EP4721067A1 - Method for quantifying interactions between constituents of a biomolecular system - Google Patents

Abstract

According to a first aspect of the disclosure, there is provided a computer implemented method of quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: receiving input data, the input data comprising data describing the bio- molecular system in a plurality of different conditions, differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio-molecular system, wherein for each of the different conditions, the input data comprises data describing the at least two parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase; determining, based on the input data, a concentration boundary between a first set of data substantially comprising data for which the concentration of the first constituent in the first phase is above a threshold value, and a second set of data substantially comprising data for which the concentration of the first constituent in the first phase is below the threshold value; determining a gradient of the concentration boundary for the concentration of the first constituent with respect to at least one other of the at least two parameters, wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that forms part of a third set of data substantially comprising data for conditions in which both the first and second phases are present; and determining, based on the gradient, a stoichiometric parameter quantifying interactions between constituents of the bio-molecular system.

Description

METHOD The work leading to this invention has received funding from the European Research &RXQFLO^XQGHU^WKH^(XURSHDQ^8QLRQ¶V^6HYHQWK^)UDPHZRUN^3URJUDPPH^^)3^^^^^^-2013) / ERC grant agreement no 337969. TECHNICAL FIELD The present disclosure relates to methods of quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases, in certain conditions. In an example, the first and second phases are respectively a dilute phase and a dense phase. BACKGROUND ART Bio-molecular phase separation (e.g. liquid-liquid phase separation (LLPS)) has emerged as an important process in cellular physiology. Many examples have been found where the formation of liquid-like, protein- and/or RNA-rich droplets serves physiological functions in cells or is implicated in neurodegenerative diseases. Liquid-liquid phase separation (LLPS), the spontaneous de-mixing of macromolecular solutions (e.g. macromolecular polymer solutions such as proteins, peptides, and nucleic acids) into coexisting dense and dilute phases, has become the subject of intense interest due to the newly-realised importance of this process in regulating biological function. For example, phase-separated protein (e.g. biomolecular protein) condensates discretise and organise cellular space, and act as microreactors by localising biomolecules. Condensates are crucial to a diverse range of elementary biochemical processes, including regulation of transcription, translation, the modulation of cellular stress responses. They are also heavily implicated in protein misfolding diseases, including motor neuron disease as well as cancer pathogenesis, making them an attractive target for therapeutic intervention. Experimentally, the phase-separating bio-molecule (e.g. a protein) is typically tagged by a florescent marker (e.g. a dye), based on which its concentration can be measured. This provides 1-D picture of the phase separating behaviour of the system. However, this is an over-simplification as many more solute dimensions are ignored - possible examples include pH, ionic strength, and buffer - for the perfectly reasonable excuse that it is near impossible to determine all of their concentrations in and out of condensates. As a result, important mechanistic information can be lost. The multi-dimensional nature of phase- separating systems makes it difficult to construct a faithful representation of the phase separation behaviour of the system from experimental data. At present, experimental data obtained by varying a small number of dimensions of a phase-separating system, e.g. only two or three dimensions, has been used to estimate how the phase separation behaviours, e.g. the position of the phase boundary, is influenced by certain changes in system conditions. However, it has been exceptionally difficult to obtain information regarding the bio-molecular interactions by which the phase separation behaviour is influenced. It is an aim of the present disclosure to at least partially address some of the above problems. SUMMARY OF THE INVENTION According to a first aspect of the disclosure, there is provided a computer implemented method of quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: receiving input data, the input data comprising data describing the bio- molecular system in a plurality of different conditions, differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio-molecular system, wherein for each of the different conditions, the input data comprises data describing the at least two parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase; determining, based on the input data, a concentration boundary between a first set of data substantially comprising data for which the concentration of the first constituent in the first phase is above a threshold value, and a second set of data substantially comprising data for which the concentration of the first constituent in the first phase is below the threshold value; determining a gradient of the concentration boundary for the concentration of the first constituent with respect to at least one other of the at least two parameters, wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that forms part of a third set of data substantially comprising data for conditions in which both the first and second phases are present; and determining, based on the gradient, a stoichiometric parameter quantifying interactions between constituents of the bio-molecular system. Optionally, the input data is obtained by: obtaining preparations of the bio-molecular system respectively in the plurality of conditions; determining, for each of the preparations of the bio-molecular system respectively in the plurality of conditions, data relating to the respective parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase. According to a second aspect of the disclosure, there is provided a method of quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: obtaining preparations of the bio-molecular system in a plurality of different conditions differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio-molecular system; determining, for each of the preparations of the bio-molecular system respectively in the plurality of conditions, data relating to the at least two parameters respectively, and a concentration of at least a first of the at least one constituents in the first phase and/or the second phase; preparing input data, the input data comprising data describing the bio- molecular system in the plurality of conditions, wherein for each of the different conditions, the input data comprises data describing the at least two parameters respectively, and the concentration of at least the first of the at least one constituents in the first phase and/or the second phase; a computer receiving the input data and performing the steps of: determining, based on the input data, a concentration boundary between a first set of data substantially comprising data for conditions in which the concentration of the first constituent in the first phase is above a threshold value, and a second set of data substantially comprising data for conditions in which the concentration