Polymer brush compositions including chain-end-immobilized cofactors and methods for the production thereof

Abstract

A method for immobilizing a target cofactor includes: functionalizing a substrate with an initiator to form a functionalized substrate; preparing a prepolymer mixture comprising a set of monomers configured to bond to the initiator; polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form a polymer brush comprising a set of polymer chains bonded to the functionalized substrate via the initiator and characterized by functionalized chain ends; reacting the target cofactor with a heterobifunctional linker to produce a conjugated cofactor; and exposing the polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains to form a cofactor-functionalized polymer brush.

Description

Polymer Brush Compositions Including Chain-End-Immobilized Cofactors and Methods for theProduction ThereofCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This Application claims the benefit of U.S. Provisional Application No. 63 / 610,615, filed on 15-DEC-2023, which is incorporated in its entirety by this reference.

[0002] This Application is related to U.S. Patent Application No. 18 / 036,678, filed on12-MAY-2023, which is incorporated in its entirety by this reference.

[0003] This Application is related to International Application No. US2024 / 046,711, filed on13 -SEP -2023, which is incorporated in its entirety by this reference.TECHNICAL FIELD

[0004] This invention relates generally to the field of enzyme biochemistry and, more specifically, to new and useful methods for immobilizing cofactors in the field of enzyme biochemistry.BRIEF DESCRIPTION OF THE FIGURES

[0005] FIGURE 1 is a flow chart representation of one variant of a production method for a polymer brush composition.

[0006] FIGURE 2 is a flowchart representation of one variant of the production method of the polymer brush composition;

[0007] FIGURE 3 is a flowchart representation of one variant of the production method of the polymer brush composition

[0008] FIGURE 4 is a schematic representation of one variant of the polymer brush composition

[0009] FIGURE 5 is a schematic representation of one variant of the polymer brush composition.

[0010] FIGURE 6 is a schematic representation of one variant of the polymer brush composition.

[0011] FIGURE 7 is a flowchart representation of one variant of the production method for the polymer brush composition.

[0012] FIGURE 8 is a flowchart representation of one variant of the production method for the polymer brush composition.

[0013] FIGURE 9 is a graphical representation of enzyme activity data characterizing examples of the polymer brush composition and a control polymer brush composition.

[0014] FIGURE 10 is a flowchart representation of one variant of the production method for the polymer brush composition.

[0015] FIGURE 11 is a flowchart representation of a production method for the control polymer brush composition.

[0016] FIGURE 12 is a graphical representation of enzyme activity data characterizing examples of the polymer brush composition and a control polymer brush composition.DESCRIPTION OF THE EMBODIMENTS

[0017] The following description of embodiments of the invention is not intended to limit the invention to these embodiments but rather to enable a person skilled in the art to make and use this invention. Variants, configurations, implementations, example implementations, and examples described herein are optional and are not exclusive to the variants, configurations, implementations, example implementations, and examples they describe. The invention described herein can include any and all permutations of these variants, configurations, implementations, example implementations, and examples.

[0018] Generally, the terms “ratio” and “proportion,” as utilized herein, refer to molar ratios and molar proportions unless otherwise specified. Furthermore, the adjective phrases “positive,” “positively charged,” and “cationic,” are interchangeable when referencing monomers or proportions herein. Likewise, the adjective phrases “negative,” “negatively charged,” and “anionic” are also interchangeable when referencing monomers or proportions herein.

[0019] Generally, the term “can,” as utilized herein, indicates an action or attribute of the method, which may or may not be executed by or be applicable to the system depending on the implementation or embodiment of the system.

[0020] Generally, the term “include,” as utilized herein, can mean “comprise,” “consist of,” or “consist essentially of’ and is not restricted to any one of the above interpretations throughout.

[0021] Generally, the term “a set of,” as utilized herein, refers to one or more of the subject objects. Additionally, the terms “first,” “second,” “third,” etc., as utilized herein, do not imply an order but simply identify multiple instances of a step or component unless an order or series is otherwise implied.

[0022] Generally, the term “polymer chain,” as utilized herein, can refer to a chain of monomers of a single species, a copolymer chain including multiple monomeric species, a block copolymer including regionally distinct sets of monomeric species, and / or chains of any conformation, such as linear, branched and / or dendritic chains. However, the term “polymer chain,” as utilized herein, typically does not refer to crosslinked or networked chains unless otherwise specified.

[0023] Generally, the term “mixture,” as utilized herein, can refer to solutions, colloids, and / or suspensions between any combination of material phases, unless otherwise specified.

[0024] Generally, the term “polymer brush,” as utilized herein, refers to a surface coating including polymers tethered to a surface or substrate. A polymer brush is characterized by a polymer chain density great enough such that polymer-polymer interactions result in an extended, or brush-like, conformation.

[0025] Generally, the term “substrate,” as utilized herein, refers to a substrate of the polymer brush composition (i.e., the surface to which polymer chains are bonded). Other substrates such as enzyme substrates are distinguished from the generic term with additional modifiers.1. Method for Production of Polymer Brush Composition Including a Quantity of Chain-End-Immobilized Cofactors

[0026] A method for immobilizing a target cofactor 130 (hereinafter “the method SI 00”) includes: functionalizing a substrate with an initiator to form a functionalized substrate in Step SI 10; preparing a prepolymer mixture including a set of monomers configured to bond to the initiator in Step S120; polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form a polymer brush including a set of polymer chains 120 bonded to the substrate via the initiator and characterized by functionalized chain ends in Step S130; and reacting the target cofactor 130 with a heterobifunctional linker 140 to produce a conjugated cofactor in Step SI 50. In particular, the heterobifunctional linker 140 is configured to: bond with the target cofactor 130 at a bonding site of the target cofactor 130 via a linker-cofactor reaction; and bond with the functionalized chain ends of the set of polymer chains 120 via a linker-chain reaction. Additionally, the method SI 00 includes exposing the polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120 to form the polymer brush composition 100 in Step SI 60.2. Method for Production of a Polymer Brush Composition for Immobilized Biocatalysis Enzyme-Coupled Reactions

[0027] As shown in FIGURE 2, a method for co-immobilizing a target enzyme 150 and a target cofactor 130 within a polymer brush includes: functionalizing a substrate with an initiator at an initiator density sufficient to effect a grafting density of the polymer brush greater than 0.1 chains per square nanometer in Step SI 10; and preparing a prepolymer mixture including a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive portion of reactive monomers, the hydrophobic proportion and hydrophilic proportion based on surface properties of the target enzyme 150 and on surface properties of a regenerative enzyme 160 capable of regenerating the target cofactor 130subsequent to consumption of the target cofactor 130 by the target enzyme 150 in Step SI 22. The method SI 00 also includes generating a polymer brush from the substrate and the prepolymer mixture via controlled radical polymerization such that: the polymer brush includes a set of polymer chains 120 covalently bonded to the substrate via the initiator; the set of polymer chains 120 is characterized by functionalized chain ends; and the polymer brush is characterized by a brush thickness less than an average pore radius of the substrate in Step SI 32. Additionally, the method SI 00 includes: exposing the polymer brush to an enzyme solution including a quantity of the target enzyme 150 and a quantity of the regenerative enzyme to produce an enzyme-impregnated polymer brush in Step S140. Furthermore, the method S100 includes producing a quantity of a conjugated cofactor by reacting a quantity of the target cofactor 130 with a quantity of a heterobifunctional linker 140 configured to: bond with the quantity of the target cofactor 130 at non-interactive bonding sites of the quantity of the target cofactor 130 via a linker-cofactor reaction; and bond with the functionalized chain ends of the set of polymer chains 120 via a linker-chain reaction in Step S150. The method S100 further includes exposing the enzyme-impregnated polymer brush to the quantity of the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120 in Step S162.3. Method for Production of a Polymer Brush Composition for Immobilized Biocatalysis with Electrochemical Cofactor Regeneration

[0028] As shown in FIGURE 3, a method for co-immobilizing a target enzyme 150 and a target cofactor 130 within a polymer brush includes: functionalizing an electrically conductive substrate with an initiator at an initiator density sufficient to effect a grafting density of the polymer brush greater than 0.1 chains per square nanometer and less than 0.6 chains per square nanometer in Step SI 12; and preparing a prepolymer mixture including a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive proportion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of the target enzyme 150 in Step S124. The method SI 00 also includes generating a polymer brush from the substrate and the prepolymer mixture via controlled radical polymerization such that: the polymer brush includes a set of polymer chains 120 covalently bonded to the substrate via the initiator; the set of polymer chains 120 is characterized by functionalized chain ends; and the polymer brush is characterized by a brush thickness greater than 1.0 nanometer in Step SI 34. Additionally, the method SI 00 includes exposing the polymer brush to an enzyme solution including the target enzyme 150 to produce an enzyme-impregnated polymer brush in Step SI 42. Furthermore, the method SI 00 includesproducing a conjugated cofactor by reacting the target cofactor 130 with a heterobifunctional linker 140 configured to: bond with the target cofactor 130 at a non-interactive bonding site of the cofactor via a linker-cofactor reaction; and bond with the functionalized chain ends of the set of polymer chains 120 via a linker-chain reaction in Step S150. The method S100 also includes exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120 in Step S162.4. Polymer Brush Composition Including Chain-End Immobilized Cofactors

[0029] As shown in FIGURE 4, a polymer brush composition 100 includes: a substrate 102; a set of polymer chains 120 bonded to the substrate 102 via an initiator 110; and a target cofactor 130 quantity of a target cofactor 130 covalently bonded to chain ends of the set of polymer chains 120 via a heterobifunctional linker 140 configured to covalently bond to the target cofactor 130 quantity within a non-interactive region of the target cofactor 130 and to the chain ends of the set of polymer chains 120.5. Enzyme-Coupled Reaction Variant of the Polymer Brush Composition

[0030] As shown in FIGURE 5, a polymer brush composition 100 for co-immobilizing a target enzyme 150, a target cofactor 130, and a regenerative enzyme 160 capable of regenerating the target cofactor 130 subsequent to consumption of the target cofactor 130 by the target enzyme 150 includes: a substrate 102; a set of polymer chains 120 bound to the substrate 102; a target enzyme 150 quantity of a target enzyme 150 immobilized within the set of polymer chains 120 via covalent bonding; a regenerative enzyme quantity of the regenerative enzyme 160 immobilized within the set of polymer chains 120 via covalent bonding; and a target cofactor 130 quantity of the target cofactor 130 immobilized at chain ends of the set of polymer chains 120 via a heterobifunctional linker 140 configured to bond to the target cofactor 130 quantity and to the chain ends of the set of polymer chains 120.6. Electrochemical Reaction Variant of the Polymer Brush Composition

[0031] As shown in FIGURE 6, a polymer brush composition 100 for co-immobilizing a target enzyme 150 and a target cofactor 130 capable of regeneration via a redox reaction includes: an electrically conductive substrate 104; a set of polymer chains 120 bound to the electrically conductive substrate 104; a target enzyme quantity of a target enzyme 150 immobilized within the set of polymer chains 120 via covalent bonding; and a target cofactor 130 quantity of the target cofactor 130 immobilized at chain ends of the set of polymer chains 120 via a heterobifunctional linker 140 configured to bond to the target cofactor 130 quantity and to the chain ends of the set of polymer chains 120.7. Applications

[0032] Generally, the method SI 00 produces a polymer brush composition 100 including a quantity of a target cofactor 130 immobilized at chain ends of the polymer brush composition 100. More specifically, the polymer brush composition 100 prevents downstream leakage of the target cofactor 130 in continuous-flow chemical processes, while simultaneously enabling diffusion and regeneration of the quantity of the target cofactor 130. The method S100 provides these advantages by effecting a high chain-end cofactor bonding density (i.e., a proportion of chain-ends occupied by an immobilized cofactor) for the polymer brush composition 100, preventing immobilization of the target cofactor 130 at non-terminal positions within the polymer brush and preserving reactive groups in-chain for enzyme immobilization with orthogonal chemistry. More specifically, the method S100 is capable of producing polymer brush compositions 100 characterized by a chain-end cofactor bonding density of greater than 50% or, in some implementations, greater than 95%. Additionally, the method SI 00 providing enhanced tunability of immobilized enzyme properties and cofactor activity, and accessibility through separate, easily controlled engineering parameters, such as polymer chain composition, polymer length, and grafting density. Furthermore, by immobilizing the quantity of the target cofactor 130 at the chain ends of the polymer brush composition 100 with high accuracy, the method SI 00 can significantly increase (e.g., by a factor of three or more) the activity of the target cofactor 130 relative to methods that immobilize the target cofactor 130 throughout polymer chains of a polymer brush composition 100.

