View ORCID Profile Traver Hart , Luis Leon-Novelo , View ORCID Profile John Paul Shen doi: https://doi.org/10.1101/2025.09.11.675497 Yue Gu 1 Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center , Houston, TX, USA 2 Department of Biostatistics and Data Science, School of Public Health, University of Texas Health Science Center at Houston , Houston, TX, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Yue Gu Traver Hart 3 Department of Systems Biology, The University of Texas MD Anderson Cancer Center , Houston, TX, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Traver Hart Luis Leon-Novelo 2 Department of Biostatistics and Data Science, School of Public Health, University of Texas Health Science Center at Houston , Houston, TX, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: Jshen8{at}mdanderson.org Luis.G.LeonNovelo{at}uth.tmc.edu John Paul Shen 1 Department of Gastrointestinal Medical Oncology, The University of Texas MD Anderson Cancer Center , Houston, TX, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for John Paul Shen For correspondence: Jshen8{at}mdanderson.org Luis.G.LeonNovelo{at}uth.tmc.edu Abstract Full Text Info/History Metrics Preview PDF Abstract Advances in functional genomic technology, notably CRISPR using Cas9 or Cas12, now allow for large-scale double perturbation screens in which pairs of genes are inactivated, allowing for the experimental detection of genetic interactions (GIs). However, as it is not possible to validate GIs in high-throughput, there is no gold standard dataset where true interactions are known. Hence, we constructed a Double-CRISPR Knockout Simulation (DKOsim), which allows users to reproducibly generate synthetic simulation data where the single gene fitness effect of each gene and the interaction of each gene pair can be specified by the investigator. We adapted Monte-Carlo randomization methods to extend single knockout simulation methods to double knockout designs, which simulate the gene-gene interactions between all possible combinations of the input genes. Using DKOsim, we generated simulated datasets that closely resemble real double knockout CRISPR datasets in terms of Log Fold Change (LFC), GI distribution, and replicate correlation. We further inferred optimal CRISPR library designs by systematically investigating critical experimental parameters including depth of coverage, guide efficiency, and the variance of initial guide distribution. This simulation scheme will help to identify optimal computational methods for GI detection and aid in the design of future dual knockout CRISPR screens. Author Summary We designed DKOsim to simulate CRISPR double knockout screens by modeling cell division behavior with both single knockout (SKO) and double knockout (DKO) constructs via Monte-Carlo randomization samplers. Running DKOsim at large scale, we identified the asymptotic tuning points that optimize genetic interaction (GI) identification performance by the delta-LFC (dLFC) method compared to the simulated truth. We show that DKOsim is tunable to approximate actual dual-CRISPR knockout screening data. Comparing replicate correlation from DKOsim with experimentally generated data, DKOsim can be tuned based on users’ desires to reproduce a similar level of randomness to that observed in variety CRISPR screening conditions. Introduction Clustered Regularly Interspaced Short Palindromic Repeats (CRISPR) was first identified in E. coli bacteria in Japan[ 1 , 2 ]. CRISPR knockout can be multiplexed into a high-throughput genetic screening method to systematically perturb genes and/or pairs of genes[ 3 ]. In 2017, combinatorial CRISPR-Cas9 screens were performed in cancer cells for the first time to allow for high-throughput identification of synthetic lethal gene pairs[ 4 , 5 ]. More recently, the Cas12a platform provides a highly efficient multiplex gene knockout, significantly increasing efficacy of gene knockout and decreasing library size and thus the cost of genetic interaction screening[ 6 , 7 ]. Combinatorial CRISPR technology has revolutionized the discovery of gene-gene interactions [defined as genetic interactions (GIs)] by allowing large-scale screening in human cell lines, organoids, and mouse models. GIs occur when the fitness effect of a gene is modified by the functional status of other genes. It is measured by comparing fitness following the CRISPR knockout of a gene pair (double knockout, DKO) vs. the knockout of each gene (single knockout, SKO). The study of GIs reveals the functional relationships between genes and pathways, specifically, the synthetic interactions and compensatory pathways. The findings serve as the foundation for systematic gene network construction, which is valuable for novel drug development in cancer research[ 8 ]. With around 200 million possible interacting gene pairs for a mammalian cell, GIs are typically rare and hard to quantify accurately from noisy data[ 8 , 9 ]. Hence, there is limited consensus on the use of existing computational tools for detecting GIs. Moreover, experimental validation of GIs in high-throughput is difficult since there are no gold standard datasets that include the true interactions. To address these challenges, we developed a probabilistic simulation framework with simulated theoretical GI truth to emulate the real laboratory CRISPR screening procedures for both SKO and DKO designs. This approach allows us to efficiently test several interacting gene pairs for GIs and approximate the underlying true GI distributions. Prior efforts in generating simulation frameworks for CRISPR screening mainly used SKO designs. In 2015, Stombaugh et al. proposed the Power Decoder Simulator[ 10 ] to generate in silico shRNA pooled screening experiments using short hairpin RNA (shRNA) to efficiently estimate the genotypic biological relevance of a set of genes based on their experimental phenotype. Building upon this, Nagy et al. (2017) developed the first CRISPR SKO discrete simulation tool, CRISPulator[ 11 ], which simulates both the Growth-based and the Fluorescence-Activated Cell Sorting (FACS)-based SKO screening to test the effects of different library designs. de Boer et al. (2020) designed MAUDE[ 12 ] (Mean Alterations Using Discrete Expression) utilizing the CRISPulator to show the consistency in the optimal cell-sorting bins configurations by quantiles via simulation, and derive the mean expression of cells containing each guide. These studies connected the designed simulation framework with empirical assumptions from real experiments but lacked systematic profiling of the screening parameters for growth-based pooled CRISPR screens that assume exponential cell growth. Moreover, since they did not consider the combinatorial CRISPR screening (i.e., DKO) design, the effects of GIs are not articulated in their simulated CRISPR design. To address the need for systemizing a CRISPR simulation scheme and the lack of a DKO simulation framework, we developed a Double-CRISPR Knockout Simulation (DKOsim) that will enable researchers to determine the DKO behavior, including the simulated theoretical true interactions. DKOsim will help identify the optimal GI detection methods and design future double-guided CRISPR experiments. The motivations of the study are visualized in Fig. 1 . We started by analyzing sets of CRISPR DKO screening data using two different computational approaches named CTG[ 13 ] and GEMINI[ 14 ]. While the SKO gene fitness scores showed high correlation, the GI scores were essentially random, with almost no overlap in the identified GIs between the two methods in HeLa cell line. Without the GI ground truth, we could not determine which method was detecting the truly interacting gene pairs. Motivated by this, we designed a systematic synthetic data simulation scheme to simulate theoretical GIs that could be treated as the underlying truth. Download figure Open in new tab Fig 1. Motivations of the Study. Two genetic interaction (GI) identification methods named CTG and GEMINI are applied to HeLa cell line in Shen et al. 2017 Double-CRISPR Knockout (DKO) datasets. Computational results are visualized in both scatterplots of CTG vs. GEMINI scores, and Venn diagram on the identified GI by CTG and GEMINI. Methods Overview and Notations We simulated the CRISPR knockout screens by modeling cell division, using Monte-Carlo randomization sampling. The common notations and conceptual methodology of the simulation scheme are summarized in Fig. 2 . We indexed genes with k ∈ {1,…, n } and used the notation SKO ( k ) to refer to a cell with only gene k to be knocked out. We used the notation DKO ( k 1 ; k 2 ) to refer to cells whose genes k 1 and k 2 were targeted for knock out. Since the order of knocking out the genes does not matter, we used k 1 and k 2 , with k 1 < k 2 , k 1 , k 2 ∈ {1,…, n } to index the dual-targeted genes in a DKO cell. Download figure Open in new tab Fig 2. Simulation Methodology. Main modules are conceptually visualized in the simulation schematic design, including KO target gene class initialization, cell division and growth modelling, and cell population transfection and selection simulation. We extended the notation to consider the guides targeting specific genes to be knocked out. We referred to the definition of guide in CRISPR screening as a synthetic RNA molecule named