of the first constituent in the first phase is below the threshold value; determining, a gradient of the concentration boundary for the concentration of the first constituent with respect to at least one other of the at least two parameters, wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that forms part of a third set of data substantially comprising data for conditions in which both the first and second phases are present; and determining, based on the gradient, a stoichiometric parameter quantifying interactions between constituents of the bio-molecular system. Optionally, the at least two parameters of the input data comprise the concentration of at least two constituent bio-molecules within the bio-molecular system. Optionally, the method of either aspect further comprises: determining, based on the input data, a phase boundary between the third set of data substantially comprising data for conditions in which both the first and second phases are present, and a fourth set of data substantially comprising data for conditions in which only the first phase is present, wherein the third set of data is defined by the determined phase boundary; wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that is on the side of the phase boundary corresponding to the presence of both the first and second phases. Optionally, the phase boundary is determined based on the data describing the concentration of at least the first of the at least two constituents in the first phase and/or the second phase. Optionally, the phase boundary is determined by: identifying a plurality of subsets of the input data, each subset comprising data for which the concentration of the first constituent varies and the other of the at least two parameters respectively have a substantially constant value, wherein the respective substantially constant value is different for each subset; for each subset, determining a portion of the phase boundary to correspond to the total concentration of the first parameter at which a ratio between the concentration of the first constituent in the first phase and/or the second phase and the total concentration of the first constituent substantially deviates from a constant value; determining the phase boundary by combining respective portions of the phase boundary for each subset. Optionally, the gradient corresponds to a portion of the concentration boundary close to an intersection with the phase boundary, preferably substantially at the intersection with the phase boundary. Optionally, the threshold value concentration of the first constituent is selected such that a tangent to the phase boundary at the threshold value, for the concentration of the first constituent with respect to the at least one other of the at least two parameters, is substantially parallel to line connecting data for which the at least one of the other constituents is constant. Optionally, a plurality of different concentration boundaries are determined, corresponding to different threshold values, and a respective plurality of gradients are determined, and a plurality of respective stoichiometric parameters are determined, and/or a stoichiometric parameter is determined based on a combination of the plurality of gradients corresponding to different threshold values. Optionally, a plurality of different gradients are determined, corresponding to different sets of input data, wherein the different sets of input data differ in the concentrations of at least one further constituent that is not one of the at least one constituents, and a plurality of respective stoichiometric parameters are determined, and/or the stoichiometric parameter is determined based on a combination of the plurality of gradients corresponding to different sets of input data. Optionally, the preparations of the bio-molecular system to have the plurality of conditions are prepared by forming the preparations of the bio-molecular system in a microfluidics device configured to systematically vary the concentrations of the at least two parameters. Optionally, the parameters are determined based on imaging of the preparations of the bio- molecular system. Optionally, the imaging is fluorescence imaging comprising fluorescence tagging of the at least one constituents. Optionally, parameters relating to the concentrations of the at least one constituents are determined based on the amplitude of fluorescence corresponding to the respective constituents. Optionally, parameters relating to the concentration of constituents in the first phase and/or the second phase are determined by analysing images of the preparations of the bio- molecular system to identify regions corresponding to the first phase and/or the second phase and determining the amplitude of fluorescence corresponding the respective constituents in the respective regions. Optionally, the at least one constituent bio-molecules consist of two constituent bio- molecules. Optionally, the first phase is a dilute phase and the second phase is a dense phase. According to third aspect of the disclosure, there is provided a method of identifying a potential drug target, comprising applying the method of any preceding aspect. Optionally, the potential drug target is one of the at least one constituents of the bio- molecular system. Optionally, when a plurality of different gradients are determined, corresponding to different sets of input data, wherein the different sets of input data differ in the concentrations of at least one further constituent that is not one of the at least one constituents, the potential drug target is the at least one further constituent that is not one of the at least one constituents. Optionally, the potential drug target is identified based on whether the stoichiometric parameter satisfies one or more predefined conditions. According to a fourth aspect of the disclosure, there is provided a method of identifying potential therapeutic agent targeting a drug target, comprising applying the method of the first or second aspects. Optionally, the therapeutic agent is one of the at least one constituents of the bio-molecular system. Optionally, the drug target is one of the at least one constituents of the bio-molecular system. Optionally, when a plurality of different gradients are determined, corresponding to different sets of input data, wherein the different sets of input data differ in the concentrations of at least one further constituent that is not one of the at least one constituents, the potential drug target is the at least one further constituent that is not one of the at least one constituents. Optionally, the potential therapeutic agent is identified based on whether the stoichiometric parameter satisfies one or more predefined conditions. According to a fifth aspect of the disclosure, there is provided a computer implemented method of estimating a phase boundary for a bio-molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: receiving input data, the input data comprising data describing the bio-molecular system in a plurality of different conditions, differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio- molecular system, wherein for each of the different conditions, the input data comprises data describing the at least two parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase; determining, based on the input data, a phase boundary between a third set of data substantially comprising data for conditions in which both the first and second phases are present, and a fourth set of data substantially comprising data for conditions in which only the first phase is present, wherein the third set of