[0033] The chain-end cofactor bonding density of the polymer brush composition 100 can be quantified through polymer brush synthesis using a labile surface bound initiator and subsequent cleavage of the polymers from the surface. Subsequent methods of solution polymer analytical chemistry, including nuclear magnetic resonance, provide sufficient information to quantify cofactor location. Alternatively, synthesis of an analogous, solution phase polymer using a sacrificial soluble initiator followed by solution-phase NMR analysis would provide the same information.

[0034] In particular, the method SI 00 includes: functionalizing a substrate 102 with an initiator 110 in Step SI 10; preparing a prepolymer mixture in Step SI 20; polymerizing a set of polymer chains 120 of the polymer brush composition 100 while maintaining functionalized chain-ends on the set of polymer chains 120 (e.g., via controlled radical polymerization) in Step S130; conjugating the target cofactor 130 with a heterobifunctional linker 140 configured to covalently bond with both the cofactor and the functionalized chain ends of the polymer brush composition 100 Step SI 50; and exposing the polymer brush to the conjugated cofactor to initiate bondingbetween the conjugated cofactor and the polymer chains of the polymer brush in Step SI 60. Thus, by tethering quantities of the target cofactor 130 to the set of polymer chains 120, the method S100 produces a polymer brush composition 100 capable of enzyme-catalyzed chemistry under continuous flow conditions without leaching quantities of the cofactor into the product stream. The polymer brush composition 100 vastly reduces consumption rates of the target cofactor 130 required for enzyme-catalyzed chemistry and increases total turnovers per cofactor, thereby improving material efficiency in the execution of enzymatic chemical processes.

[0035] The polymer brush composition 100 enables applications including enzyme-catalyzed cofactor-assisted continuous flow chemistry for industrial chemistry processes. Without the use of the polymer brush composition 100, cofactors may not be anchored to a substrate 102 and are therefore free to diffuse into the reaction product and are continuously consumed or swept away (in continuous flow chemical processes), therefore requiring replacement of the cofactor to continue the reaction. The polymer brush composition 100 alleviates this issue by tethering the cofactor to the substrate 102 while enabling limited diffusion of the cofactor to the target enzyme 150 to participate in the enzyme-catalyzed reaction. Thus, the polymer brush composition 100 reduces cofactor consumption and increases product purity for enzyme-catalyzed cofactor-assisted chemical processes.

[0036] The polymer brush composition 100 does not substantially inhibit the activity of the chain-end bonded quantities of the target cofactor 130 such that the target cofactor 130 may be consumed by quantities of a target enzyme 150 (in the process catalyzing the forward progress of an enzyme-catalyzed reaction) and regenerated multiple times while remaining tethered to the set of polymer chains 120 of the polymer brush composition 100. In a dissolved-enzyme variant of the polymer brush composition 100, the chain-end immobilized cofactor of the polymer brush composition 100 may diffuse to both the target enzyme 150 and a regenerative enzyme 160 in solution around the polymer brush composition 100. Alternatively, in applications of the dissolved-enzyme variant in which the target cofactor 130 is capable of electrochemical regeneration, the chain-end immobilized cofactor can diffuse to an electrically conductive substrate 104 instead of a regenerative enzyme 160, thereby initiating a regenerative redox reaction of the target cofactor 130 while the target cofactor 130 remains tethered to the set of polymer chains 120 of the polymer brush composition 100.

[0037] In an enzyme-coupled reaction variant, the polymer brush composition 100 is impregnated with immobilized enzymes including the target enzyme 150 and / or the regenerative enzyme 160, thereby enabling a complete enzyme-coupled reaction to occur within the polymer brush composition 100 (e.g., without the presence of additional enzymes in solution). In thisvariant of the polymer brush composition 100 the chain-end-bonded target cofactor 130 diffuses between the target enzyme 150 and the regenerative enzyme 160. Thus, the enzyme-coupled variation of the polymer brush composition 100 reduces consumption of both the target cofactor 130 and the associated enzymes in continuous-flow, enzyme-catalyzed chemical applications.

[0038] In an electrochemical reaction variant, the polymer brush composition 100 is configured with an electrochemical means for cofactor regeneration by oxidation or reduction of the target cofactor 130 subsequent to consumption of the target cofactor 130 by the target enzyme 150. In this variant, the polymer brush composition 100 includes an immobilized quantity of the target enzyme 150 and an electrically conductive substrate 104, such as a glassy carbon electrode, to which the set of polymer chains 120 are covalently bonded and with which the polymer brush composition 100 could cause reduction or oxidation of the chain-end-bonded cofactor. Thus, in this variant, the polymer brush composition 100 enables electrochemical regeneration of the co-immobilized cofactor for continuous consumption of the target cofactor 130 by the target enzyme 150.

[0039] In variants of the polymer brush composition 100 including a co-immobilized target enzyme 150 and target cofactor 130, reactions utilizing the polymer brush composition 100 are not dependent on the co-solubility of the target enzyme 150 and the target cofactor 130 in an often aqueous solvent. Thus, the method SI 00 enables the use of less reactive non-aqueous solvents, which can further preserve the activity of the target enzyme 150 and the target cofactor 130 and facilitate additional industrial applications for enzyme-catalyzed chemical processes.

[0040] As described in U.S. Patent Application 18 / 036,678, in some variants, the method S100 includes: analysis of the surface characteristics of the target enzyme 150 (and / or the regenerative enzyme 160 in the enzyme-coupled reaction variant) to determine proportions of a hydrophobic copolymer and a hydrophilic copolymer for the set of polymer chains 120 based on surface properties of the target enzyme 150 and / or the regenerative enzyme 160. The method SI 00 then includes synthesizing polymer chains characterized by the proportions of the hydrophobic copolymer and the hydrophilic copolymer via controlled radical polymerization. However, the method S100 includes additional steps not described in U.S. Patent Application 18 / 036,678, including utilizing functionalized chain ends of the polymer chains to bond with a heterobifunctional linker 140 also configured to bond with the target cofactor 130, thereby tethering the target cofactor 130 to the chain ends of the set of polymer chains 120. Additionally, as is further described below, the method SI 00 includes precise selection and control of the grafting density of the set of polymer chains 120 to the substrate 102 of the polymer brush composition 100, the molecular weight of the copolymers in the set of polymer chains 120, andthe poly dispersity of the set of polymer chains 120. By varying the above parameters, the method S100 can modify the diffusion characteristics of the chain-end-bonded target cofactor 130. Thus, the method SI 00 and the resulting polymer brush composition 100 represent a significant improvement relative to methods described in U.S. Patent Application 18 / 036,678 with respect to continuous-flow, enzyme-catalyzed chemistry.8. Polymer Brush Synthesis Equipment

[0041] Generally, a person of skill in the art will recognize that the method SI 00 may be executed autonomously, semi-autonomously, and / or by laboratory personnel via polymer brush synthesis equipment including but not limited to: reaction tubes, flasks, beakers, funnels; stirring or agitation systems; heating mantles or baths; condensers; evaporators; inert gas environments and associated purging systems; thermal sensors; mass and volume measurement devices; controlled dispensation devices; UV / visible / NIR light sources; vacuum- and / or pressure chambers; filtrations devices; pH measurement devices; high throughput liquid handling and dispensing equipment; and / or any other laboratory equipment. Additionally, the polymer brush composition 100 may be characterized using equipment including but not limited to: gel permeation chromatography equipment; nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy equipment, differential scanning calorimetry equipment; thermogravimetric analyzers; dynamic light scattering equipment; contact angle goniometer; and / or any other characterization equipment.

[0042] Additionally or alternatively, the method SI 00 may be executed as a batched process, a continuous-flow process, and / or as some combination of continuous and batch processes, utilizing equipment specialized for execution of the method SI 00.9. Production of the Polymer Brush Composition with Chain-End Immobilized Cofactor

[0043] As shown in FIGURE 1, the method SI 00 immobilizes a target cofactor 130 to chain ends of the set of polymer chains 120 via a heterobifunctional linker 140. More specifically, the method SI 00 produces a polymer brush composition 100 characterized by a high grafting density of the set of polymer chains 120 to the substrate 102, thereby increasing the available quantity of the cofactor and increasing the activity of the target enzyme 150 and / or the regenerative enzyme 160. Additionally, the method SI 00 produces a polymer brush composition 100 with a set of polymer chains 120 characterized by a high polymer molecular weight, resulting in a polymer brush thickness of less than half the pore size (i.e., diameter) of the substrate 102 and greater than one nanometer. In one implementation, the method SI 00 produces a polymer brush composition 100 characterized by a poly dispersity index between 1.00 and 2.00 (characterized via gel permeation chromatography and / or via a sacrificial soluble initiator 110). In anotherimplementation, the method SI 00 produces a polymer brush composition 100 characterized by an average polymer brush thickness between 1.0 nanometers and 10.0 nanometers, which results in increased cofactor activity relative to both shorter and longer average polymer brush thicknesses. Thus, the method SI 00 engenders high chain-end diffusivity within the polymer brush composition 100 to facilitate cyclical cofactor activity and regeneration within the polymer brush composition 100.9.1. Substrate Functionalization

[0044] The method SI 00 includes functionalizing a substrate 102 with an initiator 110 to which the set of polymer chains 120 are bound according to subsequent Steps of the method S100. More specifically, the method SI 00 includes functionalizing the substrate 102 with the initiator 110 to produce a functionalized substrate in Step SI 10. In particular, the method SI 00 includes functionalizing a carbon- or silicon-based substrate 102 with a silane initiator 110 (i.e., ((chloromethyl) phenylethyl) trimethoxy silane). In one example, the method SI 00 includes functionalizing a silica gel (i.e., amorphous silicon dioxide) substrate 102 characterized by an average pore diameter of 40 nanometers. However, the method SI 00 can include functionalizing substrates 102 other than silica gel and functionalizing silica gel substrates 102 characterized by average pore diameters greater than 40 nanometers. In another example, the method SI 00 includes functionalizing a conductive substrate 104, such as a glassy carbon electrode, to enable electrochemical regeneration of the target cofactor 130. However, the method S100 can include functionalizing other conductive substrates 104, such as graphene electrodes. Thus, by functionalizing the substrate 102, the method SI 00 provides bonding sites for the set of polymer chains 120 to extend from the substrate 102.

[0045] In one implementation, the method SI 00 includes functionalizing the substrate 102 with the initiator 110 sufficient to effect a grafting density greater than 0.1 chains per square nanometer to increase the chain-end diffusivity of the resulting polymer brush composition 100. Additionally, the method SI 00 can include functionalizing the substrate 102 with an initiator density of 1.5 molecules per square nanometer to effect a grafting density of 0.8-1.0 chains per square nanometer. In one implementation, the method SI 00 can include functionalizing the substrate 102 with an initiator density greater than 0.15 molecules per square nanometer to effect a grafting density greater than 0.1 chains per square nanometer.9.2. Prepolymer Mixture

[0046] Generally, the method SI 00 includes preparing a prepolymer mixture (or mixture), which can be combined with a polymerization catalyst to initiate polymerization. More specifically, the method includes preparing a prepolymer mixture including a set of monomers configured tobond with the initiator 110 to form the set of polymer chains 120 in Step S120. The method S100 can include preparing a prepolymer mixture by dissolving the set of monomers in a compatible solvent such that each monomeric species in the set of monomers is soluble within the solvent. In one implementation, the method SI 00 can include preparing a prepolymer mixture including a polymerization catalyst and / or polymerization cofactors prior to subsequent Steps of the method SI 00 in which the prepolymer mixture is introduced to the substrate 102.

[0047] In one implementation, the method SI 00 includes preparing a prepolymer mixture including methacrylate monomers. More specifically, in this implementation, the method SI 00 includes: functionalizing the substrate 102 with a silane initiator 110 to form the functionalized substrate 102; and preparing a prepolymer mixture including a set of methacrylate monomers configured to bond to the silane initiator 110. In this implementation, the prepolymer mixture can include a solvent such as 2,2,2-Trifluoroethanol (TFE), in which methacrylate monomers are soluble.

[0048] However, the method SI 00 can include preparing a prepolymer mixture including other monomers, such as: acrylic monomers, styrenic monomers, vinyl ester monomers, vinyl amide monomers, methacrylonitrile monomers, or any other monomer compatible with controlled radical polymerization processes.9.3. Controlled Radical Polymerization

[0049] Generally, the method SI 00 includes exposing the functionalized substrate to the prepolymer mixture in conditions favorable to polymerization (e.g., in the presence of a polymerization catalyst and / or polymerization cofactors) to initiate controlled radical polymerization of the set of monomers in the pre-polymerization solution in Step S130. More specifically, the method SI 00 includes polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush via controlled radical polymerization. In particular, the method SI 00 can include exposing the functionalized substrate to the prepolymer mixture and a polymerization catalyst, causing an extension of the set of polymer chains 120 from the functionalized substrate. Step S130 of the method S100 results in a polymer brush that includes a set of polymer chains 120 covalently bonded to the substrate 102 via the initiator 110, wherein the set of polymer chains 120 is characterized by functionalized chain ends and the polymer brush is characterized by an average brush thickness less than half an average pore size of the substrate 102.