guide-RNA (gRNA) that directs CRISPR-associated nuclease, such as Cas9 or Cas12, to a target DNA sequence[ 15 ]; in SKO cells, we assumed a single-guide (sgRNA) disrupts one gene, whereas in DKO screens, two distinct guides were combined as one dual-guide (dgRNA) to perturb two genes simultaneously. We additionally defined the construct as either gene and guide or the combination of two genes and their corresponding guides. In this way, the guide targeting gene k is indexed with j and the notation SKO ( k,j ) refer to cells on construct with only gene k targeted with guide j . Note that in SKO ( k,j ) and SKO (k ′ , j ), though the guides share the same index j , are different. Similarly, j 1 and j 2 refer to guides targeting genes k 1 and k 2 simultaneously. DKO ( k 1 , j 1 ; k 2 , j 2 ) denote cells on constructs whose genes k 1 and k 2 are targeted to be knocked out with guides j 1 and j 2 , correspondingly. We initialized the knockout (KO) target gene into one of the four main classes: Negative, Wild-Type (WT), Non-targeting Control, or Positive. The theoretical phenotype of each class of genes was drawn from pre-specified distributions, where the mean and variance of each gene class can be tuned by users as desired. Treating the initialized genes as inputs, we derived the cell division and growth behavior in both SKO ( k ) and DKO ( k 1 ; k 2 ) designs from Multi-bernoulli (Multinoulli) distributions that model the exponential cell growth with KO target genes. To simulate cell population transfection and selection procedure, we additionally incorporated the guide-efficacy effects, and defined the initial cell population at t 0 as the population that contains all pre-specified constructs SKO ( k,j ) and DKO ( k 1 , j 1 ; k 2 , j 2 ) with set of counts C 1 . After several cell doublings controlled by the users’ desires on bottlenecks, the final cell population at t 2 contained SKO ( k,j ) and DKO ( k 1 , j 1 ; k 2 , j 2 ) with set of counts C 2 . We calculated the Log2 Fold Change (LFC) at t 2 vs. t 1 to quantify the change in the relative abundance of the constructs over time. We also calculated the simulated true GI π by measuring the difference between the expected counts given DKO cell division probability vectors, with or without interactions. We summarized the analytical framework of the study in Fig. 3 , based on users’ inputs. DKOsim mimics the real CRISPR screening for both SKO and DKO designs that output the simulated growth-based screening data and calculates the LFC for all constructs with simulated theoretical GI truth. A standard analytical workflow for the simulated datasets includes SKO genes and LFC distributions visualizations, DKO gene combinations deconvolution and dLFC application. Here, we referred the term gene combination deconvolution to the signal-stratification of aggregate LFC measurements into distributions corresponding to distinct gene-class pairings, thereby isolating overlapping phenotypic signals[ 16 ]. Download figure Open in new tab Fig 3. Study Design. Analytical frameworks of the study. Cell-Behaviors Multinoulli Distribution Derivations Growth Behavior Derivations of SKO Cells For one unit of the cellular population doubling cycle, for a single cell, we define Specifically, the knockout of gene 1 will yield, in terms of cell division, one of the following three outcomes, in one unit of WT cell doubling time: (a) x 1 = 0: Cell does not divide and loses viability; (b) x 1 = 1: Cell divides once as WT; (c) x 1 = 2: Cell divides twice. These outcomes are simplified for further derivations and simulation programming. We adapted the ideas from CRISPulator; it is possible that the cell divides more than twice or that the cell starts division, but takes twice as long to divide as a WT cell. We did not choose the option “cell does not divide and remains viable”, allowing us to connect our discrete simulation approach with the continuous exponential growth-based model ( S1 Text: Connection between the Discrete and the Continuous Model ). Given x 1 ∈ {0,1,2}, the SKO cell will produce descendants. The value of x 1 depends on the theoretical phenotype p 1 ∈ [− 1,1], and we assume where ( a ) + : = max{0, a }, and the Multinoulli ( values,prob ) refers to the multi-bernoulli distribution where x = value [ j ] with probability prob [ j ]. Based on the value of p 1 , there are three possible outcomes: (a) When p 1 0, x 1 ∈ {1,2}, it is a positive phenotypic gene where p ( x 1 = 1) = 1 − p 1 , p ( x 1 = 2) = p 1 . Without loss of generality, the same deductions and notations are used for x 2 when we knock out gene 2 as in (1), but with parameter p 2 where Growth Behavior Derivations of DKO Cells For DKO gene-level outcomes, we considered the joint effects of both the variables x 1 and x 2 , with parameters p 1 and p 2 , respectively. Similar to the notations for SKO effects, we included a variable y for DKO effects. More specifically, for one unit of the cellular population doubling cycle, for a specific single cell, we denote y = # of cell divisions when both gene 1 and gene 2 are KO simultaneously in one unit of the cell doubling time, we assume y will have one of the following outcomes: (a) y = 0: Cell does not divide and loses viability; (b) y = 1: Cell divides once as wildtype; (c) y = 2: Cell divides twice; (d) y = 3: Cell divides three times. As such, given y ∈ {0,1,2,3}, under no gene-gene interaction x 1 ⊥ x 2 . We define The original single cell in the DKO design produces C y = 1 ( y ≠ 0 ) × 2 y ∈ {0,2,4,8} descendants per WT population doubling cycle. We chose this definition of y so that if the first targeted gene is a non-targeting control (this is, p 1 ≡ 0, x 1 ≡ 1 and there is no gene-gene interaction), then DKO cells behave like SKO cells based upon the second-targeted-gene, regardless of the behavior of the first targeted gene. In math, x 2 follows the multinoulli distribution in (2) and y ∼ x 2 . This is shown below in (8). The distribution of y is where is the cell division probability vector. Deriving the values of the cell division probability vector Based on the definition of additive interactions in combination perturbation[ 17 ], we calculated y as shown in (3). Its value as a function of x 1 and x 2 , is given in the following matrix: Accordingly, the joint density of ( x 1 , x 2 ) is given by the matrix where a ij ≥ 0 and . So p y in (4) is The can take any values in [0, 1 ] as long as they add up to 1. Under the condition of no gene-gene interactions, where x 1 and x 2 are independent (in math x 1 ⊥ x 2 ), the matrix above becomes Thus, under no interaction x 1 and x 2 induce the multinoulli distribution shown in (4), and for y with , this is With where So when p 1 = 0, and there is no interaction ( i . e ., when the first targeted gene is a non-targeting control), That is the same distribution of x 2 in (2). Also note that the multinoulli distribution of x 1 in (1) is the same as the multinoulli distribution of y in (6) with p 2 ≡ 0. In a later subsection, we describe the simulation of the number of divisions in an SKO or DKO cell without gene interaction from the multinoulli distribution shown in (6). We also used (6) to simulate cell divisions of a DKO cell, with interaction jiggling the values of p 1 and p 2 . Genetic Interaction Derivation To simulate the gene-gene interactions, we define the theoretical GI based on the growth rate of the cells[ 18 ] as where, C y denotes the number of descendants of the DKO cell, defined as shown in (3), after one unit of population doubling cycle. is defined in (7) and is calculated by defined as follows: Based on the GI flag I ∈ {0,1} (no interaction coded as I = 0 and interaction as I = 1) from the initial cell library detailed in Simulation System Design I, we define the resampled theoretical phenotypes with interactions as where I = 1, and i = 1,2 indexes the first and second KO genes in the cell. We defined as the resulting when replacing p 1 , p 2 by in (7), and the simulated GI π as shown in (9). When I = 0, we defined for i = 1,2 and then π = 0. Simulation System Design I: Cell Library Construction Parameters Specification Table 1 summarizes all tunable parameters used as inputs in our CRISPR KO simulation scheme. The glossary of each tunable component and its deduced products in our designed system is detailed in S1 Text: Glossary of tunable components . View this table: View inline View popup Table 1. Summary Table of Tunable Parameters in the Simulation System. SKO Gene Initialization As defined in (1), we first initialized the theoretical phenotypes for the SKO cells, p k ∈ [− 1,1], k = 1,…, n . Each SKO ( k ) corresponds to one of four classes: negative, positive, wild-type (WT), and non-targeting control. The proportion of SKO ( k )s of each class is specified by the user. The distribution of p k within each class is also prespecified by the user. Specifically, we assumed the distribution for phenotypes p k , k = 1,…, n is: Negative: Positive: WT: Non-Targeting Control: p k = 0 where 𝒩 [ a,b ] ( μ,σ 2 ) denotes the normal distribution with mean μ and variance σ 2 truncated to the interval [ a,b ]. Second, for each SKO ( k ), we defined that would later help us determine the initial relative frequency of each (SKO and DKO) construct in the library. We obtained by drawing where σ f is the standard deviation of the