data is defined by the determined phase boundary; identifying a plurality of subsets of the input data, each subset comprising data for which the concentration of the first constituent varies and the other of the at least two parameters respectively have a substantially constant value, wherein the respective substantially constant value is different for each subset; for each subset, determining a portion of the phase boundary to correspond to the total concentration of the first parameter at which a ratio between the concentration of the first constituent in the first phase and/or the second phase and the total concentration of the first constituent substantially deviates from a constant value; determining the phase boundary by combining respective portions of the phase boundary for each subset. According to a sixth aspect of the disclosure, there is provided a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of any one of the first, second or fifth aspects. According to a seventh aspect of the disclosure, there is provided a data processing system comprising means for carrying out the method of any one of the first, second or fifth aspects. According to an eight aspect of the disclosure, there is provided a computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the method of any one of the first, second or fifth aspects. BRIEF DESCRIPTION OF THE DRAWINGS Further features of the disclosure will be described below, by way of non-limiting examples and with reference to the accompanying drawings, in which: Fig. 1 illustratively shows a higher-dimensional phase space structure; Fig. 2 illustratively shows how two-dimensional data can be used to probe higher- dimensional phase space; Fig. 3 illustratively shows a small region on a higher-dimensional phase boundary; Fig. 4 shows stoichiometric parameters obtained from two-dimensional experimental data obtained from a high-dimensional bio-molecular system; Fig. 5 shows data for determining a phase boundary; Fig. 6 shows the phase boundary obtained based on the data in Fig. 5; Fig. 7 shows stoichiometric parameters obtained from two-dimensional experimental data obtained from a further bio-molecular system; and Fig. 8 shows stoichiometric parameters obtained from two-dimensional experimental data obtained from a further bio-molecular system. DETAILED DESCRIPTION The present disclosure relates to methods for quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases, in certain conditions. For example, the methods may be for measuring stoichiometric parameters quantifying interactions between constituents of a bio-molecular system. The first and second phases may respectively be a dilute phase and a dense phase, for example. The bio-molecular system may comprise a plurality of bio-molecular species in solution. In a solution of N molecular species, the phase space is characterised by an N-D coordinate ^^ ^ ^ ^^_^ǡ ǥ ǡ ^_ே^, with each ^_ఈ denoting the concentration of solute Į, for Į = 1, 2, «^^1^^ energy density ^ is written as ^^ ൌ ^^^^^, and chemical potentials and the osmotic pressure are defined as ^_ఈ^^^ ^^ ^^^^^^Ȁ^^_ఈ and ^^^^ ^^ ே Binary phase separation occurs when a pair of distinct points ^^ିand ^^ା exist that satisfy ^_ఈ^^^ି^ ^ൌ ^ ^_ఈ^^^ା^ and ^^^^ି^ ^ൌ ^^^^^ା^^(as shown in Fig. 1). ^^ି and ^^ା represent molecular compositions of the dilute and dense phases, and the tie line corresponding to this configuration is naturally characterised by the vector ^^ ^ ^^^ା ^െ ^^ିǤ Denoting the volume fraction of the dense phase as v with 0 < v < 1, the point ^^ି ^^ ^^^ then represents the average molecular composition of a system on this tie line. Due to the smooth nature of the free energy density, a set of such dilute and dense point pairs can be found and the dimensionality of this set can be worked out by counting number of equations and unknowns. The chemical potentials and osmotic pressure yield N+1 equations and the point pair introduces 2N degrees of freedom, so the total dimensionality of the solution set is 2N í (N+1) = 1í^^^L^H^^LW^LV^DQ^^1í^^-D manifold in the N-D space. We use the symbol T to represent DQ^^1^í^^-D variable that formally parameterise this manifold to facilitate discussions below. The binary phase separation assumption requires that only point pairs ^^േ^^^ can be found, instead of for example a triplet of points, and this ensures the tie lines generated do not cross each other. This fact can also be elucidated on dimensionality ground: instead of using ^ to characterise a point in the phase-separated region, we can use WKH^^1^í^^-D parameter T and volume fraction v. T specifies the tie line the system is on and v specifies the distance between the system and the dilute phase on the OLQH^^7KH^^1^í^^-D surfaces ^^േ^^^ meet each other DW^DQ^^1í^^-D surface that corresponds to the intersection between the binodal and spinodal boundaries, ZKHUH^WKH^VSLQRGDO^UHJLRQ^LV^ERXQG^E\^DQ^^1^í^^^-D surface defined by the condition డ^మ^ ^^^ ൬ డథ_^డథ_^ ^ ൌ ^. The second equation that characterises this intersection is డ^మ^ ^డమ^ ^^ ή સ ൬ డ ^ where V is the eigenvector of డథ_^డథ_^ corresponding to an eigenvalue of Fig. 1 illustratively shows a higher-dimensional phase space structure. The full phase space is characterised by the N-D coordinate ^ and comprises the dilute phase surface ^^ି^^^, the dense phase surface ^^ା^^^, and tie lines connecting point pairs on these surfaces (black and grey solid lines). The N-D space cannot be efficiently characterised by experiments. However, part of this N-D space can be probed by varying two of the molecular species, while keeping the others constant, thus reducing the high-dimensional space to a 2-D plane. This corresponds to concentrations of two solutes, and ^_ଶ, being varied while keeping ^i constant with i = 3, 4, «^ N. Therefore, the convention that the index i runs from 3 to N can be followed hereafter. This may also be generalised to varying parameters describing conditions other than constituent concentrations, such as temperature. According to the method of the disclosure, data may be obtained that describes the bio-molecular system in a plurality of different conditions, differing in at least two parameters. The parameters may include the concentration of at least one constituent bio-molecule within the bio-molecular system. In certain examples, the parameters may further comprise the concentration of at least one further constituent (i.e. the parameters may comprise the concentrations of at least two constituent bio-molecules). In other examples, the parameters may comprise at least one parameter that is not a concentration of a constituent, such as temperature of the system. For each of the different conditions, the obtained data comprises data describing the values of the at least two parameters. Optionally, the obtained data may comprise data describing the presence or absence of the first phase and/or second phase. Fig. 2 shows how 2-D experimental data coupled to dilute phase concentration measurement probes high-dimensional space. The top and middle panels show illustrations of the full phase space and corresponding 2-D experimental plane. The bottom panels show experimental data. From left to right: (A) shows the experimental plane intersects the full phase boundary to produce a 2-D phase boundary (dark red solid line); (B) shows sectioning the homogeneous space according to ^₁; (C) shows sectioning the phase- separated space according to dilute phase ^₁; (D) shows multiple sectioning of the same space. Alternating shades are assigned to the bands in (D) to better visualise the data. Denoting the pre-set ^_^ values as ^_^, this is