[0050] Generally, the set of polymer chains 120 is characterized by a linear conformation, however, other conformations are possible, as is further described below. By leveraging controlled radical polymerization, the method SI 00 enables control of molecular weight andpoly dispersity of the set of polymer chains 120 while also maintaining functionalized groups at the chain ends to which cofactors can later be covalently bound. The controlled radical polymerization process for the production of polymer brush compositions 100 is further described in U.S. Patent Application No. 18 / 036,678.

[0051] For implementations of the polymer brush composition 100 including methacrylate monomers, the method SI 00 can include initiating atom transfer radical polymerization (hereinafter “ATRP”) to control copolymer growth rates. More specifically, the method SI 00 can include polymerizing the set of methacrylate monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush via atom transfer radical polymerization. In particular, the method SI 00 can include exposing the functionalized substrate to the prepolymer mixture for a predetermined time period while maintaining temperature, solvent, and total methacrylate concentration. In one example, the method SI 00 includes preparing a copper-containing solution including CuBr and 2,2'-bipyridine in a TFE solvent and continuously stirring the copper-containing solution until the CuBr is dissolved. In this example, the method S100 then includes: degassing both solutions to remove dissolved oxygen; and combining the copper-containing solution with the functionalized substrate and the prepolymer mixture under an inert atmosphere for the duration of the predetermined time period.

[0052] As shown in FIGURE 7, in one variant, the method SI 00 can include executing a multistage controlled radical polymerization process including multiple stages of controlled radical polymerization effective to imbue the set of polymer chains 120 with specific properties. For example, in one implementation, the method SI 00 includes a first ATRP stage executed according to the ATRP process described above, a second ATRP stage in which the partially formed polymer brush composition 100 is exposed to a second prepolymer mixture including a quantity of branched monomers 128, and / or a third ATRP stage in which the ATRP process described above is resumed. In this implementation, the method SI 00 can generate a set of dendritic linear hybrid polymer chains to increase the number of functionalized chain ends for a given grafting density, thereby increasing the chain-end-bound cofactor density (by surface area) of the polymer brush composition 100. More specifically, the method SI 00 can include: preparing a branch prepolymer mixture including a set of branched monomers configured to polymerize with the set of monomers in Step SI 26; in a first polymerization stage, polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form an unbranched polymer brush including a set of polymer chains 120 bonded to the functionalized substrate via the initiator 110 and characterized by functionalized chain ends in Step S130; and, in a second polymerization stage, polymerizing the set of branched monomers in the branchedprepolymer mixture from the functionalized chain ends of the set of polymer chains 120 to form the polymer brush including a set of dendritic linear hybrid polymer chains bonded to functionalized substrate via the initiator 110 in Step S136. Thus, in this implementation, Step SI 30 of the method SI 00 can result in the polymer brush composition 100 including a set of polymer chains 120 characterized by a dendritic linear hybrid conformation.

[0053] Alternatively, the method S100 can include a multistage controlled radical polymerization process effective to generate a set of block copolymer chains in a second ATRP stage. In this implementation, the method SI 00 can include bonding the quantity of the target cofactor 130 to the block segment of the set of block polymer chains, thereby increasing the number of tethered cofactors per polymer chain.

[0054] In yet another implementation, the method SI 00 includes terminating the controlled radical polymerization process such that the average thickness of the polymer brush is greater than 1.0 nanometers and less than the smaller of the average pore radius of the substrate 102 and 10.0 nanometers to facilitate mobility of the chain-end bonded target cofactor 130, thereby improving the activity of the target cofactor 130 in enzyme-catalyzed chemical processes. As is described in further detail below, lower polymer brush thicknesses may result in higher activity of the target cofactor 130 due to potentially tangling or coiling of the polymer chains at greater polymer brush thicknesses.

[0055] In yet another implementation, the method S100 includes modifying the polymerization catalyst in the prepolymer mixture to increase polydispersity of the resulting polymer brush composition 100, thereby increasing diffusion of the chain-end bonded target cofactor 130. More specifically, the method SI 00 can include increasing the polymerization reaction temperature, modifying the polymerization solvent, reducing the ratio of inactivating complexes to activating catalyst complexes for ATRP, or mixing chain transfer agents with radical addition fragmentation transfer (hereinafter “RAFT”) to increase poly dispersity to between 1.00 and 1.60 or in some example up to 2.00.

[0056] Upon completion of the controlled radical polymerization Step of the method SI 00 for ATRP reactions, the polymer brush composition 100 includes a set of polymer chains 120 terminated by alkyl halides (e.g., carbon-bromine bonds). Thus, by utilizing controlled radical polymerization, the method SI 00 can maintain the functionality of chain ends of the set of polymer chains 120. However, the method S100 can include other forms of controlled radical polymerization (e.g., RAFT) depending on the types of monomers included in the set of polymer chains 120. Generally, RAFT polymerization yields polymers with thiol-containing chain ends as an orthogonal chemical handle for subsequent modification.

[0057] As shown in FIGURE 8, the method SI 00 can include a “grafted to” approach, as opposed to the “grafted from” approach. More specifically, in this implementation, the method SI 00 includes: introducing a polymerization catalyst to the prepolymer mixture including the initiator 110, causing polymerization of the set of polymer chains 120 in solution to form a polymer solution in Step S138; and exposing the polymer solution to the functionalized substrate, causing the set of polymer chains 120 to bond with the functionalized substrate via the initiator 110 in Step S139. In particular, in this implementation, the method can include initiating polymerization within the prepolymer mixture including an initiator 110 (e.g., via the addition of a polymerization catalyst) without exposure to the functionalized substrate. The addition of a polymerization catalyst can cause spontaneous, controlled radical polymerization of the set of monomers in the prepolymer mixture, thereby forming the set of polymer chains 120. In this implementation, the method SI 00 additionally includes a grafting step effective to bond the set of polymer chains 120 to the substrate 102 via a reactive functional group on the initiator 110.9.4. Cofactor Conjugation

[0058] Generally, the method SI 00 includes conjugating the target cofactor 130 with a heterobifunctional linker 140 to enable the target cofactor 130 to bond with the chain ends of the set of polymer chains 120 in Step S150. More specifically, the method S100 can include producing a quantity of a conjugated cofactor by reacting a quantity of the target cofactor 130 with a quantity of a heterobifunctional linker 140. The method S100 includes conjugating the target cofactor 130 with a heterobifunctional linker 140 configured to: bond with the quantity of the target cofactor 130 at non-interactive bonding sites of the target cofactor 130 via a linker-cofactor reaction; and bond with the functionalized chain ends of the set of polymer chains 120 via a linker-chain reaction. Additionally, the method SI 00 includes conjugating the target cofactor 130 via one functional group of the heterobifunctional linker 140 that is not cross-reactive with chain-end functional groups of the set of polymer chains 120, thereby preventing nonfunctional conjugates of the conjugated cofactor and multiple chain ends.

[0059] The method S100 includes conjugating the target cofactor 130 with a heterobifunctional linker 140 selected based on a target bonding location (i.e., functional group) on the target cofactor 130, such that the target bonding location is located within a non-interactive region of the target cofactor 130. Additionally, the method S100 can include conjugating the target cofactor 130 with a heterobifunctional linker 140 capable of bonding with a reactive group on the target cofactor 130 within the non-interactive region. Furthermore, the method SI 00 can include conjugating the target cofactor 130 with a heterobifunctional linker 140 selected based on a bonding site and functional group that results in a substantially orthogonal bond between theheterobifunctional linker 140 and the target cofactor 130. Thus, the method S100 enables the heterobifunctional linker 140 to bond with the target cofactor 130 at a position and orientation that reduces the effect of conjugation on the activity of the target cofactor 130 with the target enzyme 150 and / or the regenerative enzyme 160.

[0060] In implementations in which the target cofactor 130 includes a primary amine at the target bonding site, the method SI 00 can utilize a heterobifunctional linker 140 including one of NHS ester, imidoester, pentafluorophenyl ester, EDC, ECC, and hydroxymethyl phosphine functional groups. In implementations in which the target cofactor 130 includes a sulfhydryl functional group at the target bonding site, the method SI 00 can utilize a heterobifunctional linker 140 including one of maleimide, haloacetyl, pyridyl disulfide, thiosulfonate, and vinyl sulfone functional groups. In implementations in which the target cofactor 130 includes an aldehyde functional group at the target bonding site, the method SI 00 can utilize a heterobifunctional linker 140 including one of the hydrazine, alkoxy amine, and NHS ester functional groups. In implementations in which the target cofactor 130 includes an alcohol functional group, the method SI 00 can utilize a heterobifunctional linker 140 including an isocyanate functional group.

[0061] The method S100 utilizes heterobifunctional linkers 140 that are also capable of bonding with the functionalized chain ends of the set of polymer chains 120. In implementations in which the functionalized chain ends of the set of polymer chains 120 include an azide functional group, the method SI 00 can utilize a heterobifunctional linker 140 including a copper-catalyzed azide-alkyne cycloaddition with a terminal or internal alkyne or strain-promoted azide-alkyne cycloaddition using groups such as dibenzocyclooctyne (DBCO / DIBO).

[0062] In implementations in which the set of polymer chains 120 is terminated by alkyl halides, the method SI 00 can include exposing the polymer brush to a sodium azide solution to replace carbon-halide bonds with an azide. In these implementations, the method SI 00 generates reactive azide groups at chain ends of the set of polymer chains 120 in preparation for the subsequent cofactor immobilization step. In this implementation, the method SI 00 can include exposing the polymer brush to a buffered aqueous solution to preserve the structure and function of the immobilized target enzyme 150 and the immobilized regenerative enzyme 160.

[0063] In one implementation, the method S100 includes conjugating the target cofactor 130 with a heterobifunctional linker 140 under water-free conditions (e.g., an organic solvent), which both prevents the undesired hydrolysis of various functional groups on both the cofactor and the heterobifunctional linker 140 and facilitates purification after the conjugation reaction.9.5. Cofactor Immobilization

[0064] Generally, the method SI 00 can include exposing the polymer brush to the quantity of the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120 in Step S160. More specifically, the method S100 can include reacting the conjugated cofactor with the azide located on the set of polymer chains 120 to secure the quantity of the target cofactor 130 to the polymer brush composition 100. Thus, upon bonding the heterobifunctional linker 140 with the set of polymer chains 120, the target cofactor 130 can diffuse within the polymer brush composition 100 while being tethered to the set of polymer chains 120.

[0065] In one implementation, the method SI 00 includes rinsing the polymer brush upon completion of the reaction between the quantity of the conjugated cofactor and the set of polymer chains 120. Thus, in this implementation, the unreacted cofactor is cleared from the polymer brush composition 100.9.6. Examples

[0066] Generally, the method SI 00, as described above, can be utilized to immobilize a wide variety of target cofactors 130. For example, the method S100 can immobilize cofactors such as: nicotinamide adenine dinucleotide (NAD+ / NADH), nicotinamide adenine dinucleotide phosphate (NADP+ / NADPH), thiamine pyrophosphate (TPP), S-adenosyl-L-methionine (SAM) / S-adenosyl-homo-cystein (SAH), methylcobalamin, cobalamin, coenzyme A, tetrahydrofolic acid, menaquinone, ascorbic acid, flavin mononucleotide, flavin adenine dinucleotide, coenzyme F420 (8-hydroxy-5-deazaflavin), adenosine Triphosphate, 3'-Phosphoadenosine-5'-phosphosulfate, coenzyme B (7-mercaptoheptanoylthreoninephosphate), coenzyme M (2- Sulfanylethanesulfonate), coenzyme Q, cytidine triphosphate, glutathione, lipoamide, tetrahydromethanopterin, tetrahydrobiopterin, and pyrroloquinoline quinone. Thus, the method SI 00 can co-immobilize many target cofactors 130 involved in enzyme-catalyzed reactions.

[0067] The method SI 00 is limited to combinations of cofactors and enzymes that do not cause conformational changes to the cofactor that would make bonding at a non-interactive bonding site impossible. However, the method SI 00 can include immobilizing a target cofactor 130 with engineered enzymes configured to enable continued enzyme function while the target cofactor 130 is tethered to the set of polymer chains 120 of the polymer brush composition 100.