log10 normal distribution of . Following CRISPulator[ 11 ], by default, where the number 3.29 was chosen so that there is a 10-fold difference between the 95 and 5 percentiles of the initial SKO counts distribution. As a toy example, shown in S1 Table , we generated a library with n = 3 genes, 1,2, and 3 belonging to negative, WT, and non-targeting control gene classes, respectively. After sampling from the above distributions, we obtained p 1 = − 0.4, p 2 = − 0.03 and p 3 = 0. View this table: View inline View popup Download powerpoint S1 Table Toy example: Single Gene KO parameters. DKO Gene Initialization To initialize the cell library containing both SKO and DKO cells, we generated all unique combinations of gene pairs that can be targeted for KO, DKO ( k 1 ; k 2 ) with k 1 , k 2 ∈ {1,2,…, n }, k 1 < k 2 . Then we row binded the SKO ( k )s and DKO ( k 1 ; k 2 )s to generate all indices for genes k = 1,…, n and their unique combination in pairs. We aimed to generate a set of preliminary (non-standardized) frequencies for SKOs and DKOs. We defined a preliminary non-standardized ( i . e ., they do not add up to 1) frequency of cells with SKOs and DKOs. At the initial timepoint t 0 , this frequency is defined as and for DKO ( k 1 ; k 2 ). These frequencies will be used later to generate the initial library counts. Genetic Interaction Index Initialization For every DKO ( k 1 ; k 2 ) an interaction indicator was generated. Within the set of DKOs not containing a non-targeting control, we randomly selected % GI of DKOs and flagged their genes as interacting (coded as I = 1) and the rest as not interacting ( I = 0). Recall that % GI , selected by the user, is the proportion of DKO constructs with no non-targeting controls whose genes interact. For each DKO ( k 1 ; k 2 ) we defined and , that later helped us define interaction, as for i = 1,2 if there is no interaction, ; and we draw , with i = 1,2 if there is interaction, . The user-specified simulation parameter will control the magnitude of the GIs in the gene pairs. Continuing with our toy example, let’s assume that we are requesting that % GI = 100%, i . e ., 1st and 2nd targeted genes k 1 , k 2 interact. S2 Table shows an example of 3 unique genes drawn from the above distributions, with all possible combinations without considering orders. View this table: View inline View popup Download powerpoint S2 Table Toy example: Single & Double KO Genes Initialization. Rows above (below) the dashed lines represent single (double) KO genes. Genes 1 and 2 interact and, for example, for the DKO of genes 1 and 2 is the mean of and of these genes, i.e., . In rows 5 and 6, 1st(2nd)-gene p I equals 1st(2nd) gene p because there is no interaction I = 0. The second column denotes the values of k for SKO and k 1 for DKO. Guides Initialization We initialized the guides targeting each gene and categorized them based on their KO efficiency. The efficacy of the guides j targeting gene k was denoted as . We added an index H or L , to differentiate between high and low efficiency guides. Guide-efficacy (high/low) of n × n ( i . e ., # of genes × # of guides targeting each gene) guides was determined by randomly selecting % heg × n × n g guides to be highly efficient and the rest to be low efficient. Recall % heg is the percentage of high-efficacy guides chosen by the user. Based on the simulated guide-efficacy (high or low), the guide-efficacy was simulated by a tunable CRISPR model parameter, as summarized below: CRISPRn (CRISPR-nuclease): CRISPRn-100%Eff (CRISPR-nuclease with full-efficacy guides): Constructs Frequency & Counts Initialization We utilized the Dirichlet Distributions to randomly assign the initialized cell counts to guides as follows: For SKO, we determine the non-standardized relative frequency of cells with guide j targeting gene k, i . e ., SKO ( k,j ) for k = 1,…, n and j = 1,…, n g : s.t. For DKO, we computed the non-standardized relative frequency of cells with a guide j 1 targeting gene k 1 and guide j 2 targeting gene k 2 , i . e ., DKO ( k 1 , j 1 ; k 2 , j 2 ) for k 1 = 1,…, n − 1, k 2 = k 1 +1,…, n and j 1 , j 2 = 1,…, n g : s.t. For each pair of genes, across the guides, the average relative frequency of the SKOs is the same as the average relative frequency of DKOs. Hence, the initial counts of SKO and DKO are similar. Also, the distribution of SKO ( k 1 ) Log2 fold change to be similar to the distribution of DKO ( k 1 ; k 2 ) when the gene k 2 is a non-targeting control ( i . e ., no interaction). Specifically, we chose α = 100 for generating in (10) and in (11) to maintain a small variance in the relative frequencies of the SKO and DKO counts across the guides within each gene or gene-pair, respectively. Similar to the DKO gene initialization, we calculated the relative frequency of each construct ( i . e ., combinations of the targeting SKO(DKO) gene(s) and the corresponding guides) at t 0 as with k,k 1 , k 2 ∈ {1,…, n }, k 1 < k 2 and j,j 1 , j 2 ∈ {1,…, n g }. so that the relative frequencies sum up to 1. The initial construct counts are set equal to for SKO ( k,j ) and for DKO ( k 1 , j 1 ; k 2 , j 2 ), respectively, where again ⌊ x ⌉ denotes the rounding of the real number x to the nearest integer, n is the total number of unique single input genes, n g is the total number of guides corresponding to each unique KO construct, and L 0 is the requested initial library size specified by the user. Our initialized cell library with constructs from all pre-specified guides and genes is denoted as . S3 Table shows the toy example of the simulated cell library counts with n g = 2 initialization with 18 row based on S2 Table , using a coverage C = 100 yielding a library size of L 0 = 1800. View this table: View inline View popup Download powerpoint S3 Table Toy example: Initial Cell Library. Cell Growth Behavior of SKO and DKO constructs incorporating guide-efficacy Following the simulation of cell behavior with KO genes, incorporating both the guide-efficacy and GI effects, we defined for SKO ( k,j ), k = 1,…, n and j = 1,…, n g . The cell growth behavior of SKO ( k,j ) will be determined by while the DKO ( k 1 , j 1 ; k 2 , j 2 ) behavior will be determined by both and . Recall that is the efficacy of the guide j targeting gene k . For SKO ( k,j ) let and p 2 : = 0, and for DKO ( k 1 , j 1 ; k 2 , j 2 ) let and , in (7) to compute to simulate the cell division behavior. In every cell doubling cycle, the cell will divide y times with y multinomial with p y : = p y ′ in (4). Computation of Simulation True Genetic Interaction With the initialized cell library specified above, and based on the methodology demonstrated in the cell-behaviors multinomial distributions sub-section, the simulated truth cell behavior with interactions of genes k 1 and k 2 was defined as follows: 1. Using and in (7), we computed the cell division probability based on KO gene effects without GI 2. Using and in (7), we computed the cell division probability based on KO gene effects with GI 3. The gene-level GI values were computed by plugging in the values and p y in (9). The GIs were categorized as either negative, none, or positive. In the absence of an interaction and (9) produces a 0 interaction. For example, the interaction of genes 1 and 2 in the toy example in S2 Table and S4 Table p 1 = 0.4, p 2 = − 0.03 and in item 1 above; and in item 2 above; producing a simulation true interaction of -0.1506 in item 3. Simulation System Design II: Cell Population Transfection and Selection This subsection profiles the methods used for simulating cell population transfection and selection, and simulation data processing. Transfection and Selection In the simulated cell population transfection and selection stage, we used t as a cell doubling cycle counter and i e as a counter of bottleneck encounters. We initialized t = 0 and i e = 0. The number of bottleneck encounters, n e was specified by the user, and the maximum number of cell doubling cycles was set to 30. The setup was as follows: At t = 0, we initialized the current library of cell counts c 1 for every construct equal to the initial library; for SKO and for DKO. The n c dimensional vector of cell counts C 1 was calculated by binding the current counts of SKO and DKO constructs as follows: and The parameters were stored to the n c × 4 matrix M p , wherein row i contains the cell division probability vector for construct i . Hence, construct i has current counts ( C 1 ) i and the cell division vector equal to row i of M p . When i e < n e and t < 30, we iteratively run: Compute the current library size and check the bottleneck condition: where n b is the user-prespecified bottleneck size. If yes , let i e = i e + 1, and draw n r cells from the current cell library: and set the current value of C 1 equal to C ′ . Here MVHyper( n , k ) denotes the multivariate hypergeometric distribution that indicates the balls drawn from each color when k balls are extracted without replacement from a urn containing ( n ) i balls of color i , here n is a vector of dimension the number of different colors in the urn. If, for example, the current library has 50 DKO (1,1;2,1) cells, the new library will have at most 50 of these cells. Following CRISPulator, we do not model multiple infections and assume the simulated CRISPR screening is on a low multiplicity of