equivalent to generating a set of points on the plane ^_^ ൌ ^^_^^and by a suitable choice of experimental conditions, some of the points will fall into the phase-separated region and some non-phase-separated region. A binary classification is possible via image analysis to distinguish phase-separated samples from homogeneous ones, leading to a phase boundary in this 2-D plane. This procedure is equivalent to taking a 2-D cross-VHFWLRQ^RI^WKH^^1^í^^^-D phase boundary (as shown in Fig. 2A). Although the experimental data provides an accurate description of the phase boundary at the chosen cross-section, the boundary alone contains very limited information on interactions between molecular species as opposite interactions can give rise to visually similar boundaries. To better characterise the phase space, dilute phase concentration measurement of one of the solutes, ^_^, are taken and to provide further insight into the higher-dimensional space. According to the method of the disclosure, the obtained data describing the bio-molecular system in the different conditions may further comprise the concentration of at least a first of the at least one constituent in the first phase and/or the second phase, e.g. the dilute phase. Data points on the 2-D experimental plane are grouped by comparing their dilute concentration to a threshold value ^_^, and the boundary formed between them may be examined. According to the method of the disclosure, a concentration boundary between a first set of data substantially comprising data for which the concentration of the first constituent in the first phase is above a threshold value, and a second set of data substantially comprising data for which the concentration of the first constituent in the first phase is below the threshold value, may be determined. The concentration boundary may be determined by known mathematical methods such as regression. In the homogeneous region, in which the dense phase does not form, since the dilute phase concentration is equivalent to the total concentration, the newly introduced concentration boundary is perpendicular to the ^_^ axis as the grouping simply sections the phase space with the plane ^_^ ൌ ^^_^ (as shown in Fig. 2B). At the phase boundary, the ^_^ ൌ ^^_^ plane intersects the phase -D sub-boundary (yellow solid lines in Fig. 2) and this is in general curved. The sub-boundary intersects the experimental plane at a single point (0-D), and denoting its ^_ଶ coordinate as ^_ଶ this SRLQW^LV^UHIHUUHG^WR^DV^ʌ^LQ^ ensuing discussions. In the phase-separated region, since the dilute phase concentration is no longer the same as the total concentration, sectioning of phase-separated data points is non-trivial. For each of these data points, the dilute phase ^_^ can be worked out by tracing a point with coordinate ^ back to the ^^ି^^^ surface along the tie line that it lies on, so sectioning the phase- separated space requires extending the sub-boundary into this space along tie lines. The GLPHQVLRQDOLW\^RI^WKLV^H[WUXGHG^VXUIDFH^LV^^1^í^^^^^^^^ ^^1^í^^^^^ZLWK^^1^í^^^^WKH^ dimension of the sub-ERXQGDU\^DQG^WKDW^RI^WKH^WLH^OLQH^VHW^^7KLV^^1^í^^^-D surface intersects the 2-D experimental plane to produce a 1-D line boundary as a continuation of the trivial line boundary in the homogeneous space (as shown in Fig. 2C). It is worth noting that band boundaries in the phase-separated region are not straight due to the curved nature of the full phase boundary even if tie lines are parallel to each other. This procedure can be repeated for different ^_^ values to create bands in the 2D plane (as shown in Fig. 2D). Fig. 3 illustratively shows a small region on a higher-dimensional phase boundary. In a small region around ʌ, is approximately flat with surface normal ^ and the tie lines are parallel to one another with the same direction vector k. Denoting points on ^^ି^^^ around ʌ as ^ ^ ^^, they satisfy: If moving along the ^^^ ʌ^^SODQH^^WKHQ 7KLV^SURGXFHV^WKH^^1í^^-D sub-boundary as before with 2 equations satiVILHG^E\^įʌ^^^7R^ extend the sub-boundary a 2-D experimental plane, points on it can be denoted as ^ with: and if ^ LV^DOVR^RQ^D^WLH^OLQH^H[WHQGHG^IURP^WKH^SRLQW^ʌ^įʌ^^WKHQ^ The above [1 + 1 + (N í 2) + N] = 2N equations [Eq. (1) to Eq. (4)] are satisfied by the (^1^^^^XQNQRZQV^įʌ, ^ and v, leaving 1 degree of freedom in the system. For index 1, using Eq. (2) and Eq. (4) we have Next, combining Eq. (3) and Eq. (4) gives ^^_^ ൌ ^െ^^^_^ and ^^_ଶ ^ൌ ^_ଶ െ^^_ଶ െ ^^_ଶ. Substituting these into Eq. (1) and differentiating gives: so that the first term in K is the ^ ଶ : stoichiometry, and the rest is a weighted average of all other k_i¶V, with responses of the boundary in the n-th direction relative to the 2 direction as weights. In the case of N = 2 we simply have K= k₂/k₁, as expected. According to the method of the disclosure, based on the input data, a gradient of the concentration boundary for the concentration of the first constituent with respect to at least one other parameter may be determined. Preferably, the at least one other parameter is a concentration of a second constituent. Specifically, the gradient may correspond to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that forms part of a third set of data substantially comprising data for conditions in which both the first and second phases are present. Based on the gradient, a stoichiometric parameter quantifying interactions between constituents of the bio- molecular system can be determined. Data processing steps of the method may be executed by a computer, or computer system. The stoichiometric parameter may be output by the method. For example, the parameter may be output to be stored on a data storage medium and/or displayed on a user interface of the computer. Further, based on the input data, a phase boundary between the third set of data substantially comprising data for conditions in which both the first and second phases are present, and a fourth set of data substantially comprising data for conditions in which only the first phase is present may be determined. Specifically, the gradient may correspond to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that is on the side of the phase boundary corresponding to the presence of both the first and second phases. Preferably, the determined gradient corresponds to a portion of the concentration boundary close to an intersection with the phase boundary. Preferably still, the determined gradient is substantially at the intersection with the determined phase boundary. According to the method of the disclosure, the phase boundary may be determined based on the data describing the concentration of at least the first of the at least two constituents in the first phase and/or the second phase. For example, the phase boundary may be determined by identifying a plurality of subsets of the input data, each subset comprising data for which the concentration of the first constituent varies but the other of the at least two parameters respectively have a substantially constant value. The substantially constant value is different for each subset. The substantially constant value may lie within a range centred on a specific value, wherein the range is less than around 10% of the total range of the input data for a given parameter. For each subset, a portion of the phase boundary, corresponding to the substantially constant values of the other of the at least two parameters, is determined to correspond to the total concentration of the first parameter, at which a ratio between the concentration of the first constituent in the first phase and/or the second phase and the total concentration