WO2019145784A2 - Combination therapies for multi-drug resistant pathogens - Google Patents

Abstract

The present invention provides pharmaceutical compositions and methods for treating multi-drug resistant pathogens.

Description

Combination Therapies For Multi-Drug Resistant Pathogens RELATED APPLICATIONS

This application claims the benefit of priority to U.S. Provisional Application U.S.S.N. 62/622,327, filed Jan.26, 2018, the contents of which are incorporated herein by reference in their entirety. BACKGROUND OF THE INVENTION

Bacterial resistance to antibiotics is a serious threat to modern medical care. Bacteria have a remarkable ability to develop resistance to new antibiotics rendering them quickly ineffective. The Centers for Disease Control and Prevention estimate that at least 2 million people become infected with bacteria that are resistant to antibiotics each year in the United States. Patients with multi-drug resistant (MDR) infections often have limited or inadequate therapeutic options leading to high rates of mortality. In 2015, over 23,000 deaths were attributed to be caused by antibiotic resistant infections. The continuing evolution of antibacterial resistance could result in bacterial strains against which currently available antibacterial agents will be ineffective. Therefore, there is a continuing need to develop new antibacterial regimens. SUMMARY OF INVENTION

Provided herein are methods and compositions related to the treatment of an infection (e.g., a gram-negative bacteria infection, a multi-drug resistant gram-negative bacteria infection) in a subject by conjoint administration of a cephalosporin derivative and an inhibitor of β- lactamase.

In some embodiments, the invention provides a pharmaceutical composition comprising a cephalosporin derivative and an inhibitor of β-lactamase. In some embodiments, the

cephalosporin derivative is a compound of Formula (I) or a pharmaceutically acceptable salt, ester, or prodrug thereof

wherein X, Y, L, R, R¹, R², and R³ are as defined herein. In some embodiments, the inhibitor of β-lactamase is a compound having the structure of Formula II or a pharmaceutically acceptable salt thereof:

wherein R⁵ and R⁶ are as defined herein.

In some embodiments, the method comprises conjoint administering to the subject a pharmaceutical composition comprising a cephalosporin derivative and an inhibitor of β- lactamase.

In some embodiments, the method comprises conjointly administering to the subject a cephalosporin derivative and a β-lactamase inhibitor. DETAILED DESCRIPTION OF THE DRAWINGS

Fig.1 is a plot of the change in Log10 CFU at 24 h versus the free-drug AUC0-24h:MIC ratio from a dose-fractionation study of compounds AO + EF .

Fig.2 is a plot of change in Log₁₀ CFU at 24 h versus the free-drug C_max:MIC Ratio from a dose-fractionation study of compounds AO + EF.

Fig.3 is plot of change in Log₁₀ CFU at 24 h versus the free-drug % time > 0.75 mg/L from a dose-fractionation study of compounds AO + EF.

Fig.4 is a plot of change in Log10 CFU at 24 h versus the free-drug AUC0-24h:MIC ratio from a dose-fractionation study of compounds AO + EF. DETAILED DESCRIPTION

The present invention provides combinations of compounds including a cephalosporin derivative and an inhibitor of β-lactamase, as well as methods for treating subjects infected with a pathogen (e.g., multi-drug resistant gram-negative bacteria). The novel combinations provided herein can be formulated into pharmaceutical compositions (e.g., formulations) and medicaments that are useful in the methods of the invention. The invention also provides the use of the novel combinations in preparing medicaments and pharmaceutical formulations, and the use of the combinations in treating infections in a subject. I. COMPOUNDS

In certain embodiments, the cephalosporin derivative is a compound having the structure of Formula I or a pharmaceutically acceptable salt, ester, or prodrug thereof:

wherein X is CR or N;

Y is C1-C2 alkyl, CH(CH3)CO2H, or C(CH3)2CO2H;

L is CH2 or CH=CHCH2;

R is H, chloro or C₁-C₃ alkyl;

R₁ is NH₂, NHR₁₁ or NH(CH₂)_mNR₁₁R₁₂;

R₂ is NHR₂₁, NH(CH₂)_nCOOH, NH(CH₂)_nNR₂₁R₂₂, or NHC(=O)(CH₂)_nNR₂₁R₂₂;

R3 is H or NH2,

R11 and R21 are independently H, C1-C3 alkyl, or a group selected from:

R₁₂ and R₂₂ are each independently H or C₁-C₂ alkyl; and

m and n are each independently an integer from 1 to 6.

In some embodiments, X is CR or N;

Y is C1-C2 alkyl, CH(CH3)CO2H, or C(CH3)2CO2H;

L is CH2 or CH=CHCH2;

R is H, chloro or C1-C3 alkyl;

R1 is NH2, NHR11 or NH(CH2)mNR11R12;

R₂ is NHR₂₁, NH(CH₂)_nNR₂₁R₂₂, or NHC(=O)(CH₂)_nNR₂₁R₂₂;

R₃ is H;

R₁₁ and R₂₁ are independently hydrogen, C₁-C₃ alkyl, or a group selected from:

R₁₂ and R₂₂ are independently hydrogen or C₁-C₂ alkyl; and

m and n are independently an integer of 1 to 6

In some embodiments, wherein

X is CR or N;

Y is CH(CH3)CO2H or C(CH3)2CO2H;

L is CH2 or CH=CHCH2;

R is H, chloro or C1-C3 alkyl;

R1 is NH2 or NH(CH2)mNH2;

R₂ is NHR₂₁, NH(CH₂)_nNR₂₁, or NHC(=O)(CH₂)_nNR₂₁; and

R₃ is H;

R₂₁ is a group selected from:

m an

d n are independently an integer of 1 to 6.

In some embodiments, the cephalosporin derivative is a compound represented by one of the chemical formulas in Table 1.

Table 1: Exemplary cephalosporin derivatives

Representative cephalosporin derivatives are disclosed in U.S. Patent 8,329,684 and U.S. Patent PuEFcation No.2012-0264727, both of which are hereby incorporated by reference herein in their entireties, and in particular for the compounds and compositions disclosed therein.