infection (moi)[ 11 ]. By default, we chose moi λ = 0.3 and model it as a Poisson process during transfection to select the cells that have single transfection occurrence by where P ( x = 1;Poisson(0.3)) ≈ 22% of the C 1 is set to be n r , the number of cells that we kept after reaching the bottleneck. For each construct i , grow ( C 1 ) i to ( C ′ 1 ) i following the row i of M p that defines the corresponding i th cell division probability vector for both if SKO ( k,j ), and . The current value of ( C 1 ) I is set to ( C ′ 1 ) I to simulate the cell populations’ transfection and growth. In math, before growth we have ( C 1 ) i construct i cells, with each cell dividing according to (6), producing ( C ′ 1 ) i : = c 0 × 0 + c 1 × 2 + c 2 × 2 2 + c 3 × 2 3 cells after one growth cycle with ( c 0 , c 1 , c 2 , c 3 ) ∼ Multinomial ( C 1 ) i , values = (0,1,2,3), prob = p y ′ So that c 0 + c 1 + c 2 + c 3 = ( C 1 ) i . And set ( C 1 ) i = ( C ′ 1 ) i . Increase the iteration counter from t to t = t + 1. Simulation Data Processing After this iterative process (when we reach either i e = n e or t = 30), the cell library at this final timepoint t 2 was denoted as . We set the cell counts of referred as C 2 equal to C 1 , and computed the total library size . The relative frequency of each construct at t 2 was calculated as follows: where k,k 1 , k 2 ∈ {1,…, n }, k 1 < k 2 and j,j 1 , j 2 ∈ {1,…, n g } . Accordingly, we defined the n c dimensional vector of the relative frequency of constructs at , by binding the relative frequency of SKO and DKO constructs at t 2 as shown below: and Similarly, using equation (12) , we also defined the n c dimensional vector of the relative frequency of constructs at the initial timepoint by binding the relative frequency of SKO and DKO constructs at t 0 as shown below: and Based on the definition of log fold change and C pseudo included in the parameters specification subsection, we calculated the Log2 n c -dimensional Fold-Change (LFC) vector at t 2 vs. t 0 as follows: where C pseudo is the pseudo-count added to each relative frequency of the constructs to avoid − ∞ in logarithm. The rest of the sections in simulation system design are detailed in S1 Text. Supplemental Methods and Materials . Algorithmic Designs: Monte-Carlo Simulation on Large Scales Algorithm: Double CRISPR-Knockout Simulation (DKOsim) The practical computational workflow of DKOsim for large-scale applications is summarized in S1 Text: Simulation Steps , and the computational modules are presented in S1 Fig . Using the notations defined in the parameter specifications subsection, we initialized the simulated cell library as desired by users. For the purpose of modeling the competitive exponential cell growth and selection procedures after library transfection and transduction, we designed Algorithm 1 to simulate the cell population adaptations through multinouli-resampling induced by the growth bottleneck: Algorithm 1 DKOsim: Double CRISPR-Knockout Simulation Scheme via Monte-Carlo samplers* Download figure Open in new tab Results DKOsim is tunable to infer the asymptotic effects of laboratory CRISPR screening parameters We systematically ran DKOsim to investigate the tunability of the scheme and validate its use for simulating the empirically expected CRISPR screening data pattern from laboratory experiments. From the tunable parameters summarized in Table 1 , we chose six parameters to compare the simulation tunability, including coverages, percentage of high-efficacy guides, GI magnitude, dispersion of the initial frequency of SKO counts, number of guides per gene, and cell doublings. To quantify the association between the GI identifications vs. simulated GIs, we applied Delta Log fold Change (dLFC) that calculates the deviations in log fold change (LFC) from the mean LFC of all constructs targeting gene pairs to the expectation of the sum of the single mutant fitness (SMF) for the two genes[ 19 ], and measured the association by Pearson’s correlation r. Additionally, we calculated the precision and recall at 80 strongest dLFC GI identifications among the top 100 negative simulated GI hits (Precision/Recall@80) to quantify the dLFC GI identification performance. Since we were simulating both SKO and DKO, we applied BAGEL[ 20 , 21 ] to the simulated SKO data to assess the validity of the simulated essential genes, defined as genes with negative theoretical phenotypes in our designed system. Except for the tuning parameter being compared, the others were assumed to be the same for comparison. Specifically, for the simulated screenings that were compared, we summarized the default parameters of the baseline screening - Simulation (Systematic Run - Baseline) in Table 2 . View this table: View inline View popup Download powerpoint Table 2. Input Parameters in DKOsim Simulation (Systematic Run - Baseline) For experimental parameters, including coverage, guide quality, initial constructs’ counts dispersion, and cell doublings parameters, which can be directly controlled in the experimental design, we compared and visualized the effects of each by systematically running DKOsim ( Fig. 4A-K ). When increasing the coverage of the CRISPR screening experiments, the Pearson correlation r between the detected GI vs. the simulated GI monotonously increased and reached an asymptote around 0.7 at 100x ( Fig. 4A ) . Results of AUC-PR from BAGEL SKO gene essentiality identification further demonstrated that the simulated SKO essential genes asymptotically reach the optimal performance starting at 100x screening with 0.98 AUC-PR ( Fig. 4B ) . We quantified the GI identification performance of dLFC and visualized the changes in Precision/Recall@80 presented in Fig. 4C , while the changes in the AUC-PR for all negative GIs are shown in S2 Fig. A . Monotone increasing patterns are found in both, with the asymptote at 100x. the Precision@80 dominates the Recall@80 and AUC-PR, reaching an asymptote around 0.86 at 100x. Beyond this 100x asymptotic point, increments to the experimental coverage do not significantly improve either the association or identification performance between dLFC vs. simulated GI, indicating the optimal cost-effective design for screening coverage is 100x. Download figure Open in new tab Fig 4. Tunability of the Parameters in the Simulation Scheme. Delta Log Fold-Change (dLFC) is applied to simulations to measure the genetic interaction (GI) scores. (A)-(C) Simulation Runs on Coverage Effects. We use the parameters in Table 2 except for the coverage C varying from 1x to 500x: (A) Changes of Pearson correlation r on dLFC vs. simulated GI, from Coverage varying runs. (B) Changes of AUC-PR for SKO Gene Essentiality on BAGEL identifications on the simulated essential (negative phenotypic) genes, from Coverage varying runs. (C) Changes of Precision and Recall of the 80 most negative dLFC identifications on the top 100 simulated negative GI hits, from Coverage varying runs. (D)-(F) Simulation Runs on Percentage of High-Efficacy Guides Effects. We use the parameters in Table 2 except for the percentage of guides with high-efficacy % heg varying from 10% to 100% with Mode on “CRISPRn”: (D) Changes of Pearson correlation r on dLFC vs. simulated GI, from High-Efficacy Guides Percentage varying runs. (E) Changes of AUC-PR for SKO Gene Essentiality on BAGEL identifications on the simulated essential (negative phenotypic) genes, from High-Efficacy Guides Percentage varying runs. (F) Changes of Precision and Recall of the 80 most negative dLFC predictions on the top 100 simulated negative GI hits, from High-Efficacy Guides Percentage varying runs. (G)-(I) Simulation Runs on Dispersion of Initial Counts Effects. We use the parameters in Table 2 except for the dispersion of the initial frequency of SKO counts σ f varying from to : (G) Changes of Pearson correlation r on dLFC vs. simulated GI, from Initial Counts Dispersion varying runs. (H) Changes of AUC-PR for SKO Gene Essentiality on BAGEL identifications on the simulated essential (negative phenotypic) genes, from Initial Counts Dispersion varying runs. (I) Changes of Precision and Recall of the 80 most negative dLFC predictions on the top 100 simulated negative GI hits, from Initial Counts Dispersion varying runs. (J) Simulation Runs on Number of Guides per Gene Effects. We use the parameters in Table 2 except for the number of guides per gene n g tuned varying from 1 to 10 and the percentage of guides with high-efficacy % heg tuned from 10% to 100%: Changes of Pearson correlation r on dLFC vs. simulated GI, from Number of Guides per gene varying runs, colored by the percentage of high-efficacy guides. (K) Simulation Runs on Cell Doublings Effects. We use the parameters in Table 2 except for the bottleneck size n b and the number of bottleneck encounters n e tuned to control the cell doublings varying from 1 to 19: Changes in the fraction of reads in the top 5% of the guides, from Cell Doublings varying runs. (L) Simulation Runs on GI Magnitude Effects. We use the parameters in Table 2 except for the strength of the simulated GIs σ GI varying from 0.1 to 5: Changes of Precision and Recall of the 80 most negative dLFC identifications on the top 100 simulated negative GI hits, from GI Magnitude varying runs. Similarly, we compared the tunability for the percentage of high-efficacy guides. When