of the first constituent substantially deviates from a constant value. This may be determined as the kink point of a kinked linear fit of the data. Given a dataset with protein dilute phase concentration measurement c_dil and other arbitrary axes, the data may be sectioned into groups where only the total protein concentration is being varied. For instance, in a 2D protein-RNA system (Fig. 5a), a slice of the data is taken around a fixed RNA concentration (Fig. 5b - D^VHFWLRQ^RI^GDWD^DW^51$§^ 75 is highlighted) and the dilute vs. total protein concentration is plotted for these points (Fig. 5c). For each data section, a kinked linear fit is used to extract the saturation concentration c_sat as well as the homotypic response R. The functional form is where A is an unimportant normalisation factor. In Fig, 5c, the onset of phase separation is manifested as the point where the plot starts to deviate from a straight line (black arrow), and the solid black line is a kinked linear fit. By combining the estimated c_sat from many sections together, the phase boundary in the 2D plane can be calculated. The calculated phase boundary shows the same general trend as that obtained from image- based condensate detection (Fig. 6). Fig. 6 shows comparison of two ways of estimating the phase boundary. The black solid line is the phase boundary estimated from the kinked linear fit with grey shaded region indicating standard deviation from 10 repeats of the fitting with 50% dropout. Scatter points are experimental data, with red and blue indicating the presence and absence of condensates respectively. The phase boundary may be determined by known mathematical methods, such as regression, based on the data describing the presence or absence of the first phase and/or second phase for each of the different conditions. According to the method of the disclosure, a plurality of different concentration boundaries may be determined, corresponding to different threshold values, and a respective plurality of gradients may be determined. A plurality of respective stoichiometric parameters may be determined, and/or a stoichiometric parameter may be determined based on a combination of the plurality of gradients corresponding to different threshold values. For example, the stoichiometric parameter may be an average of two or more gradients, or a ratio or difference between two gradients. Eq. (7) explains why the dilute phase bands have varying gradients across the experimental 2-D plane. At different points on the 2-D phase boundary, the true N-D boundary has different ^ so even if k is constant the band gradient will still change. An interesting region is where the 2D boundary is parallel to the ^₁ direction and ^₂ assumes a very large value. In this limit, only the first term in Eq. (7) survives. In this case .^§ k₂/k₁ and as a result, effect from other components become negligible and any change in K will almost surely come from k₂/k₁. On the other hand, when the boundary is almost parallel to the ^₂ direction, ^₂ becomes small and almost surely K § ^^ This result then gives clear guidance as to which part of the phase diagram should be probed in order to gain more accurate insight on the interaction between the two specific molecular species characterised by ^₁ and ^₂. According to the method of the disclosure, the threshold value concentration of the first constituent may be selected such that a tangent to the phase boundary at the threshold value, for the concentration of the first constituent with respect to the other parameters, is substantially parallel to line connecting data for which the other parameters is constant. The at least one constituent whose concentration is varied is preferably a polymer and more preferably comprises one or more of a protein and a nucleic acid. The bio-molecular system may be part of a cell, subcellular organelle (e.g. nuclei or mitochondria) or cell lysate in some examples. Further constituents may comprise one or more of: a pH buffer, a phase separator, a salt solution, cells, cell lysates and a therapeutic drug/drug candidate. As described further below, some or all of the constituents (e.g. constituents of interest whose relative concentrations are to be measured) may additionally (to the above described components) comprise an optical marker (also referred to as a ³EDUFRGH´^^^^$^S+^EXIIHU^ may not be optically marked. Phase separators may include crowding agents (polymers of biological and non-biological origin, e.g. PEG and dextran), proteins, nucleic acids, different salts, or small molecules that induce phase separation. The therapeutic drug/drug candidate may be a small molecule or biologic, including but not limited to protein, nucleic acid, lipid, peptide, or antibody. As an example, experimental data for the well-established phase-separating system involving the protein G3BP1 and poly(A) RNA was obtained, the concentrations of G3BP1 and poly(A) RNA representing the two varied parameters (see bottom row of Fig. 2). G3BP1 is a 60kDa, RNA-binding protein involved in stress granule formation, and experiments are performed with 80mMKCl in 20mM PIPES buffer at pH 7.2. Experimentally, since the G3BP1-RNA phase boundary is parallel to the G3BP1 axis at the high-G3BP1 regime, the initial gradient of the band boundaries should give good approximations of the G3BP1:RNA stoichiometry. Indeed, by restricting the analysis to data points close to the vertical boundary, their gradients assume nearly constant values, from which a stoichiometry of RNA:G3BP1 = ^^^^^^QJ^^/^^^0 is determined. According to the method of the disclosure, input data may be obtained in which a further parameter of the biomolecular system is varied, that is not one of the at least two parameters described above. Different sets of input data may be obtained, each set comprising data describing the bio-molecular system in a plurality of different conditions, differing in the at least two parameters, but having a further parameter with a different constant value for each set. According to the method of the disclosure, a plurality of different gradients may be determined, corresponding to the different sets of input data. A plurality of respective stoichiometric parameters may be determined, and/or the stoichiometric parameter may be determined based on a combination of the plurality of gradients corresponding to different sets of input data. For example, the stoichiometric parameter may be an average of two or more gradients, or a ratio or difference between two gradients. Fig. 4 shows experimental data of G3BP1-RNA experiment with increasing amount of DDX3X (left to right). DDX3X dissolves condensates, as seen from the phase boundary (dark red solid line) shifts, while the dilute phase band boundaries (black dashed and solid lines) have the same gradient close to the vertical boundary at high [G3BP1]. Plotted phase boundaries and band boundaries are guides to the eye. Experiments were performed for the G3BP1-RNA system in the presence of two modulators (corresponding to the further parameters described above) that are known to dissolve condensates: DDX3X and suramin. G3BP1 protein is produced from an insect cell line and purified according to previously established protocols [1] and poly(A) RNA is purchased from Sigma, with molecular weight 700-3500 kDa. In the experiments each droplet is first classified based on the presence of condensates, and dilute phase concentrations of the droplets are extracted. Next, droplets are sub-divided into bands according to their dilute phase concentrations. Data can be plotted in a phase diagram with [G3BP1] and [RNA] as the