[0068] In one example, the method S100 acts on a target cofactor 130 of NADH. In this example, NADH is bound to chain ends of the set of polymer chains 120 via a heterobifunctional linker 140 including dibenzocyclooctyne (DBCO) bound to an n-hydroxysuccinimidyl ester(NHS). In this example, the method SI 00 includes conjugating NADH with the DBCO-NHS linker to form a conjugated cofactor and immobilizing this NADH-DBCO-NHS complex at chain ends of the set of polymer chains 120 of the polymer brush composition 100. In one application of this example, the immobilized NADH participates in an enzyme-coupled reaction with a target enzyme 150 of glucose dehydrogenase (GDH) and a regenerative enzyme 160 of ketoreductase (KRED) to produce chiral alcohols from an achiral ketone and glucose as the reducing equivalent. The polymer brush composition 100 enables the cofactor to access both the reducing and oxidizing enzyme freely while being covalently tethered to the substrate 102 (silica) surface, enabling many reaction cycles with the same cofactor molecule. Cofactor regeneration has been confirmed by performing the reaction without adding quantities of a supplemental cofactor while adding glucose as the reducing equivalent, and ensuring that more moles of product are generated than moles of cofactor immobilized in the polymer brush. The polymer brush composition 100 imparts high enzyme stability and enables long-lasting enzyme operation in non-aqueous solvents. This example of the polymer brush composition 100 is particularly advantageous due to the poor hydrolytic stability of the NAD+ cofactor and, therefore, can be used to improve the longevity and total turnover number achievable with the immobilized enzyme and cofactor combination.9.7. Performance

[0069] As shown in FIGURE 9, examples of the polymer brush composition 100 including a quantity of chain-end immobilized NAD+ / NADH as the target cofactor 130 exhibit significantly higher enzyme-catalyzed activity relative to a control polymer brush composition utilizing a cofactor immobilization method that results in randomized tethering locations. As is described in further detail below, the data represented by FIGURE 9 indicate the clear improvement offered by the method SI 00 over less-targeted cofactor immobilization methods. Additionally, FIGURE 9 represents a comparison between a lower-thickness example of the polymer brush composition 100 (characterized by an average brush thickness of approximately 5.9 nanometers) and a higher-thickness example of the polymer brush composition 100 (characterized by an average brush thickness of approximately 8.7 nanometers). Thus, by tuning the polymer chain length via the method SI 00 and, therefore, the polymer brush thickness, the polymer brush composition 100 may exhibit a range of activity characteristics as described in further detail below. The mechanisms responsible for these differences in activity are generalizable across many variations of the polymer brush composition 100 and, therefore, conclusions drawn based on these examples do not limit the scope of the claims or applications to this particular enzyme, cofactor, heterobifunctional linker 140, synthetic scheme, or reaction conditions.9.7.1. Overview of the Biocatalytic Cascade

[0070] The example polymer brush compositions 100 characterized by the data of FIGURE 9 utilize GDH as the cofactor regeneration enzyme, diaphorase as the target (or cofactor consuming) enzyme, and NAD+ / NADH as the immobilized cofactor. GDH is a commonly employed cofactor regeneration enzyme that consumes glucose to regenerate NADH from NAD+. Diaphorase generates fluorescent resorufin from non-fluorescent resazurin, converting NADH to NAD+ to perform this reduction. The diaphorase provides an accurate and sensitive signal of NADH activity via fluorescence to quantify differences in immobilized cofactor activity. In various applications of the polymer brush composition 100, diaphorase may be replaced with an NADH-dependent enzyme that performs a valuable chemical transformation. Additionally or alternatively, various applications of the polymer brush composition 100 can utilize a different regenerative enzyme 160 capable of performing oxidation reactions, such as by converting NADH to NAD+.9.7.2. Overview of NAD+ Immobilization

[0071] As shown in FIGURE 10, the example polymer brush compositions 100 characterized by the data of FIGURE 9 were produced via a specific example of the method SI 00. FIGURE 10 shows the initial molecular composition of the target cofactor 130, NAD+ prior to execution of the method SI 00. The only primary amine on this molecule is labeled in FIGURE 10 along with the nicotinamide moiety of NAD+, which is the redox-reactive moiety that interacts with both GDH and diaphorase in enzyme-catalyzed reactions. Therefore, this example of the method SI 00 includes conjugating NAD+ with the heterobifunctional linker 140 at a target bonding location outside of the nicatinamide moiety. Additionally, as labeled in FIGURE 10, NAD+ includes a single primary amine functional group, which provides an ideal bonding location for the heterobifunctional linker 140 without substantially affecting the function of NAD+ in the enzyme-coupled reaction. Generally, the above-described immobilization scheme is applicable to similar adenine-containing target cofactors 130, such as flavin adenine dinucleotide, adenosine triphosphate, and coenzyme A, where the adenine provides a unique primary amine target bonding location distant from the interactive region of the target cofactor 130 (e.g., nicatinamide, flavin, triphosphate).

[0072] As shown in FIGURE 10, this example of the method SI 00 includes conjugating the heterobifunctional linker 140, N-hydroxy succinimide dibenzocyclooctyne (DBCO-NHS), with NAD+ at the target bonding location in Step SI 50. In Step SI 50, the activated NHS ester of the heterobifunctional linker 140 reacts with the primary amine on the NAD+ (with the nicotinamide moiety labeled as an R group for ease of visual representation in FIGURE 10), resulting in astable amide bond. Thus, in this example of the method SI 00, DBCO provides a substantially orthogonal reactive handle for tethering to the resin.

[0073] As shown in FIGURE 10, this example of the method S100 includes generating, as described above, a polymer brush from a substrate 102 functionalized with a silane initiator 110, ((chloromethyl) phenylethyl) trimethoxysilane in Steps SI 10 and S130. The resulting polymer brush includes a set of polymer chains 120, each polymer chain including a methacrylate-based copolymer chain containing monomers. In FIGURE 10, the methacrylate copolymer side chains are labeled as R* for ease of visual representation. Upon completion of Step S130, the organohalide (shown as an organochlorine in FIGURE 10) chain end from the polymerization process is converted to an azide via nucleophilic substitution. Generally, such chain-end activation is applicable to other forms of controlled radical polymerizations, such as RAFT. However, this example is not intended to limit the method SI 00.

[0074] As shown in FIGURE 10, this example of the method SI 00 includes exposing the conjugated cofactor, DBCO-activated NAD+, to the polymer brush to cause a spontaneous reaction between the conjugated cofactor and the azide-activated chain end via strain-promoted azide-alkyne cycloaddition, producing a stable 1,2, 3 -triazole ring in Step S160.

[0075] As shown in FIGURE 11, the method S100 was modified to immobilize the NAD+ throughout the set of polymer chains 120, rather than to chain ends of the set of polymer chains 120, to produce the control polymer brush composition. To facilitate comparison with the polymer brush composition 100 produced via the example of the method SI 00 described above, the control polymer brush composition was produced to include the same NHS-DBCO heterobifunctional linker 140 and the same azide-alkyne conjugation. However, instead of tethering the cofactor to chain ends, the method for producing the control polymer brush composition included immobilizing the NAD+ to monomers randomly dispersed in the set of polymer chains 120. As shown in FIGURE 11, the method for producing the control polymer brush composition includes generating a polymer brush, as described above, including glycidyl methacrylate (GMA) monomers. The production method for the control polymer brush composition includes activating the pendant epoxide groups in the GMA-containing brush with azides in a similar procedure to Step S130 of the method S100. Similar to Step S160 of the method SI 00, the NAD-DBCO was conjugated via strain-promoted azide-alkyne cycloaddition.

[0076] Upon production of the lower-thickness polymer brush composition 100, the higher-thickness polymer brush composition 100, and the control polymer brush composition, the activity of NAD+ was measured based on the production of fluorescent resorufin from non-fluorescent resazurin via GDH. To produce the data represented in FIGURE 9, the activityof the target cofactor 130 was measured by introducing a precisely controlled amount of soluble enzymes (GDH and diaphorase) to a solution also containing each of the above-mentioned polymer brush compositions 100.

[0077] FIGURE 9 represents the results of the above-described activity tests. The activity of the diaphorase / GDH system was measured through the formation of a fluorescent product of diaphorase. The activity of each polymer brush composition 100 was also compared with the activity of a polymer brush subject to the attachment of DBCO-NAD, except that these polymer brushes were not activated with azides. Therefore, this unfunctionalized polymer brush did not include covalently bound NAD+. These unfunctionalized polymer brushes act as a comparison that controls for any NAD+ or NAD-DBCO that stuck to the resin despite extensive rinsing, and contributed to the apparent activity. Additionally, the unfunctionalized polymer brushes account for any NAD+ that was present in the enzyme-containing solution.

[0078] As shown in FIGURE 9, the activity ascribed to the immobilized target cofactor 130 (i.e., the difference between checkered and solid bars for each condition) was greatest for the lower-thickness polymer brush composition 100, moderate for the higher-thickness polymer brush composition 100, and lowest for control polymer brush composition. One hypothesis indicates that increased polymer chain length, or average polymer brush thickness, increases the diffusive range of the chain end-tethered cofactor. Therefore, under this hypothesis, thicker polymer brushes (and longer polymer chains) would result in higher immobilized target cofactor activity. However, the data shown in FIGURE 9 do not support this hypothesis. According to the data represented by FIGURE 9, various examples of the polymer brush composition 100 are characterized by a maximum target cofactor activity at a thickness between 1.0 nanometers and 10.0 nanometers. This characteristic is likely due to inaccessibility of the chain ends in thicker polymer brush compositions 100.

[0079] Additionally, the data represented in FIGURE 9 show a marked difference in immobilized target cofactor activity between both examples of the polymer brush composition 100 and the control polymer brush composition. Despite random tethering of the target cofactor 130 to the control polymer brush composition, the lower chain-end cofactor density of the control polymer brush composition is associated with a large decrease in target cofactor activity. Thus, by concentrating the immobilized target cofactor 130 at chain ends of the polymer brush composition 100, the method SI 00 provides a significant performance improvement over existing less-target methods for cofactor immobilization.10. Enzyme-Coupled Reaction Variant

[0080] As shown in FIGURE 2, in an enzyme-coupled reaction variant, the method SI 00: immobilizes a quantity of a target enzyme 150 and a quantity of a regenerative enzyme 160 within a set of polymer chains 120 extending from a substrate 102 of the polymer brush composition 100; and bonds a target cofactor 130 to chain ends of the set of polymer chains 120 via a heterobifunctional linker 140. More specifically, in this variant, the method S100 includes preparing the prepolymer mixture including including a hydrophobic proportion of hydrophobic monomers 122, a hydrophilic proportion of hydrophilic monomers 124, and / or a reactive proportion of reactive monomers 126 in Step S122. The hydrophilic proportion of hydrophilic monomers and the hydrophobic proportion of hydrophobic monomers (i.e., the ratio and total quantity of these monomers) are selected based on surface properties of a target enzyme 150. Additionally, this variant of the method SI 00 includes exposing the polymer brush to an enzyme solution including the target enzyme 150 and the regenerative enzyme 160 to produce an enzyme-impregnated polymer brush in Step S140. Furthermore, this variant of the method S100 includes exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120, thereby forming an enzyme-impregnated, cofactor-functionalized polymer brush in Step SI 62.

[0081] In the enzyme-coupled reaction variant, the method SI 00 produces a polymer brush composition 100 characterized by a high grafting density of the set of polymer chains 120 to the substrate 102, thereby improving chain-end diffusion of the target cofactor 130 to the quantity of the target enzyme 150 and the quantity of the regenerative enzyme 160 impregnated within the polymer brush composition 100. Additionally, in the enzyme-coupled reaction variant, the method SI 00 produces a polymer brush composition 100 characterized by a high copolymer molecular weight, resulting in a polymer brush thickness of less than half the pore size of the substrate 102 or 10.0 nanometers, whichever is lower and greater than one nanometer or half of the major diameter of the larger of the target enzyme 150 and the regenerative enzyme 160. Furthermore, in the enzyme-coupled reaction variant, the method SI 00 produces a polymer brush composition 100 characterized by a poly dispersity index between 1.00 and 1.60 (characterized via gel permeation chromatography and / or via a sacrificial soluble initiator 110), which results in increased chain-end diffusivity without sacrificing enzyme stability (which may decline at polydispersity indexes greater than 1.60). Thus, in the enzyme-coupled reaction variant, the method SI 00 engenders high chain-end diffusivity within the polymer brush composition 100 to facilitate a cyclical enzyme-coupled reaction to occur repeatedly within thepolymer brush composition 100 (i.e., without relying on the solubility of the target enzyme 150 and the regenerative enzyme 160 within an immersive solution) while maintaining high enzyme stability to enable continued enzymatic function in a wide range of chemical and physical environments.10.1. Substrate Functionalization

[0082] In the enzyme-coupled reaction variant, the method SI 00 includes functionalizing a substrate 102 with an initiator 110 in Step SI 10, as described above, with respect to the generic version of the method SI 00. Thus, by functionalizing the substrate 102, the method SI 00 provides bonding sites for the set of polymer chains 120 to extend from the substrate.10.2. Enzyme Surface Analysis

[0083] Generally, the enzyme-coupled reaction variant of the method SI 00 includes preparing a prepolymer mixture including a hydrophobic proportion of hydrophobic monomers and a hydrophilic proportion of hydrophilic monomers sufficient to create a high bonding affinity between the set of polymer chains 120 and the target and regenerative enzymes 160. More specifically, the method SI 00 leverages Steps described in U.S. Patent Application No. 18 / 036,678 to calculate a hydrophobic proportion for the set of polymer chains 120 and a hydrophilic proportion for the set of polymer chains 120. In one implementation of the enzyme-coupled reaction variant, the method SI 00 includes calculating a hydrophobic proportion and a hydrophilic proportion based on a weighted combination of the surface properties of the target enzyme 150 and the regenerative enzyme 160 to maximize the bonding affinity of the set of polymer chains 120 with both enzymes of the polymer brush composition 100. Alternatively, in another implementation of the enzyme-coupled reaction variant, the method SI 00 includes calculating the hydrophobic proportion and the hydrophilic proportion based on the surface properties of the target enzyme 150 or the regenerative enzyme 160, whichever is naturally less stable within the polymer brush composition 100, instead of a weighted combination of the two enzymes. Thus, the method SI 00 can enable the bonding of the set of polymer chains 120 to both the target enzyme 150 and the regenerative enzyme 160, thereby immobilizing both quantities of enzymes with the polymer brush composition 100.