the systematic runs were restricted to compare guide quality by tuning the high-efficacy guides percentages, the correlations between dLFC and simulated GIs with increasing percentage of high-efficacy guides from 10% to 100% increased monotonously, with r = 0.79 for 100% high-efficacy guides ( Fig. 4D ). Fig. 4E shows the BAGEL essentiality identification results: with the monotone increasing identification performance on better guide quality, BAGEL can correctly identify 88% simulated essential genes when all guides are highly efficient. Comparing the GI identification performance of dLFC, we visualized the changes in Precision/Recall@80 ( Fig. 4F ) and AUC-PR for all negative GIs (S2 Fig. B) by increments to the percentage of high-efficacy guides, and both metrics showed monotonically increasing trends. Specifically, Precision@80 on the top 100 negative GI hits as 0.95 dominates other metrics, indicating that dLFC can correctly identify 76 out of 80 as true simulated negative GI hits from the simulation. To demonstrate the tunability of the initial counts dispersion, following Table 1 , we systematically ran DKOsim by tuning σ f based on the z-score resulting from a 40-90% confidence level. For example, at 90% confidence, the expected z-score is 3.29, and we constructed the SKO gene frequency following a normal distribution with so that there is a 10-fold difference between the 95 th and 5 th percentiles. As defined, lower confidence leads to higher σ f , resulting in a higher dispersion of the initial count distribution. Based on this setting, we visualized the changes of the correlation r with increasing standard deviation of initial counts dispersion ( Fig. 4G ). As expected, the increments of the initial counts dispersion decrease the correlation r on dLFC vs. simulated GI, and we found that r drops to 0.54 when . We tested the BAGEL essentiality identification on simulations in this setting. Our results show that the increments of initial counts dispersion monotonously decrease the BAGEL identification performance. AUC-PR of BAGEL reaches a trough of 0.74 when , indicating that only 74% of the simulated SKO essential genes in the designed simulation system in this scenario can be correctly identified and recovered by BAGEL ( Fig. 4H ). Lastly, Fig 4I visualized the monotone decreasing trend from Precision/Recall@80 by increments of the confidence level of dispersion, where we found the precision and recall reach the lower-end as 0.65 and 0.52, respectively, at . We additionally tested the effects of the number of guides per gene ( Fig. 4J ) on different proportions (10%-100%) of high-efficacy guides. With only 10% highly efficient guides, we observed a monotone increasing trend of the Pearson correlation r on dLFC vs. simulated GI, peaking at 0.78 with 10 guides per gene. When 30% of the guides were highly efficient, 5 guides per gene with r = 0.8 is the optimum of the correlation; when either 50% and 80% of the guides were highly efficient, we observed an asymptotic optimum of the correlation at 3 guides per gene with 0.79 and 0.77, respectively; and when all of the guides were highly efficient, the correlation reached the optimum with r = 0.76 at 2 guides per gene and, unexpectedly, show a decreasing trend beyond this point, indicating dLFC might not identify the GI well in a perfect guide-efficacy scenario. Based on the simulation results, choosing 3 guides per gene would be enough in real laboratory screening by ensuring sufficient quality of the guides when ordering. For cell doublings, we mainly compared and visualized the asymptotic trends of the fraction of reads in the top 5% reads for cell doublings in Fig. 4K . From 1 to 19 cell doublings, the fraction of reads in the top 5% reads increased monotonously due to the decrease in cell diversity caused by the death of simulated cells with negative phenotypic targeted KO genes’ constructs. With 19 doublings, 100% of the reads are represented by the top 5% of guides, indicating the cell diversity reaches a minimum where the cell counts are dominated by one specific construct type, possibly in cells with dual-positive combinatorial KO gene constructs with positive GIs. Lastly, for the biological parameter, specifically GI magnitude, which is determined intrinsically by genetic characteristics in CRISPR screening and not directly controlled by the laboratory experimenter, we visualized its effects on Precision/Recall@80 of dLFC on the top 100 negative GI hits ( Fig. 4L ). Results showed that precision and recall for the top hits reached the asymptotes when σ GI is 1, where Precision@80 is 0.875, Recall@80 is 0.7, supported by asymptotic AUC-PR as 0.792 ( S2 Fig C ). DKOsim approximates patterns from actual laboratory Double-CRISPR Knockout screening data Building upon the tunability of DKOsim, we utilized the designed systems to approximate the real laboratory Double-CRISPR Knockout screening data, demonstrating the approachable feasibility of our simulation design in mimicking the CRISPR experiments in real-world settings. We collect three sets of laboratory screening data for approximation, including the combinatorial CRISPR-Cas9 screens designed by Shen et al.[ 4 ] (Shen-2017), “Big Papi” orthologous combinatorial CRISPR-Cas9 screens designed by Doench et al.[ 22 ] (Doench-2017), and “SCHEMATIC” combinatorial CRISPR platform to map synthetic lethal interactions designed by Fong et al.[ 23 ] (Fong-2024). In this section, the data approximation is restricted to the A549 cell line, a human lung adenocarcinoma cell line with a KRAS gain-of-function mutation in the oncogenic background of cancer studies. We investigated whether DKOsim can approximate the constructs’ count distribution at the initial timepoint, given the same number of perturbed genes. To approximate the Shen-2017 design 1 , we initialized Simulation (mimicking Shen) by 120 uniquely perturbed single genes, 3 guides per targeted gene with 3% GIs, and set 80% confidence (expected z-score as 2.56) on dispersion of SKO genes for DKOsim ( Fig. 5A ). Comparing the simulation results with Shen-2017 day 3 collected constructs’ counts in the A549 cell line, histograms of the log 10 counts are highly aligned between the laboratory Shen-2017 vs. Simulation (mimicking Shen), supported by the small discrepancy between the sample variances of the log 10 constructs counts distribution from the lab . simulation . To approximate the Doench-2017 design, we initialized Simulation (mimicking Doench) by 28 uniquely perturbed single genes, 5 guides per targeted gene with 3% GIs, and set 90% confidence (expected z-score as 3.29) on dispersion of SKO genes for DKOsim ( Fig. 5B ). Compared with the Doench-2017 plasmid constructs’ counts in the A549 cell line, histograms of the log 10 counts highly overlapped between the laboratory Doench-2017 vs. Simulation (mimicking Doench), where the discrepancy between the sample variances of the log 10 constructs counts distribution from the lab . simulation is even indistinguishable. To approximate the Fong-2024 design, we initialized Simulation (mimicking Fong) by 246 uniquely perturbed single genes, 3 guides per targeted gene with 3% GIs, and set 80% confidence (expected z-score as 2.56) on dispersion of SKO genes for DKOsim ( Fig. 5C ). Similarly, we compared the simulation results with Fong-2024 plasmid constructs’ counts in the A549 cell line, histograms of the log 10 counts highly overlapped between the laboratory Fong-2024 vs. Simulation (mimicking Fong). However, we found a discrepancy between the sample variances of the log 10 construct counts distribution from the lab . simulation . Download figure Open in new tab Fig 5. Simulation Approximation on Laboratory Data. Comparison of Distributions between Simulation and Laboratory Data. (A) Histograms of log10-scaled constructs’ counts at the initial timepoint on Shen-2017 A549 vs. Simulation Run (mimicking Shen). (B) Histograms of log10-scaled constructs’ counts at the initial timepoint on Doench-2017 A549 vs. Simulation Run (mimicking Doench). (C) Histograms of log10-scaled constructs’ counts at the initial timepoint on Fong-2024 A549 vs. Simulation Run (mimicking Fong). (D) Histograms of overall LFC distributions on Fong-2024 A549 vs. Simulation Run (mimicking Fong). (E) Histograms of genetic interaction (GI) scores from Schematic on Fong-2024 A549 vs. zdLFC on Simulation Run (mimicking Fong). (F) Histograms of LFC by gene-gene combinations on Fong-2024 A549 vs. Simulation Run (mimicking Fong). Based on the aligned distributions of the constructs’ counts at the initial timepoint, we studied the feasibility of our designed system in simulating the cell growth, transfection, and selection that could eventually approximate the expected functional genomic data pattern from laboratory screenings. Specifically, we chose the Fong-2024[ 23 ] design (data characteristics summarized in S4 Table ) for simulation approximation, in which this recently developed combinatorial CRISPR platform comprises a panel of 246 genes with 67 frequently mutated genes, asymmetrically crossing another 176 druggable genes, with 3 additional non-targeting controls that do not affect the functions of the cells. Among these genes, 64 genes are treated as essential, where AAVS1 is known as a safe harbor locus that should not disrupt any cell function and