In certain embodiments, the inhibitor of β-lactamase is a compound having the structure of Formula II or a pharmaceutically acceptable salt thereof:

wherein R⁵ and R⁶ are independently selected from H, hydroxyalkyl, -C(O)-NH₂, amido-, amino-, or guanidino-substituted alkyl, amido-, amino-, or guanidino-substituted alkoxyalkyl, and - (CH₂)_p-O-NHR⁷, or

R⁵ and R⁶ combine to form an amino-, or guanidino-substituted cycloalkyl ring, or an optionally substituted nitrogen-containing heterocyclyl ring;

p is an integer from 1 to 6; and

R⁷ is, independently for each occurrence, selected from H, lower alkyl, and -C(=NH)NH2.

In some embodiments, at least one of R⁵ and R⁶ is independently selected from

wherein p is an integer from 1 to 5.

In some embodiments, R⁵ and R⁶ combine to form a structure of Formula A

A

wherein

Y and Z are each independently CHR⁸, NR⁹, or absent;

R⁸ is, independently for each occurrence, selected from H, amido-, amino-, or guanidino- substituted lower alkyl, and NHR³;

R⁹ is, independently for each occurrence, selected from H, amido-, amino-, or guanidino- substituted lower alkyl and -C(=NH)NH₂; and

m and n are each independently an integer from 1 to 3;

provided that both Y and Z are not absent.

In some embodiments, the inhibitor of β-lactamase is a compound having the structure of formula III or a pharmaceutically acceptable salt thereof:

and R¹ is an amido-, amino- or guanidino substituted alkyl, an amido-, amino-, guanidino- substituted alkoxyalkyl, or -(CH₂)_p-O-NHR⁷.

In some embodiments, the inhibitor of β-lactamase is a compound having the structure of formula IV or a pharmaceutically acceptable salt thereof:

and m is less than or equal to n.

In some embodiments, the inhibitor of β-lactamase is a compound selected from

Table 2.

Table 2: Exemplary compounds of Formula II

Representative inhibitors of β-lactamase are disclosed in U.S. Patent PuEFcation No. 2017-0096430, which is hereby incorporated by reference herein in its entirety, and in particular for the compounds and compositions disclosed therein. II. PHARMACEUTICAL COMPOSITIONS In one aspect, disclosed herein is a pharmaceutical composition comprising a cephalosporin derivative and an inhibitor of β-lactamase. In some embodiments, the

pharmaceutical composition further comprises a pharmaceutically acceptable carrier.

This invention includes the use of pharmaceutically acceptable salts of the compounds of the invention in the compositions and methods disclosed herein. In certain embodiments, contemplated salts of the invention include, but are not limited to, alkyl, dialkyl, trialkyl or tetra- alkyl ammonium salts. In certain embodiments, contemplated salts of the invention include, but are not limited to, L-arginine, benenthamine, benzathine, betaine, calcium hydroxide, choline, deanol, diethanolamine, diethylamine, 2-(diethylamino)ethanol, ethanolamine, ethylenediamine, N-methylglucamine, hydrabamine, 1H-imidazole, lithium, L-lysine, magnesium, 4-(2- hydroxyethyl)morpholine, piperazine, potassium, 1-(2-hydroxyethyl)pyrrolidine, sodium, triethanolamine, tromethamine, and zinc salts. In certain embodiments, contemplated salts of the invention include, but are not limited to, Na, Ca, K, Mg, Zn or other metal salts. In certain embodiments, pharmaceutically acceptable salts include salts of compounds and their prodrugs derived from the combination of a compound and an organic or inorganic acid or base. Suitable acids include acetic acid, adipic acid, benzenesulfonic acid, (+)-7,7-dimethyl-2- oxobicyclo[2.2.l]heptane-l-methane sulfonic acid, citric acid, 1,2-ethanedisulfonic acid, dodecyl sulfonic acid, fumaric acid, glucoheptonic acid, gluconic acid, glucuronic acid, hippuric acid, HBr, HCl, HI, 2-hydroxyethanesulfonic acid, lactic acid, lactobionic acid, maleic acid, methane sulfonic acid, methylbromide acid, methyl sulfuric acid, 2-naphthalenesulfonic acid, nitric acid, oleic acid, 4,4‘ methylenebis[3-hydroxy-2-naphthalenecarboxylic acid], phosphoric acid, polygalacturonic acid, stearic acid, succinic acid, sulfuric acid, sulfosalicylic acid, tannic acid, tartaric acid, terphthalic acid, and p-toluenesulfonic acid.

The pharmaceutically acceptable acid addition salts can also exist as various solvates, such as with water, methanol, ethanol, dimethylformamide, and the like. Mixtures of such solvates can also be prepared. The source of such solvate can be from the solvent of

crystallization, inherent in the solvent of preparation or crystallization, or adventitious to such solvent.

The compositions and methods of the present invention may be utilized to treat an individual in need thereof. In certain embodiments, the individual is a mammal such as a human, or a non-human mammal. When administered to an animal, such as a human, the composition is preferably administered as a single pharmaceutical composition or paired pharmaceutical compositions together comprising, for example, a cephalosporin derivative and an inhibitor of β- lactamase combination and a pharmaceutically acceptable carrier. For example, the different therapeutic compounds can be administered either in the same formulation or in a separate formulation, either concomitantly or sequentially.

In another aspect, disclosed herein is a method of preparing a pharmaceutical composition for parenteral administration, comprising combining separate pharmaceutical compositions and optionally a pharmaceutically acceptable carrier. For example, a

pharmaceutical composition comprising a cephalosporin derivative may be combined with a pharmaceutical composition comprising an inhibitor of β-lactamase and optionally a diluent, such as an aqueous solution (e.g., saline solution), to prepare a pharmaceutical composition suitable for parenteral administration (e.g., intravenous).

Pharmaceutically acceptable carriers are well known in the art and include, for example, aqueous solutions such as water or physiologically buffered saline or other solvents or vehicles such as glycols, glycerol, oils such as olive oil, or injectable organic esters. In preferred embodiments, when such pharmaceutical compositions are for human administration, particularly for invasive routes of administration (i.e., routes, such as injection or implantation, that circumvent transport or diffusion through an epithelial barrier), the composition is pyrogen- free, or substantially pyrogen-free. The excipients can be chosen, for example, to effect delayed release of an agent or to selectively target one or more cells, tissues or organs. The

pharmaceutical composition can be in dosage unit form such as tablet, capsule (including sprinkle capsule and gelatin capsule), granule, lyophile for reconstitution, powder, solution, syrup, suppository, injection or the like. The composition can also be present in a transdermal delivery system, e.g., a skin patch. The composition can also be present in a solution suitable for topical administration, such as an eye drop.