[0084] In the enzyme-coupled reaction variant, the method SI 00 calculates proportions of methacrylate monomers characterized by a linear conformation for inclusion in the polymer brush composition 100. In one example, the method SI 00 includes calculating a hydrophobic proportion of poly(ethylene glycol) methyl ether methacrylate (PEGMA), ethylene glycol phenyl ether methacrylate, and / or isopropyl methacrylate. In another example, the method SI 00 includes calculating a hydrophilic proportion of sulfobetaine methacrylate (SBMA) and / orzwitterionic 2 -methacryloyloxy ethyl phosphorylcholine. However, the method SI 00 can utilize other methacrylate monomers for inclusion in the set of polymer chains 120 of the polymer brush composition 100.

[0085] In one implementation, the method SI 00 includes calculating a hydrophobic proportion and a hydrophilic proportion based on a proportion of the solvent-accessible surface area (hereinafter “SASA”) of the target enzyme 150 and a proportion of the SASA of the regenerative enzyme 160 exhibiting a hydrophobic nature. In one example of this implementation, the method SI 00 calculates the hydrophobic proportion and the hydrophilic proportion based on a weighted average of the proportion of the SASA of the target enzyme 150 exhibiting a hydrophobic nature and the proportion of the SASA of the regenerative enzyme 160 exhibiting a hydrophobic nature. In this example, the method SI 00 can include weighing the relative contributions of the proportion of the SASA of the target enzyme 150 exhibiting a hydrophobic nature and the proportion of the SASA of the regenerative enzyme 160 exhibiting a hydrophobic nature based on a total SASA of the target enzyme 150 and a total SASA of the regenerative enzyme 160. For example, if the total SASA of the target enzyme 150 accounts for 40% of the combined SASA of the target enzyme 150 and the regenerative enzyme 160, the method SI 00 can apply a weight of 0.40 to surface properties of the target enzyme 150 for the purposes of calculating the hydrophobic proportion and the hydrophilic proportion. Thus, the method SI 00 can calculate a proportion of hydrophobic and hydrophilic monomers in the set of polymer chains 120 that are likely to bond with both the target enzyme 150 and the regenerative enzyme 160.

[0086] As described in International Application No. US2024 / 046,711, in some implementations, the method SI 00 can include calculating proportions of additional types of monomers for inclusion in the set of polymer chains 120 characterized by a variety of primary affinities, such as charged monomers (i.e., positively charged monomers and / or negatively charged monomers), aromatic hydrophobic monomers, and aliphatic hydrophobic monomers. In these implementations, the method SI 00 can calculate proportions of charged monomers, aromatic hydrophobic monomers, and / or aliphatic hydrophobic monomers, based on corresponding surface affinities of both the target enzyme 150 and the regenerative enzyme 160. Similar to the above-described implementations, the method SI 00 can include weighing the relative contributions of the target enzyme 150 and the regenerative enzyme 160 based on SASA or any other property of the target enzyme 150 and regenerative enzyme 160.

[0087] Further discussion of the detection and classification of surface regions on enzymes for the purpose of immobilization of a target enzyme 150 in a polymer brush composition 100 is described in U.S. Patent Application No. 18 / 036,678.10.3. Prepolymer Mixture

[0088] In the enzyme-coupled reaction variant, the method SI 00 includes preparing a prepolymer mixture or solution including a catalyst for polymerization of a proportion of hydrophobic monomers and the proportion of hydrophilic monomers, a quantity of hydrophobic monomers in the hydrophobic proportion, a quantity of hydrophilic monomers in the hydrophilic proportion (i.e., as a molar ratio), and / or a quantity of reactive monomers in a reactive proportion in Step S122. More specifically, the method S100 includes preparation of a prepolymer mixture configured to initiate controlled radical polymerization upon exposure to the functionalized substrate.

[0089] In one implementation, the method SI 00 includes preparing a polymerization mixture including a quantity of reactive monomers to provide a reactive handle for subsequent covalent bonding and immobilization with the target enzyme 150 and the regenerative enzyme 160. The inclusion of reactive handles supplements the affinity of the target enzyme 150 and the regenerative enzyme 160 for the polymer brush via surface interactions caused by inclusion of the hydrophilic and hydrophobic monomers in the specified proportions. Thus, the combination of the hydrophobic monomers and hydrophilic monomers in the specified proportions in addition to the inclusion of the reactive monomers facilitates covalent bonding between the reactive monomers, the target enzymes 150, and the regenerative enzymes 160. In one implementation of the method SI 00 including the production of a methacrylate-based polymer brush composition 100, the method SI 00 can include preparing a polymerization mixture including a quantity of glycidyl methacrylate as the quantity of reactive monomer, thereby introducing epoxide groups functioning as the reactive handle for immobilization of the target enzyme 150 and the regenerative enzyme 160.10.4. Controlled Radical Polymerization

[0090] In the enzyme-coupled reaction variant, the method SI 00 includes exposing the functionalized substrate to the prepolymer mixture to initiate controlled radical polymerization of the quantity of hydrophobic monomers in the hydrophobic proportion, the quantity of hydrophilic monomers in the hydrophilic proportions, the quantity of the reactive monomer in the reactive proportion, and / or proportions of additional quantities of monomers in the prepolymer mixture in Step SI 32. More specifically, the method SI 00 can generate a polymer brush from the functionalized substrate and the prepolymer mixture via controlled radical polymerization such that: the polymer brush includes a set of polymer chains 120 covalently bonded to the substrate 102 via the initiator 110; the set of polymer chains 120 is characterized by functionalized chain ends; and the polymer brush characterized by a brush thickness less thanan average pore radius of the substrate 102 or less than 10.0 nanometers, whichever is lower, and greater than half of a major diameter of a largest enzyme from among the target enzyme 150 and the regenerative enzyme 160. By leveraging controlled radical polymerization, the method SI 00 enables control of molecular weight and poly dispersity of the set of polymer chains 120 of the polymer brush composition 100 while also maintaining functionalized groups at the end of the set of polymer chains 120 to which cofactors can later be covalently bound. The controlled radical polymerization process for the production of polymer brush compositions 100 is further described in U.S. Patent Application No. 18 / 036,678.

[0091] As described above with respect to other variants of the method SI 00, for implementations of the polymer brush composition 100 incorporating methacrylate monomers, the method SI 00 can include initiating atom transfer radical polymerization (hereinafter “ATRP”) to control copolymer growth rates. More specifically, the method SI 00 can include exposing the functionalized substrate to the prepolymer mixture for a predetermined time period while maintaining temperature, solvent, and total methacrylate concentration.

[0092] As described above with respect to other variants of the method SI 00, the enzyme-coupled reaction variant of the method SI 00 can include executing a multistage controlled radical polymerization process effective to imbue the set of polymer chains 120 with specific properties, such as a dendritic linear conformation or a block copolymer conformation.

[0093] In the enzyme-couple variant, the method SI 00 includes terminating the controlled radical polymerization process such that the average molecular weight of the set of polymer chains 120 (i.e., the average length of the set of polymer chains 120 or the thickness of the polymer brush composition 100) is less than the average pore radius of the substrate 102 by at least the radius of the target enzyme 150 or the radius of the regenerative enzyme 160, whichever is greater, to enable diffusion of the target enzyme 150 and the regenerative enzymes 160 into the polymer brush composition 100. For non-porous substrates 102, the method SI 00 can include continuing the controlled radical polymerization process until the average molecular weight of the set of polymer chains 120 corresponds to an average brush thickness associated with greater rates of target cofactor and target enzyme activity (i.e., less than 10.0 nanometers).

[0094] As described above with respect to other variants of the method SI 00, the enzyme-coupled reaction variant includes modifying the polymerization catalyst in the prepolymer mixture to increase poly dispersity of the resulting polymer brush composition 100, thereby increasing diffusion of the chain-end bonded target cofactor 130. More specifically, in the enzyme-coupled reaction variant, the method SI 00 can include increasing the polymerization reaction temperature, modifying the polymerization solvent, reducing the ratio of inactivatingcomplexes to activating catalyst complexes for ATRP, or mixing chain transfer agents with RAFT to increase poly dispersity to between 1.00 and 1.60.

[0095] As described above with respect to other variants of the method SI 00, upon completion of the controlled radical polymerization Step of the method SI 00 for ATRP reactions, the polymer brush composition 100 includes a set of polymer chains 120 terminated by alkyl halides (e.g., a carbon-bromine bonds), which remain preserved during the enzyme co-immobilization Step described below. Additionally, the polymer brush resulting from Step SI 32 includes a set of polymer chains 120 including a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and / or a reactive portion of reactive monomers. Thus, by utilizing controlled radical polymerization, the method SI 00 can maintain the functionality of chain ends of the set of polymer chains 120 and / or reactive monomers present with the set of polymer chains 120. However, the method S100 can include other forms of controlled radical polymerization (e.g., RAFT) depending on the types of monomers included in the set of polymer chains 120.

[0096] As described above with respect to other variants of the method SI 00, the enzyme-coupled reaction variant can also include a “grafted to” approach, as opposed to the “grafted from” approach, shown in FIGURE 8.10.4.1. Chain-End Functionalization

[0097] In some implementations, the method SI 00 can include functionalizing chain-end reactive groups of the set of polymer chains 120 prior to immobilizing the target enzyme 150 and the regenerative enzyme 160 within the polymer brush. In implementations of the method SI 00 utilizing azide chain-end groups, the method SI 00 can include functionalizing the azide groups via nucleophilic substitution (i.e., converting an organohalide to an azide) prior to immobilizing the target enzyme 150 and the regenerative enzyme 160 in the polymer brush. In particular, the method SI 00 includes functionalizing the azide groups prior to enzyme immobilization because the elevated temperatures and solvents utilized during azide functionalization may denature or otherwise damage the enzymes if the enzymes are already impregnated into the polymer brush.10.5. Enzyme Co-immobilization

[0098] In the enzyme-coupled reaction variant, the method SI 00 includes exposing the polymer brush to an enzyme solution including the target enzyme 150 and the regenerative enzyme 160 to produce an enzyme-impregnated polymer brush in Step S140. More specifically, in the enzyme-coupled variant, the method SI 00 can include exposing the polymer brush to an enzyme solution including: a target enzyme quantity of the target enzyme 150 capable of catalyzing a reaction with the target cofactor 130; and a regenerative enzyme quantity of the regenerativeenzyme 160 capable of catalyzing a regeneration reaction of the target cofactor 130 subsequent to consumption of the target cofactor 130 by the target enzyme 150. In particular, the enzyme-coupled reaction variant includes exposing the polymer brush to an immobilization solution configured to facilitate attachment of the target enzyme 150 and the regenerative enzyme 160 to the polymer brush composition 100. Thus, the method SI 00 includes impregnating the polymer brush with the target enzyme 150 and the regenerative enzyme 160 prior to chain-end attachment of the conjugated cofactor.

[0099] In one implementation, the method SI 00 includes exposing the polymer brush to an immobilization solution configured with a pH and ionic strength selected based on an isoelectric point of the target enzyme, a relative size of the target enzyme, a net charge of the target enzyme, an isoelectric point of the regenerative enzyme, a relative size of the regenerative enzyme, and a net charge of the regenerative enzyme. The method SI 00 includes selecting the pH and ionic strength based on the above factors to preserve the function of the target enzyme 150 and the function of the regenerative enzyme 160 while in solution and upon covalent bonding with the polymer brush. Thus, the method SI 00 can include preparing an enzyme solution configured to maximize enzyme stability and function during the immobilization process.