is treated as the negative control. The cell line was infected at a multiplicity of infection (MOI) of 0.3 to ensure >100x coverage in library production. Each gene was targeted by 3 independent guides in this asymmetric library. Within all possibly interacting 12282 gene pairs, 400 pairs were under FDR < 10%, and we treated of the gene pairs as truly interacting pairs. While screening, two biological replicates were included, each with independent viral transduction on low numbers of cell passages. View this table: View inline View popup S4 Table Summary Table for Fong 2024 Data Characteristics. To approximate the laboratory design, in our Simulation (mimicking Fong) initialization ( Fig. 5D Input Parameters ), we included 246 genes: 64 negative phenotypic genes to align with the number of essentials, 178 wild-type genes to align with the number of nonessentials, and 4 non-targeting controls to align with the AAVS and 3 non-targeting controls from Fong-2024. Each gene was targeted by 3 independent guides, and the asymmetric design in the lab was extended to a symmetric library where all the initialized genes could interact with each other. To further mimic the design, we set coverage C =1000x with MOI=0.3 to align with the high laboratory coverage, and 3 times cell doublings to align with the low number of passages. Additionally, we simulated 2 biological replicates, each transduced independently. LFC was calculated for each replicate and aggregated by mean in the final output after all simulated cell growth, transfection, and selections to approximate Fong-2024’s data pattern. We compared the overall LFC distributions from the Fong-2024 versus the A549 cell line simulation ( Fig. 5D ). Within the same range, DKOsim Simulation (mimicking Fong) approximates Fong-2024’s LFC pattern with almost perfect overlaps, supported by the mere difference between the LFC sample variances . simulation . For approximation, we applied dLFC to the distributions of GI scores in Simulation (mimicking Fong) to identify the simulated GIs, followed by z-standardization to the identification scores named zdLFC. Comparing the distributions of zdLFC with the SCHEMATIC interaction scores from Fong-2024 ( Fig. 5E ). At the same time, the overall shape is aligned and most interaction scores fall within -2.5 to 2.5, zdLFC approximates SCHEMATIC scores with merely rightward distribution and a few more spikes, possibly due to the inclusion of the simulated positive GI in our design. In contrast, SCHEMATIC is specifically designed for identifying actionable synthetic lethal (negative) interactions. We then compared the LFC distributions for its unique gene combinations. Utilizing the 64 gene essentiality labels from Fong-2024, we deconvoluted both the laboratory LFC and the simulated LFC by unique gene combos. To align with laboratory design, we treated our simulated negative genes as essentials, kept the non-target controls the same as Fong-2024, and categorized the rest of the simulated genes, including wildtype and positive genes, as unknown. The deconvolution results ( Fig. 5F ) demonstrated that LFC of the simulated co-essential genes, co-unknown genes, and essential with unknown combos are well approximating the laboratory data. The trend of alignment is most prominent among the co-unknown genes representing the predominant construct category in Simulation (mimicking Fong), where we found almost perfect alignment between the simulation and laboratory data. However, LFC for gene combos consists of the simulated non-targeting control genes tending to have smaller variability compared to Fong-2024, mainly due to our strict definition of non-targeting controls in having 0 theoretical phenotypes. Since the non-targeting controls are explicitly defined not to affect the exponential cell growth, this results in markedly reduced variability in the simulation, compared to data generated from actual laboratory experiments. DKOsim simulates the noise of existence from laboratory experimental replicates and is reproducible from randomness While DKOsim is applicable to approximate data from laboratory CRISPR experiments in real-world settings, we ensured the design of this simulation system to achieve a high degree of reproducibility. Reproducibility, as defined in our context, primarily encompasses two aspects: DKOsim is reproducible both in terms of the stochastic consistency across the Monte-Carlo randomizations and in the sense that users across any discipline can obtain consistent simulation results, given adherence to the defined analytical scheme. We measured the reproducibility of DKOsim using the Pearson correlation r between the two replicates of the simulation from randomization results in our design, on the asymptotic effects of the experimental parameters coverage, high-efficacy guides percentage, and initial counts dispersions. For coverage from 1x to 500x, DKOsim asymptotically gained higher reproducibility between replicates, shown by the increasing correlations, where at 100x, the correlation asymptotically approached 0.95 and reached 0.99 up to 500x ( Fig. 6A ). A monotone increasing trend was seen in the replicates’ reproducibility as the percentage of high-efficacy guides increased from 10% to 100%. When all guides are 100% efficient in knocking out the target genes, the correlation between the replicates was 0.87, indicating a highly consistent LFC between the two replicates ( Fig. 6B ), as empirically expected, improved guide quality is contributing to greater reproducibility of the experiments. For the dispersion of initial counts, a monotone decreasing trend in the replicates’ reproducibility was seen, given a larger standard deviation of log10-scaled initial counts ( Fig. 6C ), with correlation r dropping from 0.95 to 0.91 with higher dispersion. Download figure Open in new tab Fig 6. Reproducibility of the Simulated CRISPR Experiments. (A)-(C) Systematic Tunability Effects on the simulation reproducibility: (A) Changes of Pearson correlation r on LFC between two replicates of the simulation runs, from Coverage varying runs. (B) Changes of Pearson correlation r on LFC between two replicates of the simulation runs, from High-Efficacy Guides Percentage varying runs. (C) Changes of Pearson correlation r on LFC between two replicates of the simulation runs, from Initial Counts Dispersion varying runs. (D)-(E) Comparison of reproducibility on dual-CRISPR screening experiments between laboratory and simulation data: (D) Barplots of Pearson correlation r on the relative frequency of guides and LFC between laboratory replicates with dual-vector designs on two independent viral transduction vs. Simulation (mimicking Fong). (E) Barplots of Pearson correlation r on the relative frequency of guides and LFC between laboratory replicates with single-vector design on one pooled-viral transduction vs. Simulation (Systematic Run - Baseline). We compared the reproducibility between the laboratory experimental replicates and the simulated replicates in DKOsim across different experimental screening designs. We additionally collected laboratory data from the combinatorial CRISPR-Cas9 metabolic screens designed by Zhao et al.[ 24 ] (Zhao-2018), and the “in4mer” CRISPR-Cas12a multiplex knockout screens designed by Hart et al.[ 6 ] (Hart-2024). Following the original combinatorial CRISPR screening design of Shen et al.[ 4 ], Zhao-2018 and Fong-2024[ 23 ] reproduced the dual-vectorized DKO setup with independent lentiviral transductions per context, where each replicate was independently initiated to ensure reproducibility. This approach offers greater flexibility in scaling the interacting gene pool and captures the full biological variability signals in replication from guide integration and infection noise, but introduces more stochastic dropouts depending on guide quality, and higher labor complexity from dual transduction in practical experimental runs. We compared the correlation of the replicates with the dual vectorized design using Simulation (mimicking Fong) which was designed to approximate the Fong-2024 A549 data ( Fig. 6D ). Two sets of the correlations were compared, first on the relative abundance of constructs at final timepoint, and on the LFC between the final timepoint vs. the initial timepoint from the independent transduction. We found increasing replicate correlations from the relative abundance compared to the original design of Shen-2017, and the close agreement with Fong-2024 implies that the simulation accurately models and captures the biological noise arising from cell growth and the selection process. While DKOsim approximated the noise signals from replicates, it maintained the highest LFC correlations when compared with other dual-vectorized DKO laboratory data. Both Doench et al. and Hart et al. built single-vector lentiviral delivery design. The Doench-2017[ 22 ] design encoded the dual-sgRNA in a single lentiviral construct and conducted one viral transduction per replicate, yielding high precision and reproducibility with cleaner delivery but sacrificing the true biological independence. In contrast, the Hart-2024 design had one lentiviral construct encoding up to 4 guide RNAs using Cas12 with one-time viral transduction in the pooled in4mer library. Within the same transduction, multiple sequencing was conducted to measure