A pharmaceutically acceptable carrier can contain physiologically acceptable agents that act, for example, to stabilize, increase solubility or to increase the absorption of a compound such as a cephalosporin derivative and an inhibitor of β-lactamase combination of the invention. Such physiologically acceptable agents include, for example, carbohydrates, such as glucose, sucrose or dextrans, antioxidants, such as ascorbic acid or glutathione, chelating agents, low molecular weight proteins or other stabilizers or excipients. The choice of a pharmaceutically acceptable carrier, including a physiologically acceptable agent, depends, for example, on the route of administration of the composition. The preparation or pharmaceutical composition can be a self- emulsifying drug delivery system or a self-microemulsifying drug delivery system. The pharmaceutical composition (preparation) also can be a liposome or other polymer matrix, which can have incorporated therein, for example, an inhibitor and/or agent combination of the invention. Liposomes, for example, which comprise phospholipids or other lipids, are nontoxic, physiologically acceptable and metabolizable carriers that are relatively simple to make and administer.

The phrase "pharmaceutically acceptable" is employed herein to refer to those compounds, materials, compositions, and/or dosage forms which are, within the scope of sound medical judgment, suitable for use in contact with the tissues of human beings and animals without excessive toxicity, irritation, allergic response, or other problem or complication, commensurate with a reasonable benefit/risk ratio.

The phrase "pharmaceutically acceptable carrier" as used herein means a

pharmaceutically acceptable material, composition or vehicle, such as a liquid or solid filler, diluent, excipient, solvent or encapsulating material. Each carrier must be "acceptable" in the sense of being compatible with the other ingredients of the formulation and not injurious to the patient. Some examples of materials which can serve as pharmaceutically acceptable carriers include: (1) sugars, such as lactose, glucose and sucrose; (2) starches, such as corn starch, pregelatinized starch and potato starch; (3) cellulose, and its derivatives, such as hydroxypropyl methyl cellulose, hydroxypropyl cellulose, hydroxylethyl cellulose, microcrystalline cellulose, sodium carboxymethyl cellulose, methyl cellulose, ethyl cellulose and cellulose acetate; (4) powdered tragacanth; (5) malt; (6) gelatin; (7) talc; (8) excipients, such as cocoa butter and suppository waxes; (9) oils, such as peanut oil, cottonseed oil, safflower oil, sesame oil, olive oil, corn oil and soybean oil; (10) glycols, such as propylene glycol; (11) polyols, such as glycerin, sorbitol, mannitol, xylitol and polyethylene glycol; (12) esters, such as ethyl oleate and ethyl laurate; (13) agar; (14) buffering agents, such as magnesium hydroxide and aluminum

hydroxide; (15) alginic acid and its salts; (16) pyrogen-free water; (17) isotonic saline; (18) Ringer's solution; (19) ethyl alcohol; (20) phosphate buffer solutions; and (21) other non-toxic compatible substances employed in pharmaceutical formulations. A pharmaceutical composition (preparation) can be administered to a subject by any of a number of routes of administration including, for example, orally (for example, drenches as in aqueous or non-aqueous solutions or suspensions, tablets, disintegrating tablets, capsules (including sprinkle capsules and gelatin capsules), boluses, powders, granules, pastes for application to the tongue); absorption through the oral mucosa (e.g., suEFngually); anally, rectally or vaginally (for example, as a pessary, cream or foam); parenterally (including intramuscularly, intravenously, subcutaneously or intrathecally as, for example, a sterile solution or suspension); nasally; intraperitoneally; subcutaneously; transdermally (for example as a patch applied to the skin); and topically (for example, as a cream, ointment or spray applied to the skin, or as an eye drop). The compound may also be formulated for inhalation. In certain

embodiments, a compound may be simply dissolved or suspended in sterile water. Details of appropriate routes of administration and compositions suitable for same can be found in, for example, U.S. Pat. Nos.6,110,973, 5,763,493, 5,731,000, 5,541,231, 5,427,798, 5,358,970 and 4,172,896, as well as in patents cited therein. In some embodiments, intravenous routes of administration are preferred.

The formulations may conveniently be presented in unit dosage form and may be prepared by any methods well known in the art of pharmacy. The amount of active ingredient which can be combined with a carrier material to produce a single dosage form will vary depending upon the host being treated and/or the particular mode of administration. The amount of active ingredient that can be combined with a carrier material to produce a single dosage form will generally be that amount of the compound which produces a therapeutic effect. Generally, out of one hundred percent, this amount will range from about 1 percent to about ninety-nine percent of active ingredient, preferably from about 5 percent to about 70 percent, most preferably from about 10 percent to about 30 percent.

Methods of preparing these formulations or compositions include the step of bringing into association an active compound, such as a cephalosporin derivative and an inhibitor of β- lactamase combination of the invention, with the carrier and, optionally, one or more accessory ingredients. In general, the formulations are prepared by uniformly and intimately bringing into association a cephalosporin derivative and an inhibitor of β-lactamase combination of the present invention with liquid carriers, or finely divided solid carriers, or both, and then, if necessary, shaping the product. Formulations of the invention suitable for parental administration (e.g., intravenous) may be in the form of a pharmaceutically effective unit dose of the cephalosporin derivative and inhibitor of β-lactamase or a pharmaceutical composition disclosed herein provided in solution in a container. Exemplary containers include but are not limited to a vial, a mono vial, an ampoule, a syringe, a packet, a pouch, an IV bag and an auto-injector.

Formulations of the invention suitable for oral administration may be in the form of capsules (including sprinkle capsules and gelatin capsules), cachets, pills, tablets, lozenges (using a flavored basis, usually sucrose and acacia or tragacanth), lyophile, powders, granules, or as a solution or a suspension in an aqueous or non-aqueous liquid, or as an oil-in-water or water- in-oil liquid emulsion, or as an elixir or syrup, or as pastilles (using an inert base, such as gelatin and glycerin, or sucrose and acacia) and/or as mouth washes and the like, each containing a predetermined amount of a cephalosporin derivative and an inhibitor of β-lactamase combination of the present invention as active ingredients. Compositions or compounds may also be administered as a bolus, electuary or paste.