[0100] In one implementation, the method SI 00 includes exposing the polymer brush to the immobilization solution for 18-30 hours at a temperature between 0 and 4 degrees Celsius, with mixing to enable full consumption of epoxide groups of the reactive monomers in the set of polymer chains 120 of the polymer brush via bonding with nucleophiles on the surfaces of the target enzyme 150 and / or the regenerative enzyme 160. Thus, the method SI 00 can prevent further bonding with these epoxide groups during subsequent Steps.

[0101] In implementations of the method SI 00 including reactive monomers, the enzyme-coupled reaction variant can functionalize the reactive proportion of reactive monomers within the polymer brush prior to exposure to the enzyme solution. For example, the method SI 00 can include activating the polymer brush with an NHS-mal eimide, thereby enabling covalent attachment of the target enzyme 150 and the regenerative enzyme 160 via solvent-accessible cysteines and amines. Thus, the method SI 00 can include functionalization of reactive monomers in the set of polymer chains 120 to facilitate covalent bonding between the set of polymer chains 120 and the target and regenerative enzymes 160.10.6. Cofactor Conjugation

[0102] As described above with respect to other variants of the method SI 00, the enzyme-coupled reaction variant includes conjugating the target cofactor 130 with a heterobifunctional linker 140 to enable the target cofactor 130 to bond with the chain ends of theset of polymer chains 120 in Step S150. More specifically, the method S100 can include producing a quantity of a conjugated cofactor by reacting a quantity of the target cofactor 130 with a quantity of a heterobifunctional linker 140. The method S100 includes conjugating the target cofactor 130 with a heterobifunctional linker 140 configured to: bond with the quantity of the target cofactor 130 at non-interactive bonding sites of the quantity of the target cofactor 130 via a linker-cofactor reaction; and bond with the functionalized chain ends of the set of polymer chains 120 via a linker-chain reaction. Additionally, the method SI 00 includes conjugating the target cofactor 130 via one functional group of the heterobifunctional linker 140 that is not cross-reactive with chain-end functional groups of the set of polymer chains 120, thereby preventing nonfunctional conjugates of the conjugated cofactor and multiple chain ends. Furthermore, the method S100 can include conjugating the target cofactor 130 with a heterobifunctional linker 140 that is not cross-reactive with functional groups of the target enzyme 150, regenerative enzyme 160, or reactive monomers of the set of polymer chains 120.

[0103] In one implementation, the method S100 includes a cofactor conjugation reaction performed in advance of exposing to the quantity of the heterobifunctional linker 140 and the quantity of the target cofactor 130 to the enzyme-impregnated polymer brush, thereby preventing unwanted reactions between the heterobifunctional linker 140 and the target enzyme 150 or between the heterobifunctional linker 140 and the regenerative enzyme 160. Thus, in this implementation, the method SI 00 ensures that the introduction of the heterobifunctional linker 140 does not interfere with enzyme function within the polymer brush composition 100.10.7. Cofactor Immobilization

[0104] In the enzyme-coupled variation, the method SI 00 can include exposing the enzyme-impregnated polymer brush to the quantity of the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120 in Step S162. More specifically, the method S100 can include exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120, thereby forming an enzyme-impregnated, cofactor-functionalized polymer brush.

[0105] In one implementation, the method SI 00 can include reacting the conjugated cofactor with the azide located on the set of polymer chains 120 to secure the quantity of the target cofactor 130 to the polymer brush composition 100. Thus, upon bonding of the heterobifunctional linker 140 with the set of polymer chains 120, the target cofactor 130 can diffuse within the polymer brush composition 100 while being tethered to the set of polymer chains 120.

[0106] In another implementation, the method SI 00 includes rinsing a solution including the quantity of the conjugated cofactor upon completion of the reaction between the quantity of the conjugated cofactor and the set of polymer chains 120. Thus, in this implementation, the unreacted cofactor is cleared from the polymer brush composition 100.10.8. Examples

[0107] In the enzyme-coupled reaction variant, the method SI 00 can be utilized to co-immobilize multiple combinations of the target enzyme 150, the regenerative enzyme 160, and the target cofactor 130. For example, the method S100 can co-immobilize cofactors such as: nicotinamide adenine dinucleotide (NAD+ / NADH), nicotinamide adenine dinucleotide phosphate (NADP+ / NADPH), thiamine pyrophosphate (TPP), S-adenosyl-L-methionine (SAM) / S-adenosyl-homo-cystein (SAH), methylcobalamin, cobalamin, coenzyme A, tetrahydrofolic acid, menaquinone, ascorbic acid, flavin mononucleotide, flavin adenine dinucleotide, coenzyme F420 (8-hydroxy-5-deazaflavin), adenosine Triphosphate, 3'-Phosphoadenosine-5'-phosphosulfate, coenzyme B (7-mercaptoheptanoylthreoninephosphate), coenzyme M (2- Sulfanylethanesulfonate), coenzyme Q, cytidine triphosphate, glutathione, lipoamide, tetrahydromethanopterin, tetrahydrobiopterin, and pyrroloquinoline quinone. Thus, the method SI 00 can co-immobilize many target cofactors 130 involved in enzyme-coupled reactions. The method SI 00 is limited to combinations of cofactors and enzymes that do not cause conformational changes to the cofactor that would make bonding at a non-interactive bonding site impossible. However, the method SI 00 can include co-immobilizing a target cofactor 130 with engineered enzymes configured to enable continued enzyme function while the target cofactor 130 is tethered to the set of polymer chains 120 of the polymer brush composition 100.

[0108] In one example, the method SI 00 acts on a target enzyme 150 of glucose dehydrogenase (GDH), a regenerative enzyme 160 of ketoreductase (KRED), and a target cofactor 130 of NADH. In this example, the GDH and KRED are co-immobilized within the polymer brush composition 100 while NADH is bound to chain ends of the set of polymer chains 120 via a heterobifunctional including dibenzocyclooctyne (DBCO) bound to an n-hydroxysuccinimidyl ester (NHS). The method SI 00 includes conjugating NADH with the DBCO-NHS linker to form a conjugated cofactor and immobilizing this NADH-DBCO-NHS complex at chain ends of the set of polymer chains 120 of the polymer brush composition 100. Upon completion of the method SI 00, the polymer brush composition 100 can produce chiral alcohols from an achiral ketone and glucose as the reducing equivalent. The polymer brush composition 100 enables the cofactor to access both the reducing and oxidizing enzyme freelywhile being covalently tethered to the substrate 102 (silica) surface, enabling many reaction cycles with the same cofactor molecule. Cofactor regeneration can be confirmed by performing the reaction without adding quantities of a supplemental cofactor while adding glucose as the reducing equivalent, and ensuring that more moles of product are generated than moles of cofactor immobilized in the polymer brush. The polymer brush composition 100 imparts high enzyme stability and enables long-lasting enzyme operation in non-aqueous solvents. This example of the polymer brush composition 100 is particularly advantageous due to the poor hydrolytic stability of the NAD+ cofactor and, therefore, can be used to improve the longevity and total turnover number achievable with the immobilized enzyme and cofactor combination.

[0109] In other examples, the method SI 00 can immobilize target enzymes 150 including by not limited to imine reductase, reductive aminase, ene reductase, monoamine oxidase, baeyer-villiger monooxidase, and / or halohydrin dehalogenase.

[0110] In other examples, the method SI 00 can immobilize regenerative enzymes 160 including but not limited to formate dehydrogenase, glucose dehydrogenase, alcohol dehydrogenase, phosphite dehydrogenase, glucose-6-phosphate dehydrogenase, hydrogenase, lactate dehydrogenase, leucine dehydrogenase, amino acid dehydrogenases, NADH oxidase, glutamate dehydrogenase, and nitroreductase.

[0111] In the enzyme-coupled reaction variant, the method SI 00 produces a polymer brush composition 100 including: a target cofactor 130 quantity of the target cofactor 130 immobilized to chain ends of the set of polymer chains 120 and capable of regeneration via an enzyme-catalyzed regeneration reaction; a target enzyme quantity of a target enzyme 150 capable of catalyzing a reaction with the target cofactor 130 and immobilized within the set of polymer chains 120; and a regenerative enzyme quantity of a regenerative enzyme 160 capable of catalyzing the enzyme-catalyzed regeneration reaction; and immobilized within the set of polymer chains 120. In one implementation, the polymer brush composition 100 can include the set of polymer chains 120 characterized by a poly dispersity index between 1.00 and 1.60. In another implementation, the polymer brush composition 100 can be characterized by an average brush thickness between 1.0 and 10.0 nanometers. In yet another implementation, the polymer brush composition 100 can be characterized by an average polymer brush thickness of less than half the pore size of the substrate 102 and greater than half of the major diameter of the larger of the target enzyme 150 and the regenerative enzyme 160.

[0112] Additionally, in the enzyme-coupled reaction variant, the method SI 00 can produce a polymer brush composition 100 including a set of polymer chains 120 including a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilicmonomers, and / or a reactive portion of reactive monomers. In this variant of the polymer brush composition 100, the hydrophilic proportion and the hydrophobic proportion are based on: surface properties of the target enzyme 150 capable of catalyzing a reaction with the target cofactor 130; and surface properties of the regenerative enzyme 160 capable of catalyzing a regeneration reaction of the target cofactor 130 subsequent to consumption of the target cofactor 130 by the target enzyme 150. This variant of the polymer brush composition 100 can also include: a target enzyme quantity of the target enzyme 150 immobilized within the set of polymer chains 120 via covalent bonding with the reactive proportion of the reactive monomers in the set of polymer chains 120; and a regenerative enzyme quantity of the regenerative enzyme 160 immobilized within the set of polymer chains 120 via covalent bonding with the reactive proportion of the reactive monomers in the set of polymer chains 120. Alternatively, implementations of the polymer brush composition 100 excluding the quantity of reactive monomers can include: a target enzyme quantity of the target enzyme 150 immobilized within the set of polymer chains 120 via surface interactions between the target enzyme 150 and the hydrophobic proportion of the hydrophobic monomers and the hydrophilic proportion of the hydrophilic monomers; and a regenerative enzyme quantity of the regenerative enzyme 160 immobilized within the set of polymer chains 120 via surface interactions between the regenerative enzyme 160 and the hydrophobic proportion of the hydrophobic monomers and the hydrophilic proportion of the hydrophilic monomers. Thus, in this implementation, the target enzyme 150 and the regenerative enzyme 160 are co-immobilized within the polymer brush composition 100 based on surface interactions instead of covalent bonds between these enzymes and the quantity of reactive monomers.

[0113] In one implementation of the polymer brush composition 100, the target enzyme quantity and the regenerative enzyme quantity are substantially equal, thereby enabling substantially equal rates of cofactor consumption and regeneration within the polymer brush composition 100.10.9. Performance

[0114] As shown in FIGURE 12, examples of the enzyme-coupled reaction variant of the polymer brush composition 100 that include co-immobilized quantities of the target cofactor 130, the target enzyme 150, and the regenerative enzyme 160 maintain enzyme activities without the addition of dissolved enzymes to the polymer brush composition 100. More specifically, FIGURE 12 shows that both the target enzyme 150 and the regenerative enzyme 160 remain active while immobilized within the polymer brush composition 100.

[0115] The example of the polymer brush composition 100 characterized by the data represented in FIGURE 12 is configured to stabilize the less stable enzyme from among GDH and diaphorase, resulting in a monomeric ratio of 90% poly(ethylene glycol) methyl ether methacrylate (PEGMA) to 10% 2-aminoethyl methacrylate hydrochloride (AMA) for the set of polymer chains 120. As described above, the example polymer brush was first functionalized by azides prior to addition of the enzyme solution in Step S140. Upon functionalization of the polymer brush by azides, the polymer brush was activated with NHS-maleimide, thereby facilitating attachment of the GDH and diaphorase to the polymer brush. Also prior to Step S140, the enzyme solution was prepared that included the GDH and the diaphorase, was characterized by an enzyme concentration of 5 milligrams per milliliter, and was characterized by a pH between 6.5 and 8.0. The enzyme solution was then added to the polymer brush in Step S140, thereby producing an enzyme-impregnated polymer brush including the GDH and diaphorase In Step SI 62, the conjugated cofactor, DBCO-activated NAD+, was immobilized at chain ends of the enzyme-impregnated polymer brush including the quantity of GDH and the quantity of diaphorase.