the constructs’ counts, resulting in two technical replicates at the final timepoints. This approach ensures high precision and reproducibility on pre-defined KO gene combos and minimizes the possible dropout and noise. But as with the Doench design, the one-time lentiviral transduction predisposes the replicates’ reproducibility towards the technical consistency rather than full biological independence. Under this experimental design of a single vector, we compared the replicates’ correlation with Simulation (Systematic Run - Baseline) designed to systematically infer the optimal CRISPR library designs ( Fig. 6E ). Two sets of correlations were compared, first on the relative abundance of constructs at the final timepoint, and on the LFC between the final timepoint vs. the plasmid library. Results showed that while all screening yielded strong reproducibility, the replicates’ correlation closely agrees with Hart-2024 and is identical to Doench-2017, indicating that the simulation can also be utilized to capture the noises in single-vectorized DKO design for both biological and technical replicates. This conclusion is further supported by the LFC correlations, where the simulated LFC correlates better than the technical replicates from Hart-2024 and falls between the Doench-2017 A549 and A375 cell lines. Discussion GIs are rare, and many challenges remain in systematically profiling them without the possibility of validating all gene pairs in high-throughput experiments and in constructing gold standard datasets with true interaction values. On the one hand, laboratory experimental scientists invest a lot of time and resources in performing multiplexed CRISPR screening, which presents both biological and technical difficulties. On the other hand, many existing computational tools have devoted much effort to minimizing the CRISPR screening data noise in order to perform the most robust estimation of gene-gene interactions. But without the underlying truths of the GI values, and systematic quantitative views of the experimental CRISPR screening schemes and parameters, it is only possible to validate the partial interaction detections in restricted cell lines by gathering a large amount of screening data across multiple platforms with different library designs and varying data quality, resulting in a tremendous amount of uncertainty. To address the aforementioned problems, we designed a Double-CRISPR Knockout Simulation Scheme (DKOsim), which systematizes a Monte-Carlo simulation methodology applicable to mimic both the SKO and DKO laboratory CRISPR knockout screening experiments and data patterns, while ensuring high tunability and reproducibility. Utilizing DKOsim on a large scale, users can simulate desired CRISPR screening datasets with the underlying true values of GIs as input, which serves the goals of both inferring the optimal experimental design for CRISPR knockout screening and supporting the statistical rigor in method development to perform inference on interaction values. Accordingly, to better demonstrate the working logics of our designed scheme, we probabilistically derived the cell growth behaviors’ distributions for both SKO and DKO cells, and defined the simulated GI based on the growth rate of the cells. We incorporated the guide-efficacy design into our simulation and summarized all the tunable components in this simulation system. To make the large-scale implementation practically feasible, we designed an algorithm for DKOsim to compile the entire theoretical framework in generating a simulated cell population that mimics the practical laboratory experimental process. As evident from the simulation results, the approximation to data patterns from practical laboratory experiments shows superior alignments between the simulation and laboratory data in many ways, and as expected, the distribution of the simulated GI values recapitulates the laboratory-derived interaction scores. This shows the unprecedented potential of applying DKOsim to generate analyzable synthetic data for downstream analysis. Furthermore, the DKOsim simulation framework was designed to achieve both stochastic consistency and real-world fidelity. Specifically, it aims to reproduce stable and coherent outcomes across parallelly repeated runs, despite the inherent randomness of Monte Carlo processes, while also capturing the biological and technical variability characteristic across many CRISPR screening experimental designs. In addition to modeling experimental noise realistically, DKOsim emphasizes user-level reproducibility: the platform provides a well-documented and modular simulation pipeline, ensuring that researchers from diverse backgrounds can reliably reproduce results by following the same defined workflow and pipeline. This dual reproducibility, emphasized on algorithmic robustness and user consistency, makes DKOsim a versatile tool for benchmarking and evaluating CRISPR-based double-knockout screening strategies. Limitations exist in the current scheme, which will be addressed in future work. First, we are only modeling the on-targeting effects of the screening. The off-target effects might be an important consideration to incorporate into the current scheme. Second, we simplified the cell growth assumptions for derivations and simulation programming; the cells may divide more than twice in unequal time intervals. Taking the continuous time effects into the current model might reflect more signals in approximating the true biological variability. Lastly, DKOsim is mainly designed to simulate DKO CRISPR screening, though it also simulates SKO effects. Its scalability to increase the number of initialized single genes is not perfected at the current stage. Supporting Information S1 Text. Supplemental Methods and Materials Connection between the Discrete and the Continuous Model In this subsection, we show the connection to derive a mathematical transformation between the discrete Multinoulli-based simulation model and the continuous exponential growth-based simulation model. With the model in (1) and (3), for one unit of cell doubling, we defined the following notations: Under SKO, the original cell yield descendants Under DKO, the original cell yield descendants C y = 1( y ≠ 0) × 2 y ∈ {0,2,4,8} For SKO gene, given We consider the following cases for possible input of p 1 : 0 ≤ p 1 ≤ 1: − 1 ≤ p 1 < 0: Without loss of generality, for SKO effects of gene 2, k 2 = log 2 ( 1 + p 2 ) + 1 . Thus, under the assumption of independence s.t. x 1 ⊥ x 2 , as in (3), given We consider the following three cases for all possible combinations of inputting p 1 and p 2 : p 1 , p 2 ≥ 0: p 1 , p 2 ≤ 0: p 1 ≥ 0, p 2 ≤ 0: Therefore, we conclude that when x 1 ⊥ x 2 , where The linear relationship between E ( C y ) and without genetic interactions also supports the conclusion that the cell growth rate is purely dependent on the theoretical phenotypes of the genes and the genetic interaction under the truth are not affected by the choice of guide-efficacy. Glossary of tunable components n = The number (#) of different genes: # of single target genes to be knocked out in both SKO and DKO, and combination pairs. C = The coverage of the experiment: # of cell representations per construct. n g = # of guides per gene. % GI = The percentage (%) of genetic interactions: the % of interacting gene pairs among the gene pairs not containing a non-targeting control. % of each gene type: for k = 1,…, n , we define Negative (% neg ): p k 0, genes whose KO results in benefiting the cell viability and lead to cell division faster than WT. Wild-Type (WT) (% wt ): p k ≈ 0, genes whose KO unaltered cell viability and cell will divide normally, presents variance . Non-targeting Control (CTRL) (% ctrl ): p k = 0, functioning the same as WT, but flagged for statistical analysis later, strictly equal to 0 without variance . Note: It is assumed that Non-targeting controls do not interact with any other genes . σ f = standard deviation of the log 10 of the initial frequency distribution of the SKO gene % heg = % of high-efficacy guides Cell Doubling Time via Bottleneck specification: n b = size: a threshold that indicates the ceiling of cell growth. Once the colony exceeds this number, it reaches a bottleneck. At this point, the colony is split to reduce the cell number. n e = # of encounters: # of times that the colony of cells will be allowed to pass the threshold n b and then reduced by splitting it. Note: Both n b and n e are designed to control the cell doubling time. To simplify the computational complexity, we set n b to an integer that indicates how many times it is relative to the initial library size, and users can increase the cell doubling time by increasing either n b or n e as desired to implement more simulated cell passage procedures . λ = Multiplicity of infection ( moi ): the % of cells that are transfected by any virus, built upon the following assumptions : Follows a Poisson process during transfection λ < 0.5 and only select cells with single transfection occurrence: Based on users’ inputs, the following cell library parameters are further calculated: n c = # of unique constructs For example, if n g = 2, two guides are targeting each gene. Denoting a and b as the two guides targeting gene 1, gene 1 yields two constructs 1, a and 1, b . Denoting c