To prepare solid dosage forms for oral administration (capsules (including sprinkle capsules and gelatin capsules), tablets, pills, dragees, powders, granules and the like), the active ingredient is mixed with one or more pharmaceutically acceptable carriers, such as sodium citrate or dicalcium phosphate, and/or any of the following: (1) fillers or extenders, such as starches, lactose, sucrose, glucose, mannitol, and/or silicic acid; (2) binders, such as, for example, carboxymethylcellulose, alginates, gelatin, polyvinyl pyrrolidone, hydroxypropyl cellulose, hydroxypropyl methylcellulose, sucrose and/or acacia; (3) humectants, such as glycerol; (4) disintegrating agents, such as sodium starch glycolate, croscarmellose sodium, crospovidone, carboxymethylcellulose calcium, agar-agar, calcium carbonate, potato or tapioca starch, alginic acid, certain silicates, and sodium carbonate; (5) solution retarding agents, such as paraffin; (6) absorption accelerators, such as quaternary ammonium compounds; (7) wetting agents, such as, for example, polyoxyethylene-polyoxypropylene copolymer, cetyl alcohol and glycerol monostearate; (8) absorbents, such as kaolin and bentonite clay; (9) lubricants, such as talc, calcium stearate, magnesium stearate, solid polyethylene glycols, sodium lauryl sulfate, and mixtures thereof; (10) complexing agents, such as, modified and unmodified cyclodextrins; (11) coloring agents; and (12) controlled release agents, such as hydroxypropyl methylcellulose, polyethylene oxide, polyvinyl acetate, polyvinyl alcohol and polymethacrylate copolymers . In the case of capsules (including sprinkle capsules and gelatin capsules), tablets and pills, the pharmaceutical compositions may also comprise buffering agents. Solid compositions of a similar type may also be employed as fillers in soft and hard-filled gelatin capsules using such excipients as lactose or milk sugars, as well as high molecular weight polyethylene glycols and the like.

A tablet may be made by compression or molding, optionally with one or more accessory ingredients. Compressed tablets may be prepared using binder (for example, gelatin or hydroxypropylmethyl cellulose), lubricant, inert diluent, preservative, disintegrant (for example, sodium starch glycolate or cross-linked sodium carboxymethyl cellulose), surface-active or dispersing agent. Molded tablets may be made by molding in a suitable machine a mixture of the powdered compound moistened with an inert liquid diluent.

The tablets, and other solid dosage forms of the pharmaceutical compositions, such as dragees, capsules (including sprinkle capsules and gelatin capsules), pills and granules, may optionally be scored or prepared with coatings and shells, such as enteric coatings and other coatings well known in the pharmaceutical-formulating art. They may also be formulated so as to provide slow or controlled release of the active ingredient therein using, for example, hydroxypropylmethyl cellulose in varying proportions to provide the desired release profile, other polymer matrices, liposomes and/or microspheres. They may be sterilized by, for example, filtration through a bacteria-retaining filter, or by incorporating sterilizing agents in the form of sterile solid compositions that can be dissolved in sterile water, or some other sterile injectable medium immediately before use. These compositions may also optionally contain opacifying agents and may be of a composition that they release the active ingredient(s) only, or preferentially, in a certain portion of the gastrointestinal tract, optionally, in a delayed manner. Examples of embedding compositions that can be used include polymeric substances and waxes. The active ingredient can also be in micro-encapsulated form, if appropriate, with one or more of the above-described excipients.

Liquid dosage forms useful for oral administration include pharmaceutically acceptable emulsions, lyophiles for reconstitution, microemulsions, solutions, suspensions, syrups and elixirs. In addition to the active ingredient, the liquid dosage forms may contain inert diluents commonly used in the art, such as, for example, water or other solvents, cyclodextrins and derivatives thereof, solubilizing agents and emulsifiers, such as ethyl alcohol, isopropyl alcohol, ethyl carbonate, ethyl acetate, benzyl alcohol, benzyl benzoate, propylene glycol, 1,3-butylene glycol, oils (in particular, cottonseed, groundnut, corn, germ, olive, castor and sesame oils), glycerol, tetrahydrofuryl alcohol, polyethylene glycols and fatty acid esters of sorbitan, and mixtures thereof.

Besides inert diluents, the oral compositions can also include adjuvants such as wetting agents, emulsifying and suspending agents, sweetening, flavoring, coloring, perfuming and preservative agents.

Suspensions, in addition to the active compounds, may contain suspending agents as, for example, ethoxylated isostearyl alcohols, polyoxyethylene sorbitol and sorbitan esters, microcrystalline cellulose, aluminum metahydroxide, bentonite, agar-agar and tragacanth, and mixtures thereof.

Formulations of the pharmaceutical compositions for administration to the mouth may be presented as a mouthwash, or an oral spray, or an oral ointment.

Formulations of the pharmaceutical compositions for rectal, vaginal, or urethral administration may be presented as a suppository, which may be prepared by mixing one or more active compounds with one or more suitable nonirritating excipients or carriers comprising, for example, cocoa butter, polyethylene glycol, a suppository wax or a salicylate, and which is solid at room temperature, but liquid at body temperature and, therefore, will melt in the rectum or vaginal cavity and release the active compound.

Formulations which are suitable for vaginal administration also include pessaries, tampons, creams, gels, pastes, foams or spray formulations containing such carriers as are known in the art to be appropriate.

Alternatively or additionally, compositions can be formulated for delivery via a catheter, stent, wire, or other intraluminal device. Delivery via such devices may be especially useful for delivery to the bladder, urethra, ureter, rectum, or intestine.

Dosage forms for the topical administration include powders, sprays, ointments, pastes, creams, lotions, gels, solutions, patches and inhalants. The active compound(s) may be mixed under sterile conditions with a pharmaceutically acceptable carrier, and with any preservatives, buffers, or propellants that may be required.

The ointments, pastes, creams and gels may contain, in addition to an active compound, excipients, such as animal and vegetable fats, oils, waxes, paraffins, starch, tragacanth, cellulose derivatives, polyethylene glycols, silicones, bentonites, silicic acid, talc and zinc oxide, or mixtures thereof.

Powders and sprays can contain, in addition to an active compound, excipients such as lactose, talc, silicic acid, aluminum hydroxide, calcium silicates and polyamide powder, or mixtures of these substances. Sprays can additionally contain customary propellants, such as chlorofluorohydrocarbons and volatile unsubstituted hydrocarbons, such as butane and propane.