axes, phase-separated points are coloured red and non-phase- separated points are blue. Alternating shades of blue and red are assigned to each dilute phase band and boundaries between these bands correspond to dilute phase cuts as outlined earlier. In the presence of DDX3X (as shown in Fig. 4), the homogeneous blue points form bands that have boundaries perpendicular to the G3BP1 axis, as the dilute phase concentration simply corresponds to total concentration in non-phase-separated droplets. For the phase-separated droplets, it should first be noted that the boundaries are not straight especially close to the re-entrant corner. This curvature is a signature of the multi- dimensional nature of the phase space. Close to the G3BP1 axis, however, the boundary is perpendicular to the RNA axis and thereby the local ^_RNA is very large, and the band boundaries have similar gradients very close to this edge. It is then reasonable to assume gradients of the boundaries are good approximations of the G3BP1-RNA tie line gradient, and further that tie line gradients are constant in the phase space probed. It is interesting to note that at increasing DDX3X concentrations the phase boundary shifts towards higher G3BP1 and RNA concentrations as condensates are dissolved, while the band boundaries have similar initial gradient at high [G3BP1]. This indicates a mostly constant [G3BP1]:[RNA] stoichiometry even at different [DDX3X] (as shown in Fig. 5). On the other hand, suramin also dissolves condensates and the initial gradient of band boundaries changes as suramin is added (as shown in Fig. 5), so the data can be interpreted as suramin having a modulating effect of G3BP1-RNA cross interaction. Figs. 7 and 8 shows further experimental data in the form of phase diagrams, showing the calculated stochiometric parameter in the form of the gradient of the dashed line. Fig. 7 relates to PEG-induced phase separation of beta-catenin modulated by beta-catenin binding factor (BBF) peptide. Left-right, Fig. 7 shows phase diagrams with increasing concentration of BBF. Blue points are homogeneous and red points are phase-separated. A darker shade is assigned to points with dilute phase [BC] > 2uM. The slope of the boundary decreases (dashed lines), indicating a reduction in beta-catenin contribution to phase separation with an increase in BBF concentration. Fig. 8 shows phase diagrams for heterotypic phase separation of beta-catenin with co- factor protein TCF7L2 at constant PEG concentration (3.25%) and increasing concentration of BBF peptide. The slope of dilute phase band boundary (at dilute phase [BC] of 4uM) decreases with BBF, indicating inhibitory effect of BBF on TCF7L2- enhanced beta-catenin phase separation. The stoichiometric parameter(s) may be used in a method of identifying a potential drug target or a potential therapeutic agent targeting a drug target. For example, based on whether the stoichiometric parameter satisfies one or more predefined conditions, a potential drug target or a potential therapeutic agent targeting a drug target may be validated or invalidated, i.e. screened. The potential drug target or potential therapeutic agent, may be one of the at least one constituents of the bio-molecular system that is a varied parameter to which the gradients described above directly relate. Alternatively, the potential drug target or potential therapeutic agent targeting a drug target, may be the at least one further constituent defining the different sets of input data described above. The input data may be obtained by obtaining preparations of the bio-molecular system respectively in the plurality of conditions. Then for each of the preparations of the bio- molecular system respectively in the plurality of conditions, parameters relating to the respective total concentrations of the at least two constituents in the bio-molecular system, the presence or absence of the first phase and/or second phase, and the concentration of at least a first of the at least two constituents in the first phase and/or the second phase, may be determined. For example, the data may be obtained using the methods and devices described in patent publication number WO 2021/234410, which is hereby incorporated in its entirety by reference. Accordingly, the method of obtaining the input data may comprise: generating a stream of micro-droplets, each microdroplet representing a preparation of the bio-molecular system. The method comprises varying the at least two parameters, the parameters including the concentration of the at least one constituent bio-molecule within the bio-molecular system in the micro-droplets, and measuring the relative concentrations of the constituents of, and the phases present in, the micro-droplets. Optionally, the conditions in the micro-droplets are varied by varying the relative concentrations of constituents in the micro-droplets. Alternatively, or additionally, the conditions in the micro-droplets are varied by varying the temperature of the micro- droplets. Optionally the temperature of the micro-droplets is varied by controlling the temperature of a channel in which the micro-droplets flow. Optionally, the stream of micro-droplets is a continuous stream. Optionally, the measuring is performed continuously on the stream of micro-droplets. Optionally, the micro-droplets are collected and measuring is performed on the collected micro-droplets. Optionally, the stream of micro-droplets is generated by injecting a stream of a first fluid comprising the constituents into a stream of a second fluid, the second fluid being immiscible with the first fluid. Optionally, respective streams of constituents of the micro- droplets join to form the stream of the first fluid. Optionally, the relative concentrations of the constituents are varied by varying relative flow rates of the respective streams of the constituents of the micro-droplets. Optionally, the streams flow in channels of a microfluidics system. Optionally, the relative concentrations of the constituents are measured by a first optical means. Optionally, the first optical means illuminates the micro-droplets with illumination light and detects a response. Optionally, the relative concentrations of the constituents are determined based on the respective responses of the constituents to the illumination light. Optionally, each of the constituents responds differently to the illumination light. Optionally, each of the constituents comprises a different fluorophore which emits light of a specific wavelength in response to the illumination light. Optionally, the phases present in the micro-droplets are measured by a second optical means. Optionally, the second optical means obtains images of the micro-droplets and the phases present in the micro-droplets are determined based on characteristics of the image indicative of particular phases. Alternatively, the second optical means obtains a light- scattering profile of the micro-droplets and the phases of the macromolecule present in the micro-droplets are determined based on characteristics of the light scattering profile indicative of particular phases. It should be understood that variations of the above described examples are possible without departing from the spirit or scope of the disclosure. [1]: S. Qamar, G. Z. Wang, S. J. Randle, F. S. Ruggeri, J. A. Varela, J. Q. Lin, E. C. Phillips, A. Miyashita, D. Williams, F. Str• ohl, W. Meadows, R. Ferry, V. J. Dardov, G. G. Tartaglia, L. A. Farrer, G. S. Kaminski Schierle, C. F. Kaminski, C. E. Holt, P. E. Fraser, G. Schmitt-Ulms, D. Klenerman, T. Knowles, M. Vendruscolo, and P. St George-Hyslop, Cell 173, 720 (2018).