[0116] FIGURE 12 shows that the activity of the example of the polymer brush composition 100 including co-immobilized GDH, diaphorase, and NAD+, exceeded the activity of all controls, which exhibited measurable but significantly less activity resulting from the residual presence of GDH, diaphorase, and / or NAD+ within the control polymer brush compositions 100 as a result of incomplete rinsing. A first control polymer brush composition was azide-functionalized, but no NAD+ was immobilized post-functionalization. A second control polymer brush composition was not functionalized, and no NAD+ was added to the polymer brush. A third control polymer brush composition was not functionalized, however NAD+ was added. Therefore, the third control polymer brush composition exhibited some activity based on the residual NAD+ remaining in the polymer brush. However, this residual NAD+ likely remained mobile within the polymer brush and therefore was not as active as the chain-end-bonded NAD+. The data represented in FIGURE 12 indicate that by co-immobilizing the target cofactor 130, the target enzyme 150, and the regenerative enzyme 160, greater enzyme activity can be achieved relative to polymer brushes containing a mobile target cofactor 130 that is simply entangled within the polymer brush.11. Electrochemical Reaction Variant

[0117] In an electrochemical reaction variant, the method SI 00 includes co-immobilizing a target enzyme 150 and a target cofactor 130 capable of regeneration via a redox reaction in a polymer brush composition 100. However, instead of regenerating quantities of the immobilizedtarget cofactor 130 via a regenerative enzyme 160, in the electrochemical reaction variant, the method SI 00 utilizes electrochemical reduction or oxidation of the target cofactor 130 to regenerate the target cofactor 130 subsequent to consumption by the target enzyme 150. More specifically, in this variant, the method SI 00 includes: functionalizing an electrically conductive substrate 104 with the initiator 110 to form the functionalized substrate in Step SI 12; preparing the prepolymer mixture including the set of monomers further including a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and / or a reactive portion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme 150 capable of catalyzing a reaction with the target cofactor 130 in Step S124; generating a polymer brush from the electrically conductive substrate 104 and the prepolymer mixture such that: the polymer brush includes a set of polymer chains 120 covalently bonded to the electrically conductive substrate 104 via the initiator 110 and the set of polymer chains 120 is characterized by functionalized chain ends in Step SI 34; and exposing the polymer brush to an enzyme solution including the target enzyme 150 to produce an enzyme-impregnated polymer brush in Step S142. Steps SI 50 and Step SI 62 are executed in a similar manner to other variants of the method SI 00.

[0118] In this variant, the method SI 00 includes functionalizing a conductive substrate 104, such as a glassy carbon electrode, and tunes parameters such as grafting density, poly dispersity, and molecular weight of the set of polymer chains 120 to facilitate diffusion of the chain-end bonded target cofactor 130 toward the electrically conductive substrate surface. Thus, the method SI 00 enables the cofactor to electrochemically interact with the charged electrically conductive substrate 104in order to regenerate the cofactor.

[0119] The electrochemical reaction variant of the method SI 00 enables many applications of enzyme chemistry that are unfeasible or inefficient under normal circumstances. For example, direct catalytic oxidation of methane to methanol is an appealing application of the electrochemical reaction variant of the method SI 00. Methane tends to over-oxidize to carbon dioxide using non-enzymatic catalysts. Methane monooxygenases (MMOs) are unique in that they can selectively oxidize methane to methanol while avoiding over-oxidation. However, MMOs require a cofactor and a complex electron transport chain to regenerate the oxidized cofactor. Coimmobilization of the enzyme and cofactor on a redox-capable electrode enables many turnovers of the MMO enzyme without a complex electron transport chain and can be used to generate methanol directly from methane.

[0120] The method SI 00 includes a similar series of Steps to the enzyme-coupled reaction variant including: substrate functionalization, enzyme surface analysis, polymer brushsynthesis, prepolymer mixture production, controlled radical polymerization, enzyme immobilization, cofactor conjugation, and cofactor immobilization. The following sections highlight major differences between the enzyme-coupled reaction variant and the electrochemical reaction variant.11.1. Substrate Functionalization

[0121] As described above, the method S100 includes functionalizing a substrate 102 with an initiator 110 at a controlled grafting density in Step S 112. In the electrochemical reaction variant, the method SI 00 utilizes a conductive substrate 104 such as a glassy carbon electrode instead of a silica substrate. Additionally, in the electrochemical reaction variant, the grafting density is controlled within a range of 0.1 to 0.6 chains per square nanometer to enable diffusion of chain-end bonded cofactors toward the electrically conductive substrate surface for regeneration via a redox reaction (densities higher than 0.6 chains per square nanometer may prevent sufficient diffusion to the substrate surface and result in unwanted interactions between pairs of tethered cofactors near the substrate surface). Generally, to effect a grafting density between 0.1 and 0.6, the method S100 can include functionalizing the substrate with the initiator 110 at an initiator 110 density between 0.15 and 0.9 molecules per square nanometer. Thus, in the electrochemical reaction variant, the method SI 00 adapts the Step SI 10 to maintain the grafting density of the set of polymer chains 120 within a predetermined range and utilize a conductive substrate 104 in Step SI 12.

[0122] In implementations of the method SI 00 in which the electrically conductive substrate 104 is a glassy carbon electrode, the method SI 00 can include functionalizing the electrically conductive substrate 104 with a silane initiator 110, as described above with respect to the enzyme-coupled reaction variant. Thus, the functionalization Step of the method SI 00 is substantially similar to the functionalization Step of the enzyme-coupled reaction variant, with the exception of the differences described above.11.2. Enzyme Surface Analysis

[0123] As described above with respect to the enzyme-coupled reaction variant, the method SI 00 includes analyzing hydrophobic patches at the surface of the enzyme to calculate a hydrophobic proportion and a hydrophilic proportion of hydrophobic and hydrophilic monomers, respectively, as described in U.S. Patent Application No. 18 / 036,678. However, instead of analyzing surfaces of both the target enzyme 150 and a regenerative enzyme 160 in the electrochemical reaction variant, the method SI 00 includes analysis of surface properties of the target enzyme 150. Thus, the method S100 is more similar to the process described in U.S. Patent Application No. 18 / 036,678. As described above, the method S100 can also includeanalysis of additional surface properties of the target enzyme 150 and the calculation of additional proportions of monomers compatible with the analyzed surface affinities as described in International Application No. US2024 / 046,711.11.3. Polymer Brush Synthesis

[0124] As described above with respect to the enzyme-coupled reaction variant, the method SI 00 in the electrochemical reaction variant includes: preparing the prepolymer mixture including a set of monomers including a hydrophobic proportion of hydrophobic monomers, and a hydrophilic proportion of hydrophilic monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme 150 capable of catalyzing a reaction with the target cofactor 130 in Step S124; and exposing the functionalized substrate to the prepolymer mixture to initiate controlled radical polymerization of the quantity of hydrophobic monomers in the hydrophobic proportion, the quantity of hydrophilic monomers in the hydrophilic proportions, the quantity of the reactive monomer in the reactive proportion, and / or proportions of additional quantities of monomers in the prepolymer mixture in Step SI 34. More specifically, the method SI 00 includes generating a polymer brush from the electrically conductive substrate 104 and the prepolymer mixture via controlled radical polymerization such that: the polymer brush includes a set of polymer chains 120 covalently bonded to the electrically conductive substrate 104 via the initiator 110; and the set of polymer chains 120 are characterized by functionalized chain ends.

[0125] However, unlike the enzyme-coupled reaction variant in the electrochemical reaction variant, the average brush thickness of the polymer brush composition 100 produced by the method SI 00 may not be limited based on the pore size of the electrically conductive substrate 104 as, in some implementations of the electrochemical reaction variant, the method SI 00 utilizes a non-porous conductive substrate 104. However, due to decreased activity observed at higher brush thicknesses, as described above, the method SI 00 can limit Step SI 34 to producing polymer brushes characterized by a thickness of less than 10.0 nanometers. Thus, the method SI 00 can include initiating controlled radical polymerization to effect an average brush thickness greater than one nanometer or greater than half the major diameter of the target enzyme 150 and less than 10.0 nanometers.

[0126] Additionally, the method SI 00 includes executing controlled radical polymerization such that the polymer brush composition 100 is characterized by a poly dispersity index between 1.20 and 2.00. In the electrochemical reaction variant of the method S100, the polymer brush composition 100 is characterized by relatively higher poly dispersity when compared to the enzyme-coupled reaction variant in order to further increase chain enddiffusivity, thereby enabling diffusion toward the electrically conductive substrate 104 for regeneration of the cofactor via a redox reaction.

[0127] Otherwise, the method S100 includes executing the controlled radical polymerization process as described above.11.4. Enzyme Immobilization

[0128] Upon extension of the set of polymer chains 120, the electrochemical reaction variant of the method SI 00 includes exposing the polymer brush to an enzyme solution including the target enzyme 150 to produce an enzyme-impregnated polymer brush in Step S142. More specifically, in the electrochemical reaction variant, the method SI 00 includes exposing the polymer brush to an enzyme solution containing a quantity of the target enzyme without a regenerative enzyme 160 being present.

[0129] As described above with respect to the enzyme-coupled reaction variant, the method SI 00 causes reactive groups on the enzyme surface to bond with the quantity of the reactive monomer within the set of polymer chains 120, causing immobilization of the target enzyme 150. Alternatively, in implementations without reactive monomers with the set of polymer chains 120, the target enzyme 150 is immobilized within the polymer brush via interaction between the distribution of monomers within the set of polymer chains 120 and the surface characteristics of the target enzyme 150.11.5. Cofactor Conjugation

[0130] In the electrochemical reaction variant, the method SI 00 includes cofactor conjugation as described above with respect to the other variants of the method SI 00. Although different cofactors may be compatible with the electrochemical reaction variant, the Steps for conjugation of the cofactor with a heterobifunctional linker 140 are substantially similar to the Steps described above.11.6. Cofactor Immobilization

[0131] In the electrochemical reaction variant, the method SI 00 includes cofactor immobilization as described above with respect to the electrochemical reaction variant in Step SI 62. More specifically, the method SI 00 can include exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains 120.11.7. Examples

[0132] Generally, the method SI 00 can be utilized to co-immobilize multiple combinations of the target enzyme 150 and the target cofactor 130 capable of being regenerated via reduction or oxidation. For example, the method S100 can co-immobilize cofactors such as:NAD+ / NADH, NADP+ / NADPH, menaquinone, ascorbic acid, flavin mononucleotide, flavin adenine dinucleotide, coenzyme F420 (8-hydroxy-5-deazaflavin), coenzyme Q, glutathione, tetrahydrobiopterin, pyrroloquinoline quinone. Thus, the method SI 00 can co-immobilize many target cofactors 130 that may be electrochemically regenerated.

[0133] Additionally, the method SI 00 can utilize cofactors that require additional ions (e.g., metallic ions, hydrogen ions) in addition to reduction or oxidation to be regenerated. In these examples, metallic salts or other ionic species may be added to the solution such that these ions can participate in the reduction or oxidation reaction precipitated by the electrically conductive substrate 104.

[0134] In one example, the method SI 00 produces a polymer brush composition 100 including a target enzyme 150 of MMO and a target cofactor 130 of NADH. In this example, the method SI 00 enables the direct electrochemical oxidation of NADH to NAD+ due to high chain-end diffusivity within the polymer brush composition 100, enabling contact with and oxidation of NADH at the electrode surface. The tethering of NAD+ to chain ends prevents undesired side reactions, including the formation of enzymatically inactive (NAD)2, by controlling the local concentration of tethered NAD+ at the electrode interface and limiting contact between multiple NAD+ molecules at the electrode interface.

[0135] In another example, the method S100 produces a polymer brush composition 100 characterized by a poly dispersity index between 1.20 and 2.00; and a brush thickness of greater than 1.0 nanometer.

[0136] In yet another example, the method SI 00 produces a polymer brush composition 100 including: a set of polymer chains 120 including a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive portion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme 150 capable of catalyzing a reaction with the target cofactor 130; and a target enzyme quantity of the target enzyme 150 immobilized within the set of polymer chains 120 via covalent bonding with the reactive proportion of the reactive monomers in the set of polymer chains 120.

[0137] In yet another example, the method SI 00 produces a polymer brush composition 100 including: a set of polymer chains 120 including a hydrophobic proportion of hydrophobic monomers and a hydrophilic proportion of hydrophilic monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme 150 capable of catalyzing a reaction with the target cofactor 130; and a target enzyme quantity of the target enzyme 150 immobilized within the set of polymer chains 120 via surface interactionsbetween the target enzyme 150 and the hydrophobic proportion of the hydrophobic monomers and the hydrophilic proportion of the hydrophilic monomers.

[0138] As a person skilled in the art will recognize from the previous detailed description and from the figures and claims, modifications and changes can be made to the embodiments of the invention without departing from the scope of this invention as defined in the following claims.