Examples of suitable aqueous and nonaqueous carriers that may be employed in the pharmaceutical compositions of the invention include water, ethanol, polyols (such as glycerol, propylene glycol, polyethylene glycol, and the like), and suitable mixtures thereof, vegetable oils, such as olive oil, and injectable organic esters, such as ethyl oleate. Proper fluidity can be maintained, for example, by the use of coating materials, such as lecithin, by the maintenance of the required particle size in the case of dispersions, and by the use of surfactants.

These compositions may also contain adjuvants such as preservatives, wetting agents, emulsifying agents and dispersing agents. Prevention of the action of microorganisms may be ensured by the inclusion of various antibacterial and antifungal agents, for example, paraben, chlorobutanol, phenol sorbic acid, and the like. It may also be desirable to include isotonic agents, such as sugars, sodium chloride, and the like into the compositions. In addition, prolonged absorption of the injectable pharmaceutical form may be brought about by the inclusion of agents that delay absorption such as aluminum monostearate and gelatin.

For use in the methods of this invention, active compounds can be given per se or as a pharmaceutical composition containing, for example, 0.1 to 99.5% (more preferably, 0.5 to 90%) of active ingredient in combination with a pharmaceutically acceptable carrier.

Actual dosage levels of the active ingredients in the pharmaceutical compositions may be varied so as to obtain an amount of the active ingredient that is effective to achieve the desired therapeutic response for a particular patient, composition, and mode of administration, without being toxic to the patient.

The selected dosage level will depend upon a variety of factors including the activity of the particular compound or combination of compounds employed, or the ester, salt or amide thereof, the route of administration, the time of administration, the rate of excretion of the particular compound(s) being employed, the duration of the treatment, other drugs, compounds and/or materials used in combination with the particular compound(s) employed, the age, sex, weight, condition, general health and prior medical history of the patient being treated, and like factors well known in the medical arts.

A physician or veterinarian having ordinary skill in the art can readily determine and prescribe the therapeutically effective amount of the pharmaceutical composition required. For example, the physician or veterinarian could start doses of the pharmaceutical composition or compound at levels lower than that required in order to achieve the desired therapeutic effect and gradually increase the dosage until the desired effect is achieved. By“therapeutically effective amount” is meant the concentration of a compound that is sufficient to elicit the desired therapeutic effect. It is generally understood that the effective amount of the compound will vary according to the weight, sex, age, and medical history of the subject. Other factors which influence the effective amount may include, but are not limited to, the severity of the patient's condition, the disorder being treated, the stability of the compound, and, if desired, another type of therapeutic agent being administered with the compounds of the invention. A larger total dose can be delivered by multiple administrations of the agent. Methods to determine efficacy and dosage are known to those skilled in the art (Isselbacher et al. (1996) Harrison’s Principles of Internal Medicine 13 ed., 1814-1882, herein incorporated by reference).

In general, a suitable daily dose of an active compound used in the compositions and methods of the invention will be that amount of the compound that is the lowest dose effective to produce a therapeutic effect. Such an effective dose will generally depend upon the factors described above. In certain embodiments, a suitable daily dose is between from about

0.1 g/day to about 50 g/day, from about 0.1 g/day to about 25 g/day, from about 0.1 g/day to about 20 g/day, from about 0.1 g/day to about 18 g/day, from about 0.1 g/day to about 16 g/day, from about 0.1 g/day to about 14 g/day, from about 0.1 g/day to about 12 g/day, from about 0.1 g/day to about 10 g/day, from about 0.1 g/day to about 8 g/day, f from about 0.1 g/day to about 6 g/day, from about 0.1 g/day to about 4 g/day, from about 0.5 g/day to about 50 g/day, from about 0.5 g/day to about 25 g/day, from about 0.5 g/day to about 20 g/day, from about 0.5 g/day to about 18 g/day, from about 0.5 g/day to about 16 g/day, from about 0.5 g/day to about 14 g/day, from about 0.5 g/day to about 12 g/day, from about 0.5 g/day to about 10 g/day, from about 0.5 g/day to about 8 g/day, from about 0.5 g/day to about 6 g/day, from about 0.5 g/day to about 4 g/day, from about 1 g/day to about 50 g/day, from about 1 g/day to about 25 g/day, from about 1 g/day to about 20 g/day, from about 1 g/day to about 18 g/day, from about 1 g/day to about 16 g/day, from about 1 g/day to about 14 g/day, from about 1 g/day to about 12 g/day, from about 1 g/day to about 10 g/day, from about 1 g/day to about 8 g/day, from about 1 g/day to about 6 g/day, from about 1 g/day to about 4 g/day, from about 2 g/day to about 50 g/day, from about 2 g/day to about 25 g/day, from about 2 g/day to about 20 g/day, from about 2 g/day to about 18 g/day, from about 2 g/day to about 16 g/day, from about 2 g/day to about 14 g/day, from about 2 g/day to about 12 g/day, from about 2 g/day to about 10 g/day, from about 2 g/day to about 8 g/day, from about 2 g/day to about 6 g/day, or from about 2 g/day to about 4 g/day. In certain embodiments, a suitable daily dose is between from about 1 g/day to about 16 g/day, from about 1 g/day to about 14 g/day, from about 2 g/day to about 16 g/day, from about 2 g/day to about 14 g/day, from about 2 g/day to about 12 g/day, or from about 2 g/day to about 10 g/day.

In certain embodiments, a suitable daily dose is about 25, 20, 15, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 g/day, preferably about 6 g/day.

The dose may be administered in as many divided doses as is convenient. If desired, the effective daily dose of the active compounds may be administered as one, two, three, four, five, six or more sub-doses administered separately at appropriate intervals throughout the day, optionally, in unit dosage forms. In certain embodiments of the present invention, the active compounds may be administered one, two, three or four times daily. In preferred embodiments, the active compound will be administered 4 times daily.

The compounds of the invention may administered by parental injection, e.g., by continuous infusion or bolus injection. For example, a compound can be constantly or repeatedly administered in small amounts, e.g., at least every hour over the treatment period, such that the serum levels of the compound do not fluctuate widely over the course of administration, e.g., to achieve a substantially steady state serum level of the active compound for the duration of treatment. For continuous infusion, an intravenous drip, a pulsatile electronic syringe driver, a portable syringe pump, or a constant infusion pump may be employed.