Claims

CLAIMS 1. A computer implemented method of quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: receiving input data, the input data comprising data describing the bio-molecular system in a plurality of different conditions, differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio-molecular system, wherein for each of the different conditions, the input data comprises data describing the at least two parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase; determining, based on the input data, a concentration boundary between a first set of data substantially comprising data for which the concentration of the first constituent in the first phase is above a threshold value, and a second set of data substantially comprising data for which the concentration of the first constituent in the first phase is below the threshold value; determining a gradient of the concentration boundary for the concentration of the first constituent with respect to at least one other of the at least two parameters, wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that forms part of a third set of data substantially comprising data for conditions in which both the first and second phases are present; and determining, based on the gradient, a stoichiometric parameter quantifying interactions between constituents of the bio-molecular system.

2. The method of claim 1, wherein the input data is obtained by: obtaining preparations of the bio-molecular system respectively in the plurality of conditions; determining, for each of the preparations of the bio-molecular system respectively in the plurality of conditions, data relating to the respective parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase.

3. A method of quantifying interactions between constituents of a bio-molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: obtaining preparations of the bio-molecular system in a plurality of different conditions differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio-molecular system; determining, for each of the preparations of the bio-molecular system respectively in the plurality of conditions, data relating to the at least two parameters respectively, and a concentration of at least a first of the at least one constituents in the first phase and/or the second phase; preparing input data, the input data comprising data describing the bio-molecular system in the plurality of conditions, wherein for each of the different conditions, the input data comprises data describing the at least two parameters respectively, and the concentration of at least the first of the at least one constituents in the first phase and/or the second phase; a computer receiving the input data and performing the steps of: determining, based on the input data, a concentration boundary between a first set of data substantially comprising data for conditions in which the concentration of the first constituent in the first phase is above a threshold value, and a second set of data substantially comprising data for conditions in which the concentration of the first constituent in the first phase is below the threshold value; determining, a gradient of the concentration boundary for the concentration of the first constituent with respect to at least one other of the at least two parameters, wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that forms part of a third set of data substantially comprising data for conditions in which both the first and second phases are present; and determining, based on the gradient, a stoichiometric parameter quantifying interactions between constituents of the bio-molecular system.

4. The method of any preceding claim, wherein the at least two parameters of the input data comprise the concentration of at least two constituent bio-molecules within the bio-molecular system.

5. The method of any preceding claim, further comprising: determining, based on the input data, a phase boundary between the third set of data substantially comprising data for conditions in which both the first and second phases are present, and a fourth set of data substantially comprising data for conditions in which only the first phase is present, wherein the third set of data is defined by the determined phase boundary; wherein the gradient corresponds to a portion of the concentration boundary corresponding to a subset of the first set of data and the second set of data that is on the side of the phase boundary corresponding to the presence of both the first and second phases.