and d as the guides targeting gene 2, the gene pair 1;2 yields 4 constructs: (1) 1, a ;2, c , (2) 1, a ;2, d , (3) 1, b ;2, c and (4) 1, b ;2, d . The “,” separates the gene from the guide targeting it, and the “;” separates the genes. The first term in the expression above is the number of constructs with 2 genes, while the second term is the number of constructs with one gene. L 0 = Initial library size: # of cells before transfection at baseline. : = n c × CC is the average number of cells per construct. n comb = # of combinatorial genes for both SKO and DKO. n r = Resampling Size: # of cells to sample (without replacement) once a bottleneck has been reached. C pseudo = pseudo-count: a constant added to the relative frequency of the constructs at both the initial timepoint t 0 and later timepoint t 2 to avoid − ∞ when calculating log fold change is the integer less than or equal to a . Simulation System Design II: Cell Population Transfection and Selection Independent Viral Transduction and Replications Typically, in CRISPR experiments, the biological experimental replicates start in library cloning and lentivirus production[ 4 ], or after the lentiviral library infection[ 25 ]. Building upon the assumptions of independent viral transduction in the cell library, we treated the initialized S KO and DKO genes as the plasmid (pDNA) in the simulation model with guide-efficacy designs. As such, two independent sets of the initialized cell library containing both KO genes and targeting guides following the methods specified in the Guides Initialization Section are constructed for cell population transduction, transfection, and selection, where each set of the initialized library is named as replicate A (repA) and replicate B (repB), respectively. Two simulated replications, RepA and RepB , are set at the stage of cell library initialization: for each simulation run, given the same sets of initialized SKO(k) and DKO(k 1 ;k 2 ), we set up two cell libraries with guides: 1. Cell library repA containing SKO A ( k,j ) and DKO A ( k 1 , j 1 ; k 2 , j 2 ) 2. Cell library repB containing SKO B ( k,j ) and DKO B ( k 1 , j 1 ; k 2 , j 2 ) We implemented independent cell population transfection and selection on both. We mainly calculated Pearson’s Correlation r between the relative frequency of the constructs and the LFC by replicates at each timepoint to measure the reproducibility of the simulated experiments. The primary purpose of designing two replicates was to demonstrate the reproducibility in our CRISPR experimental simulations, and to align with practical laboratory designs that often incorporate at least two biological replicates for a complete screening. LFC Z-Standardization To compare the LFC on the same scales across different simulated designs, based on , we aggregated LFC from (15) in both replicates by means. Additionally, by adopting ideas from LFC Z-score [ 26 ] and gene Zscore [ 27 ] ), for each construct i , we incorporated the z-standardized Log2 Fold-Change (zLFC) at t 2 vs. t 0 by where μ control and σ control are the mean and standard deviation of the LFC values among the constructs in the control group ( i . e ., the control group contains sets of SKO ( k,j ) and DKO ( k 1 , j 1 ; k 2 , j 2 ) where k,k 1 , k 2 are all Non-Targeting Controls), given by the following: where r ∈ control group and R is the total number of unique constructs in the control group. Experimental Procedure Tracking To track the transfection and selection progress throughout the simulation stages for iterations and bottleneck encounters, we created a log files to dynamically collect all information during the sampling and cell growth procedure, including the following entities: simulation sample name, replication, timestamp of starting and completing execution, counters of iterations (cell doubling cycles), and counters of encountered bottlenecks. Simulation System Design III: Optimization and Utility To reduce the computational cost of the simulation, we further optimized our schematic designs of the system by vectorization and parallel computing. Optimization To fully accelerate the simulations, we optimized the cell library construction, cell population transfection, and selections as follows: Vectorized the row-wise processing of the cell library Defined the matrix M p that stores the cell division probabilities Vectorized the cell counts computation for each construct from multinouli growth functions by (4) along the sequence of the cell library entities with its corresponding in M p Utility For utility designs, we wrapped up the methods and simulations into four main functions as follows: initialize_gene_cell_lib0(): Cell Library Initialization on SKO ( k ), DKO ( k 1 ; k 2 ) and . initialize_guide_cell_lib0(): Cell Library Initialization on , and . define_phenotype_gi(): Cell Division Probability Vectors Calculations on run_replicate(): Cell Population Transfection and Selection Simulation on two replicates. We practically ran the simulations by utilizing the written functions in standard stepwise pipelines. Parallel Computing in High-Performance Computing We additionally employed parallel computing to utilize the high-performance computing cluster resources, as shown below: Parallel cell library initialization on two replicates using initialize_gene_cell_lib0(). Parallel computation of . using define_phenotype_gi(). Parallel simulation of cell population transfection and selection process in two replicate cell libraries using run_replicate(). For this, we requested 40 cores with 256G RAM memory, with a total runtime of 240 hours allotted for the parallel computing nodes. The runtime is tracked in units of hours, and we collected it by the end of each simulation. Algorithmic Designs: Monte-Carlo Simulation on Large Scales Simulation Steps We summarized the practical computational workflow of our simulation design to DKOsim on large scales as follows ( S5 Fig ): Set up initial parameters Defined main functions Initialized the theoretical phenotypes for the 1st and 2nd target genes and , correspondingly Initialized the interaction index among all gene pairs from pre-specified genes Initialized SKO ( k ) and DKO ( k 1 ; k 2 ) Initialized guides that target the 1st and 2nd genes j 1 and j 2 with type and efficiency Initialized the cell library with constructs containing all pre-specified genes and guides SKO ( k,j ) and DKO ( k 1 , j 1 ; k 2 , j 2 ) Calculated cell division probability vectors and genetic interaction π Defined the cell population transfection and selection, including cell growth by p y ′ and sub-sampling from a hypergeometric distribution using equation (13) Utilized compiled functions to run simulations in two replicates to store the simulated data S1 Fig. Overview of Double-CRISPR Knockout Simulation Schematic Workflow. S2 Fig. AUC-PR for all Negative GIs on asymptotic runs of dLFC identifications . Delta log fold-change (dLFC) is applied to simulations to measure the genetic interaction (GI) scores. Simulated GIs are restricted to negative values for calculating AUC-PR. Line plots show the changes of AUC-PR for all simulated negative GIs on asymptotic runs of: (A) Coverage; (B) Percentage of high-efficacy guides effects; (C) GI Magnitude; (D) Confidence level for initial counts dispersion (%); (E) Number of guides per gene. S1 Table. Toy example: Single Gene KO parameters . S2 Table. Toy example: Single & Double KO Genes Initialization. S3 Table. Toy Example: Initial Cell Library . S4 Table. Summary Table for Fong 2024 Data Characteristics . S1 Data. Statistics of DKOsim Systematic Runs . (XLSX) S2 Data. DKOsim Run 95 (Systematic Run - Baseline) data with dLFC scores . (CSV) S3 Data. DKOsim Run 139 (mimicking Fong 2024) data with dLFC scores . 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Share Double-CRISPR Knockout Simulation (DKOsim): A Monte-Carlo Randomization System to Model Cell Growth Behavior and Infer the Optimal Library Design for Growth-Based Double Knockout Screens Yue Gu , Traver Hart , Luis Leon-Novelo , John Paul Shen bioRxiv 2025.09.11.675497; doi: https://doi.org/10.1101/2025.09.11.675497 Share This Article: Copy Citation Tools Double-CRISPR Knockout Simulation (DKOsim): A Monte-Carlo Randomization System to Model Cell Growth Behavior and Infer the Optimal Library Design for Growth-Based Double Knockout Screens Yue Gu , Traver Hart , Luis Leon-Novelo , John Paul Shen bioRxiv 2025.09.11.675497; doi: https://doi.org/10.1101/2025.09.11.675497 Citation Manager Formats BibTeX Bookends EasyBib EndNote (tagged) EndNote 8 (xml) Medlars Mendeley Papers RefWorks Tagged Ref Manager RIS Zotero Tweet Widget Facebook Like Google Plus One Subject Area Systems Biology Subject Areas All Articles Animal Behavior and Cognition (7635) Biochemistry (17691) Bioengineering (13892) Bioinformatics (41937) Biophysics (21452) Cancer Biology (18588) Cell Biology (25504) Clinical Trials (138) Developmental Biology (13378) Ecology (19899) Epidemiology (2067) Evolutionary Biology (24320) Genetics (15609) Genomics (22506) Immunology (17736) Microbiology (40394) Molecular Biology (17181) Neuroscience (88605) Paleontology (666) Pathology (2832) Pharmacology and Toxicology (4824) Physiology (7641) Plant Biology (15156) Scientific Communication and Education (2045) Synthetic Biology (4294) Systems Biology (9825) Zoology (2271)