The compounds of the invention (e.g., cephalosporin derivative, a β-lactamase inhibitor) may be administered simultaneously or sequentially in separate unit dosage forms or together in a single unit dosage form. In certain embodiments, relative amounts of compounds when combined in a single unit dosage form can be described as a weight ratio. For example, the composition may be formulated such that the weight ratio of the cephalosporin derivative to the inhibitor of β-lactamase is in the range from about 1:6 to about 6:1, preferably from about 1:5 to about 5:1, and even more preferably from about 4:1 to about 1:4.

The patient receiving this treatment may be any animal in need, including primates, in particular humans, and other mammals such as equines, cattle, swine and sheep; and poultry and pets in general.

Wetting agents, emulsifiers and lubricants, such as sodium lauryl sulfate and magnesium stearate, as well as coloring agents, release agents, coating agents, sweetening, flavoring and perfuming agents, preservatives and antioxidants can also be present in the compositions.

Examples of pharmaceutically acceptable antioxidants include: (1) water-soluble antioxidants, such as ascorbic acid, cysteine hydrochloride, sodium bisulfate, sodium

metabisulfite, sodium sulfite and the like; (2) oil-soluble antioxidants, such as ascorbyl palmitate, butylated hydroxyanisole (BHA), butylated hydroxytoluene (BHT), lecithin, propyl gallate, alpha-tocopherol, and the like; and (3) metal-chelating agents, such as citric acid,

ethylenediamine tetraacetic acid (EDTA), sorbitol, tartaric acid, phosphoric acid, and the like.

An effective amount of the composition may be administered in a single dose per day or in fractional doses over the day, for example two to three times a day. By way of example, the administration of a composition according to the invention may be performed at a rate, for example, of 3 times a day or more, generally over a prolonged period of at least a week, 2 weeks, 3 weeks, 4 weeks, or even 4 to 15 weeks, optionally comprising one or more periods of stoppage or being repeated after a period of stoppage. As one of skill in the art will appreciate,

compositions of the present invention, not having adverse effects upon administration to a subject, may be administered daily to the subject.

Preferred embodiments of this invention are described herein. Of course, variations, changes, modifications and substitution of equivalents of those preferred embodiments will become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations, changes, modifications and substitution of equivalents as appropriate, and the inventors intend for the invention to be practiced otherwise than specifically described herein. Those of skill in the art will readily recognize a variety of non-critical parameters that could be changed, altered or modified to yield essentially similar results. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly

contradicted by context.

While each of the elements of the present invention is described herein as containing multiple embodiments, it should be understood that, unless indicated otherwise, each of the embodiments of a given element of the present invention is capable of being used with each of the embodiments of the other elements of the present invention and each such use is intended to form a distinct embodiment of the present invention. III. METHODS

In certain aspects, the invention provides methods for treating an infection (e.g., a gram- negative bacterial infection), comprising administering a pharmaceutical composition to a subject in need of treatment. The pharmaceutical compositions disclosed herein are useful in treating an infection from a multi-drug resistant pathogen (e.g., a gram-negative bacteria).

In another aspect, the invention provides methods of treating an infection (e.g., a gram- negative bacterial infection) in a subject in need thereof, comprising conjointly administering to the subject a cephalosporin derivative and a β-lactamase inhibitor. As used herein, the phrase “conjoint administration” and“conjointly administering” refers to any form of administration of two or more different therapeutic compounds such that the second compound is administered while the previously administered therapeutic compound is still effective in the body (e.g., the two compounds are simultaneously effective in the patient, which may include synergistic effects of the two compounds). For example, the different therapeutic compounds can be administered either in the same formulation or in a separate formulation, either concomitantly or sequentially. In certain embodiments, the different therapeutic compounds can be administered within one hour, 12 hours, 24 hours, 36 hours, 48 hours, 72 hours, or a week of one another. Thus, an individual who receives such treatment can benefit from a combined effect of different therapeutic compounds. Because the β-lactamase inhibitor serves to inhibit degradation of the cephalosporin derivative, preferably the β-lactamase inhibitor is administered prior to, or at least concurrently with, the cephalosporin derivative, so as to be in effect at or close to the time that cephalosporin derivative is absorbed. In one aspect, the infection may refer to a bacterial infection of any organ or tissue in the body caused by a pathogen, preferably, Gram-negative bacteria. These organs or tissue include, without limitation, skeletal muscle, skin, bloodstream, kidneys, heart, lung and bone. For example, a composition of the invention, can be administered to a subject to treat, without limitation, skin and soft tissue infections (e.g., complex skin infections), bacteremia, intra- abdominal infections and urinary tract infections (e.g., UTI). In addition, a composition of the invention may be used to treat community acquired respiratory infections, including, without limitation, otitis media, sinusitis, chronic bronchitis and pneumonia (including community- acquired pneumonia, hospital-acquired pneumonia and ventilator associated pneumonia), including pneumonia caused by drug-resistant Pseudomonas aeruginosa. In certain embodiments, a composition of the invention, can be administered to a subject to treat mixed infections that comprise different types of Gram-negative bacteria, or which comprise both Gram-positive and Gram-negative bacteria. These types of infections include intra-abdominal infections and obstetrical/gynecological infections In certain embodiments, a composition of the invention may also be administered to a subject to treat an infection including, without limitation, endocarditis, nephritis, septic arthritis, intra-abdominal sepsis, bone and joint infections and osteomyelitis. In certain embodiments, a composition of the invention may also be directly injected or

administered into an abscess, ventricle or joint.

In some embodiments, the infection may be a gynecological infection, a respiratory tract infection (RTI), a sexually transmitted disease, syphilis, a urinary tract infection, an acute exacerbation of chronic bronchitis (ACEB), acute otitis media, acute sinusitis, an infection caused by drug resistant bacteria, sepsis, catheter-related sepsis, chancroid, chlamydia, community-acquired pneumonia (CAP), a complicated skin and skin structure infection, a uncomplicated skin and skin structure infection, endocarditis, febrile neutropenia, gonococcal cervicitis, gonococcal urethritis, hospital-acquired pneumonia (HAP), osteomyelitis, or an intra- abdominal infection (IAI).