6. The method of claim 5, wherein the phase boundary is determined based on the data describing the concentration of at least the first of the at least two constituents in the first phase and/or the second phase.

7. The method of claim 6, wherein the phase boundary is determined by: identifying a plurality of subsets of the input data, each subset comprising data for which the concentration of the first constituent varies and the other of the at least two parameters respectively have a substantially constant value, wherein the respective substantially constant value is different for each subset; for each subset, determining a portion of the phase boundary to correspond to the total concentration of the first parameter at which a ratio between the concentration of the first constituent in the first phase and/or the second phase and the total concentration of the first constituent substantially deviates from a constant value; determining the phase boundary by combining respective portions of the phase boundary for each subset.

8. The method of claim 6 or 7, wherein the gradient corresponds to a portion of the concentration boundary close to an intersection with the phase boundary, preferably substantially at the intersection with the phase boundary.

9. The method of claim 6, 7 or 8, wherein the threshold value concentration of the first constituent is selected such that a tangent to the phase boundary at the threshold value, for the concentration of the first constituent with respect to the at least one other of the at least two parameters, is substantially parallel to line connecting data for which the at least one of the other constituents is constant.

10. The method of any preceding claim, wherein a plurality of different concentration boundaries are determined, corresponding to different threshold values, and a respective plurality of gradients are determined, and a plurality of respective stoichiometric parameters are determined, and/or a stoichiometric parameter is determined based on a combination of the plurality of gradients corresponding to different threshold values.

11. The method of any preceding claim, wherein a plurality of different gradients are determined, corresponding to different sets of input data, wherein the different sets of input data differ in the concentrations of at least one further constituent that is not one of the at least one constituents, and a plurality of respective stoichiometric parameters are determined, and/or the stoichiometric parameter is determined based on a combination of the plurality of gradients corresponding to different sets of input data.

12. The method of claim 11, wherein the preparations of the bio-molecular system to have the plurality of conditions are prepared by forming the preparations of the bio- molecular system in a microfluidics device configured to systematically vary the concentrations of the at least two parameters.

13. The method of claim 11 or 12, wherein the parameters are determined based on imaging of the preparations of the bio-molecular system.

14. The method of claim 13, wherein the imaging is fluorescence imaging comprising fluorescence tagging of the at least one constituents.

15. The method of claim 14, wherein parameters relating to the concentrations of the at least one constituents are determined based on the amplitude of fluorescence corresponding to the respective constituents.

16. The method of claim 14 or 15 wherein parameters relating to the concentration of constituents in the first phase and/or the second phase are determined by analysing images of the preparations of the bio-molecular system to identify regions corresponding to the first phase and/or the second phase and determining the amplitude of fluorescence corresponding the respective constituents in the respective regions.

17. The method of any preceding claim, wherein the at least one constituent bio- molecules consist of two constituent bio-molecules.

18. The method of any preceding claim, wherein the first phase is a dilute phase and the second phase is a dense phase.

19. A method of identifying a potential drug target, comprising applying the method of any preceding claim.

20. The method of claim 19, wherein the potential drug target is one of the at least one constituents of the bio-molecular system.

21. The method of claim 19 or 20, when dependent on claim 11 or any other claim dependent thereon, wherein the potential drug target is the at least one further constituent that is not one of the at least one constituents.

22. The method of any one of claims 19 to 21, wherein the potential drug target is identified based on whether the stoichiometric parameter satisfies one or more predefined conditions.

23. A method of identifying potential therapeutic agent targeting a drug target, comprising applying the method of any one of claims 1 to 18.

24. The method of claim 22, wherein the therapeutic agent is one of the at least one constituents of the bio-molecular system.

25. The method of claim 23 or 24, wherein the drug target is one of the at least one constituents of the bio-molecular system.

26. The method of claim 24, when dependent on claim 11 or any other claim dependent thereon, wherein the potential drug target is the at least one further constituent that is not one of the at least one constituents.

27. The method of any one of claims 23 to 26, wherein the potential therapeutic agent is identified based on whether the stoichiometric parameter satisfies one or more predefined conditions.

28. A computer implemented method of estimating a phase boundary for a bio- molecular system that exhibits phase separation into binary first and second phases in certain conditions, comprising: receiving input data, the input data comprising data describing the bio-molecular system in a plurality of different conditions, differing in at least two parameters, the parameters including the concentration of at least one constituent bio-molecule within the bio-molecular system, wherein for each of the different conditions, the input data comprises data describing the at least two parameters, and the concentration of at least a first of the at least one constituents in the first phase and/or the second phase; determining, based on the input data, a phase boundary between a third set of data substantially comprising data for conditions in which both the first and second phases are present, and a fourth set of data substantially comprising data for conditions in which only the first phase is present, wherein the third set of data is defined by the determined phase boundary; identifying a plurality of subsets of the input data, each subset comprising data for which the concentration of the first constituent varies and the other of the at least two parameters respectively have a substantially constant value, wherein the respective substantially constant value is different for each subset; for each subset, determining a portion of the phase boundary to correspond to the total concentration of the first parameter at which a ratio between the concentration of the first constituent in the first phase and/or the second phase and the total concentration of the first constituent substantially deviates from a constant value; determining the phase boundary by combining respective portions of the phase boundary for each subset.

29. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method of any one of claims 1 to 18 or 28.

30. A data processing system comprising means for carrying out the method of any one of claims 1 to 18 or 28.

31. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the method of any one of claims 1 to 18 or 28.