Claims

CLAIMSWe Claim:

1. A method for immobilizing a target cofactor comprising:• functionalizing a substrate with an initiator to form a functionalized substrate;• preparing a prepolymer mixture comprising a set of monomers configured to bond to the initiator;• polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form a polymer brush comprising a set of polymer chains: o bonded to the functionalized substrate via the initiator; and o characterized by functionalized chain ends;• reacting the target cofactor with a heterobifunctional linker to produce a conjugated cofactor, the heterobifunctional linker configured to: o bond with the target cofactor at a bonding site of the target cofactor via a linker-cofactor reaction; and o bond with the functionalized chain ends of the set of polymer chains via a linker-chain reaction; and• exposing the polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains to form a cofactor-functionalized polymer brush.

2. The method of Claim 1, wherein polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush comprises polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush via controlled radical polymerization.

3. The method of Claim 1, wherein functionalizing the substrate with the initiator to produce the functionalized substrate comprises functionalizing the substrate with the initiator to produce the functionalized substrate characterized by an initiator density effective to achieve a grafting density of the polymer brush greater than 0.1 polymer chains per square nanometer.

4. The method of Claim 1, wherein polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate comprises polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brushcomprising a set of polymer chains:• bonded to the funcitonalized substrate via the initiator;• characterized by functionalized chain ends; and• the polymer brush characterized by an average brush thickness greater than 1.0 nanometer and less than an average pore radius of the substrate.

5. The method of Claim 1, where the target cofactor is selected from a group consisting of:• nicotinamide adenine dinucleotide;• nicotinamide adenine dinucleotide phosphate;• thiamine pyrophosphate;• S-adenosyl-L-methionine;• S-adenosyl-homo-cysteine (SAH);• methylcobalamin;• cobalamin;• coenzyme A;• tetrahydrofolic acid;• menaquinone;• ascorbic acid;• flavin mononucleotide;• flavin adenine dinucleotide;• coenzyme F420;• adenosine Triphosphate;• 3'-Phosphoadenosine-5'-phosphosulfate;• 7-mercaptoheptanoylthreoninephosphate;• 2-Sulfanylethanesulfonate;• coenzyme Q;• cytidine triphosphate;• glutathione;• lipoamide;• tetrahydromethanopterin;• tetrahydrobiopterin; and• pyrroloquinoline quinone.

6. The method of Claim 1 :• wherein preparing the prepolymer mixture comprises preparing the prepolymer mixture comprising the set of monomers comprising a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive proportion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on: o surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor; and o surface properties of a regenerative enzyme capable of catalyzing a regeneration reaction of the target cofactor subsequent to consumption of the target cofactor by the target enzyme;• further comprising: o exposing the polymer brush to an enzyme solution comprising the target enzyme and the regenerative enzyme to produce an enzyme-impregnated polymer brush; and• wherein exposing the polymer brush to the conjugated cofactor comprises exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains to form an enzyme-impregnated, cofactor-functionalized polymer brush.

7. The method of Claim 6, wherein polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate comprises polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush comprising the set of polymer chains:• bonded to the functionalized substrate via the initiator;• characterized by functionalized chain ends; and• characterized by an average brush thickness less than an average pore radius of the substrate and greater than half of a major diameter of a largest enzyme from among the target enzyme and the regenerative enzyme.

8. The method of Claim 6, wherein polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate comprises polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush comprising the set of polymer chains:• bonded to the functionalized substrate via the initiator;• characterized by functionalized chain ends; and• characterized by a poly dispersity index between 1.00 and 1.60.

9. The method of Claim 6:• wherein the target cofactor comprises nicotinamide adenine dinucleotide;• wherein the target enzyme comprises glucose dehydrogenase; and• wherein the regenerative enzyme is selected from a group consisting of: o formate dehydrogenase; o glucose dehydrogenase; o alcohol dehydrogenase; o phosphite dehydrogenase; o glucose-6-phosphate dehydrogenase; o hydrogenase o lactate dehydrogenase; o leucine dehydrogenase; o amino acid dehydrogenases; o NADH oxidase; o glutamate dehydrogenase; and o nitroreductase.

10. The method of Claim 1 :• wherein the target cofactor is capable of regeneration via a redox reaction;• wherein functionalizing the substrate with the initiator comprises functionalizing an electrically conductive substrate with the initiator to form the functionalized substrate;• wherein preparing the prepolymer mixture comprises preparing the prepolymer mixture comprising the set of monomers comprising a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive portion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor;• further comprising: o exposing the polymer brush to an enzyme solution comprising the target enzyme to produce an enzyme-impregnated polymer brush; and• wherein exposing the polymer brush to the conjugated cofactor comprises exposing theenzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains to form an enzyme-impregnated, cofactor-functionalized polymer brush.

11. The method of Claim 10, wherein polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate comprises polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush comprising the set of polymer chains:• bonded to the functionalized substrate via the initiator;• characterized by functionalized chain ends; and• characterized by a poly dispersity index between 1.20 and 2.00.

12. The method of Claim 10:• wherein the target cofactor comprises nicotinamide adenine dinucleotide; and• wherein the target enzyme that consumes nicotinamide adenine dinucleotide.

13. The method of Claim 1 :• wherein functionalizing the substrate comprises functionalizing the substrate with a silane initiator to form the functionalized substrate;• wherein preparing the prepolymer mixture comprises preparing the prepolymer mixture comprising a set of methacrylate monomers configured to bond to the silane initiator;• wherein polymerizing the set of monomers in the prepolymer mixture comprises polymerizing the set of methacrylate monomers in the prepolymer mixture from the functionalized substrate to form the polymer brush via atom transfer radical polymerization.

14. The method of Claim 1 :• further comprising: o preparing a branch prepolymer mixture comprising a set of branched monomers configured to polymerize with the set of monomers;• wherein polymerizing the set of monomers in the prepolymer mixture comprises: o in a first polymerization stage, polymerizing the set of monomers in the prepolymer mixture from the functionalized substrate to form an unbranched polymer brush comprising the set of polymer chains:■ bonded to the functionalized substrate via the initiator; and■ characterized by functionalized chain ends; o in a second polymerization stage, polymerizing the set of branched monomers in the branched prepolymer mixture from the functionalized chain ends of the set of polymer chains to form the polymer brush comprising a set of dendritic linear hybrid polymer chains:■ bonded to the functionalized substrate via the initiator; and■ characterized by functionalized chain ends.

15. The method of Claim 1, wherein polymerizing the set of monomers in the prepolymer mixture comprises exposing the functionalized substrate to the prepolymer mixture and a polymerization catalyst causing extension of the set of polymer chains from the functionalized substrate.

16. The method of Claim 1, wherein polymerizing the set of monomers in the prepolymer mixture comprises:• introducing a polymerization catalyst to the prepolymer mixture, causing polymerization of the set of polymer chains in solution to form a polymer solution; and• exposing the polymer solution to the functionalized substrate causing the set of polymer chains to bond to the functionalized substrate via the initiator.

17. The method of Claim 1 :• wherein preparing the prepolymer mixture comprises preparing the prepolymer mixture comprising the set of monomers comprising a hydrophobic proportion of hydrophobic monomers, and a hydrophilic proportion of hydrophilic monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor;• further comprising exposing the polymer brush to an enzyme solution comprising the target enzyme and the regenerative enzyme to produce an enzyme-impregnated polymer brush; and• wherein exposing the polymer brush to the conjugated cofactor comprises exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains to form an enzyme-impregnated, cofactor-functionalized polymer brush.

18. The method of Claim 1 :• wherein preparing the prepolymer mixture comprises preparing the prepolymer mixture comprising the set of monomers comprising a hydrophobic proportion of hydrophobic monomers, and a hydrophilic proportion of hydrophilic monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme;• further comprising exposing the polymer brush to an enzyme solution to produce an enzyme-impregnated polymer brush, the enzyme solution comprising: o a target enzyme quantity of a target enzyme capable of catalyzing a reaction with the target cofactor; and o a regenerative enzyme quantity of a regenerative enzyme capable of catalyzing a regeneration reaction of the target cofactor subsequent to consumption of the target cofactor by the target enzyme; and• wherein exposing the polymer brush to the conjugated cofactor comprises exposing the enzyme-impregnated polymer brush to the conjugated cofactor to initiate covalent bonding of the conjugated cofactor to the functionalized chain ends of the set of polymer chains to form an enzyme-impregnated, cofactor-functionalized polymer brush.

19. A polymer brush composition comprising:• a substrate;• a set of polymer chains bonded to the substrate via an initiator; and• a target cofactor quantity of a target cofactor covalently bonded to chain ends of the set of polymer chains via a heterobifunctional linker configured to covalently bond to the target cofactor quantity within a non-interactive region of the target cofactor and to the chain ends of the set of polymer chains.

20. The polymer brush composition of Claim 19, characterized by a chain-end cofactor bonding frequency greater than 95%.

21. The polymer brush composition of Claim 19, wherein the set of polymer chains is characterized by a linear conformation.

22. The polymer brush composition of Claim 19, wherein the set of polymer chains is characterized by a dendritic linear hybrid conformation.

23. The polymer brush composition of Claim 19:• wherein the set of polymer chains comprises a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive portion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on: o surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor; and o surface properties of a regenerative enzyme capable of catalyzing a regeneration reaction of the target cofactor subsequent to consumption of the target cofactor by the target enzyme; and• further comprising: o a target enzyme quantity of the target enzyme immobilized within the set of polymer chains via covalent bonding with the reactive proportion of the reactive monomers in the set of polymer chains; and o a regenerative enzyme quantity of the regenerative enzyme immobilized within the set of polymer chains via covalent bonding with the reactive proportion of the reactive monomers in the set of polymer chains.

24. The polymer brush composition of Claim 19:• wherein the set of polymer chains comprises a hydrophobic proportion of hydrophobic monomers, a hydrophilic proportion of hydrophilic monomers, and a reactive portion of reactive monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor; and• further comprising a target enzyme quantity of the target enzyme immobilized within the set of polymer chains via covalent bonding with the reactive proportion of the reactive monomers in the set of polymer chains.

25. The polymer brush composition of Claim 19:• wherein the set of polymer chains comprises a hydrophobic proportion of hydrophobic monomers and a hydrophilic proportion of hydrophilic monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on: o surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor; and o surface properties of a regenerative enzyme capable of catalyzing a regeneration reaction of the target cofactor subsequent to consumption of the target cofactor by the target enzyme; and• further comprising: o a target enzyme quantity of the target enzyme immobilized within the set of polymer chains via surface interactions between the target enzyme and the hydrophobic proportion of the hydrophobic monomers and the hydrophilic proportion of the hydrophilic monomers; and o a regenerative enzyme quantity of the regenerative enzyme immobilized within the set of polymer chains via surface interactions between the regenerative enzyme and the hydrophobic proportion of the hydrophobic monomers and the hydrophilic proportion of the hydrophilic monomers.

26. The polymer brush composition of Claim 19:• wherein the set of polymer chains comprises a hydrophobic proportion of hydrophobic monomers and a hydrophilic proportion of hydrophilic monomers, wherein the hydrophobic proportion and hydrophilic proportion are based on surface properties of a target enzyme capable of catalyzing a reaction with the target cofactor; and• further comprising a target enzyme quantity of the target enzyme immobilized within the set of polymer chains via surface interactions between the target enzyme and the hydrophobic proportion of the hydrophobic monomers and the hydrophilic proportion of the hydrophilic monomers.

27. The polymer brush composition of Claim 19:• wherein the substrate comprises an electrically conductive substrate;• wherein the target cofactor is capable of regeneration via a redox reaction;• further comprising a target enzyme quantity of a target enzyme: o capable of catalyzing a reaction with the target cofactor; and o immobilized within the set of polymer chains.

28. The polymer brush composition of Claim 27, wherein the set of polymer chains is characterized by:• a polydispersity index between 1.20 and 2.00; and• a brush thickness of greater than 1.0 nanometer.

29. The polymer brush composition of Claim 19:• wherein the target cofactor is capable of regeneration via an enzyme-catalyzed regeneration reaction; and• further comprising: o a target enzyme quantity of a target enzyme:■ capable of catalyzing a reaction with the target cofactor; and■ immobilized within the set of polymer chains; and o a regenerative enzyme quantity of a regenerative enzyme:■ capable of catalyzing the enzyme-catalyzed regeneration reaction; and■ immobilized within the set of polymer chains.

30. The polymer brush composition of Claim 29, wherein the set of polymer chains is characterized by:• a polydispersity index between 1.00 and 1.60; and• an average brush thickness less than an average pore radius of the substrate and greater than half of a major diameter of a largest enzyme from among the target enzyme and the regenerative enzyme

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