In certain embodiments, infection may refer to an infection caused by Gram-negative bacteria, also referred to as a "Gram-negative infection." In one aspect, the Gram-negative infection is an infection resistant to one or more antibiotics. In one aspect, the Gram-negative infection is a multi-drug resistant infection. Representative Gram-negative pathogens known to express β-lactamases include, but are not limited to Acinetobacter spp. (including Acinetobacter baumannii), Citrobacter spp., Escherichia spp. (including Escherichia coli), Haemophilus influenzae, Morganella morganii, Pseudomonas aeruginosa, Klebsiella spp. (including

Klebsiella pneumoniae), Enterobacter spp. (including Enterobacter cloacae and Enterobacter aerogenes), Pasteurella spp., Proteus spp. (including Proteus mirabilis), Serratia spp. (including Serratia marcescens), and Providencia spp. Bacterial infections can be caused or exacerbated by Gram-negative bacteria including strains which express β-lactamases that may confer resistance to penicillins, cephalosporins, monobactams and/or carbapenems.

In certain embodiments, the subject is a mammal, e.g., a human. IV. DEFINITIONS

The term“acyl” is art-recognized and refers to a group represented by the general formula hydrocarbylC(O)-, preferably alkylC(O)-.

The term“acylamino” is art-recognized and refers to an amino group substituted with an acyl group and may be represented, for example, by the formula hydrocarbylC(O)NH-.

The term“acyloxy” is art-recognized and refers to a group represented by the general formula hydrocarbylC(O)O-, preferably alkylC(O)O-.

The term“alkoxy” refers to an alkyl group, preferably a lower alkyl group, having an oxygen attached thereto. Representative alkoxy groups include methoxy, ethoxy, propoxy, tert- butoxy and the like.

The term“alkoxyalkyl” refers to an alkyl group substituted with an alkoxy group and may be represented by the general formula alkyl-O-alkyl.

The term“alkenyl”, as used herein, refers to an aliphatic group containing at least one double bond and is intended to include both "unsubstituted alkenyls" and "substituted alkenyls", the latter of which refers to alkenyl moieties having substituents replacing a hydrogen on one or more carbons of the alkenyl group. Such substituents may occur on one or more carbons that are included or not included in one or more double bonds. Moreover, such substituents include all those contemplated for alkyl groups, as discussed below, except where stability is prohibitive. For example, substitution of alkenyl groups by one or more alkyl, carbocyclyl, aryl, heterocyclyl, or heteroaryl groups is contemplated.

An“alkyl” group or“alkane” is a straight chained or branched non-aromatic hydrocarbon which is completely saturated. Typically, a straight chained or branched alkyl group has from 1 to about 20 carbon atoms, preferably from 1 to about 10 unless otherwise defined. Examples of straight chained and branched alkyl groups include methyl, ethyl, n-propyl, iso-propyl, n-butyl, sec-butyl, tert-butyl, pentyl, hexyl, pentyl and octyl. A C₁-C₆ straight chained or branched alkyl group is also referred to as a "lower alkyl" group.

Moreover, the term "alkyl" (or "lower alkyl") as used throughout the specification, examples, and claims is intended to include both "unsubstituted alkyls" and "substituted alkyls", the latter of which refers to alkyl moieties having substituents replacing a hydrogen on one or more carbons of the hydrocarbon backbone. Such substituents, if not otherwise specified, can include, for example, a halogen, a hydroxyl, a carbonyl (such as a carboxyl, an alkoxycarbonyl, a formyl, or an acyl), a thiocarbonyl (such as a thioester, a thioacetate, or a thioformate), an alkoxyl, a phosphoryl, a phosphate, a phosphonate, a phosphinate, an amino, an amido, an amidine, an imine, a cyano, a nitro, an azido, a sulfhydryl, an alkylthio, a sulfate, a sulfonate, a sulfamoyl, a sulfonamido, a sulfonyl, a heterocyclyl, an aralkyl, or an aromatic or heteroaromatic moiety. It will be understood by those skilled in the art that the moieties substituted on the hydrocarbon chain can themselves be substituted, if appropriate. For instance, the substituents of a substituted alkyl may include substituted and unsubstituted forms of amino, azido, imino, amido, phosphoryl (including phosphonate and phosphinate), sulfonyl (including sulfate, sulfonamido, sulfamoyl and sulfonate), and silyl groups, as well as ethers, alkylthios, carbonyls (including ketones, aldehydes, carboxylates, and esters), -CF₃, -CN and the like. Exemplary substituted alkyls are described below. Cycloalkyls can be further substituted with alkyls, alkenyls, alkoxys, alkylthios, aminoalkyls, carbonyl-substituted alkyls, -CF3, -CN, and the like.

The term“Cx-y” when used in conjunction with a chemical moiety, such as, acyl, acyloxy, alkyl, alkenyl, alkynyl, or alkoxy is meant to include groups that contain from x to y carbons in the chain. For example, the term“C_x-yalkyl” refers to substituted or unsubstituted saturated hydrocarbon groups, including straight-chain alkyl and branched-chain alkyl groups that contain from x to y carbons in the chain, including haloalkyl groups such as trifluoromethyl and 2,2,2- trifluoroethyl, etc. C0 alkyl indicates a hydrogen where the group is in a terminal position, a bond if internal. The terms“C2-yalkenyl” and“C2-yalkynyl” refer to substituted or unsubstituted unsaturated aliphatic groups analogous in length and possible substitution to the alkyls described above, but that contain at least one double or triple bond respectively. The term“alkylamino”, as used herein, refers to an amino group substituted with at least one alkyl group.

The term“alkylthio”, as used herein, refers to a thiol group substituted with an alkyl group and may be represented by the general formula alkylS-.

The term“alkynyl”, as used herein, refers to an aliphatic group containing at least one triple bond and is intended to include both "unsubstituted alkynyls" and "substituted alkynyls", the latter of which refers to alkynyl moieties having substituents replacing a hydrogen on one or more carbons of the alkynyl group. Such substituents may occur on one or more carbons that are included or not included in one or more triple bonds. Moreover, such substituents include all those contemplated for alkyl groups, as discussed above, except where stability is prohibitive. For example, substitution of alkynyl groups by one or more alkyl, carbocyclyl, aryl, heterocyclyl, or heteroaryl groups is contemplated.

The term“amide”, as used herein, refers to a group

wherein each R¹⁰⁰ independently represent a hydrogen or hydrocarbyl group, or two R¹⁰⁰ are taken together with the N atom to which they are attached complete a heterocycle having from 4 to 8 atoms in the ring structure.

The terms“amine” and“amino” are art-recognized and refer to both unsubstituted and substituted amines and salts thereof, e.g., a moiety that can be represented by

wherein each R¹⁰⁰ independently represents a hydrogen or a hydrocarbyl group, or two R¹⁰⁰ are taken together with the N atom to which they are attached complete a heterocycle having from 4 to 8 atoms in the ring structure.

The term“aminoalkyl”, as used herein, refers to an alkyl group substituted with an amino group.

The term“aralkyl”, as used herein, refers to an alkyl group substituted with an aryl group. The term“aryl” as used herein include substituted or unsubstituted single-ring aromatic groups in which each atom of the ring is carbon. Preferably the ring is a 5- to 7-membered ring, more preferably a 6-membered ring. The term“aryl” also includes polycyclic ring systems having two or more cyclic rings in which two or more carbons are common to two adjoining rings wherein at least one of the rings is aromatic, e.g., the other cyclic rings can be cycloalkyls, cycloalkenyls, cycloalkynyls, aryls, heteroaryls, and/or heterocyclyls. Aryl groups include benzene, naphthalene, phenanthrene, phenol, aniline, and the like.

The term“carbamate” is art-recognized and refers to a group

wherein R⁹⁰ and R¹⁰⁰ independently represent hydrogen or a hydrocarbyl group, such as an alkyl group, or R⁹⁰ and R¹⁰⁰ taken together with the intervening atom(s) complete a heterocycle having from 4 to 8 atoms in the ring structure.

The terms“carbocycle”, and“carbocyclic”, as used herein, refers to a saturated or unsaturated ring in which each atom of the ring is carbon. The term carbocycle includes both aromatic carbocycles and non-aromatic carbocycles. Non-aromatic carbocycles include both cycloalkane rings, in which all carbon atoms are saturated, and cycloalkene rings, which contain at least one double bond.“Carbocycle” includes 5-7 membered monocyclic and 8-12 membered bicyclic rings. Each ring of a bicyclic carbocycle may be selected from saturated, unsaturated and aromatic rings. Carbocycle includes bicyclic molecules in which one, two or three or more atoms are shared between the two rings. The term“fused carbocycle” refers to a bicyclic carbocycle in which each of the rings shares two adjacent atoms with the other ring. Each ring of a fused carbocycle may be selected from saturated, unsaturated and aromatic rings. In an exemplary embodiment, an aromatic ring, e.g., phenyl, may be fused to a saturated or unsaturated ring, e.g., cyclohexane, cyclopentane, or cyclohexene. Any combination of saturated, unsaturated and aromatic bicyclic rings, as valence permits, is included in the definition of carbocyclic. Exemplary“carbocycles” include cyclopentane, cyclohexane,

bicyclo[2.2.1]heptane, 1,5-cyclooctadiene, 1,2,3,4-tetrahydronaphthalene, bicyclo[4.2.0]oct-3- ene, naphthalene and adamantane. Exemplary fused carbocycles include decalin, naphthalene, 1,2,3,4-tetrahydronaphthalene, bicyclo[4.2.0]octane, 4,5,6,7-tetrahydro-1H-indene and bicyclo[4.1.0]hept-3-ene.“Carbocycles” may be substituted at any one or more positions capable of bearing a hydrogen atom.

A“cycloalkyl” group is a cyclic hydrocarbon which is completely saturated.

“Cycloalkyl” includes monocyclic and bicyclic rings. Typically, a monocyclic cycloalkyl group has from 3 to about 10 carbon atoms, more typically 3 to 8 carbon atoms unless otherwise defined. The second ring of a bicyclic cycloalkyl may be selected from saturated, unsaturated and aromatic rings. Cycloalkyl includes bicyclic molecules in which one, two or three or more atoms are shared between the two rings. The term“fused cycloalkyl” refers to a bicyclic cycloalkyl in which each of the rings shares two adjacent atoms with the other ring. The second ring of a fused bicyclic cycloalkyl may be selected from saturated, unsaturated and aromatic rings. A“cycloalkenyl” group is a cyclic hydrocarbon containing one or more double bonds.

The term“carbocyclylalkyl”, as used herein, refers to an alkyl group substituted with a carbocycle group.

The term“carbonate” is art-recognized and refers to a group -OCO2-R¹⁰⁰, wherein R¹⁰⁰ represents a hydrocarbyl group.

The term“carboxy”, as used herein, refers to a group represented by the formula -CO₂H. The term“ester”, as used herein, refers to a group -C(O)OR¹⁰⁰ wherein R¹⁰⁰ represents a hydrocarbyl group.

The term“ether”, as used herein, refers to a hydrocarbyl group linked through an oxygen to another hydrocarbyl group. Accordingly, an ether substituent of a hydrocarbyl group may be hydrocarbyl-O-. Ethers may be either symmetrical or unsymmetrical. Examples of ethers include, but are not limited to, heterocycle-O-heterocycle and aryl-O-heterocycle. Ethers include “alkoxyalkyl” groups, which may be represented by the general formula alkyl-O-alkyl.

The terms“halo” and“halogen” as used herein means halogen and includes chloro, fluoro, bromo, and iodo.

The terms“hetaralkyl” and“heteroaralkyl”, as used herein, refers to an alkyl group substituted with a hetaryl group.

The term "heteroalkyl", as used herein, refers to a saturated or unsaturated chain of carbon atoms and at least one heteroatom, wherein no two heteroatoms are adjacent.

The terms“heteroaryl” and“hetaryl” include substituted or unsubstituted aromatic single ring structures, preferably 5- to 7-membered rings, more preferably 5- to 6-membered rings, whose ring structures include at least one heteroatom, preferably one to four heteroatoms, more preferably one or two heteroatoms. The terms“heteroaryl” and“hetaryl” also include polycyclic ring systems having two or more cyclic rings in which two or more carbons are common to two adjoining rings wherein at least one of the rings is heteroaromatic, e.g., the other cyclic rings can be cycloalkyls, cycloalkenyls, cycloalkynyls, aryls, heteroaryls, and/or heterocyclyls. Heteroaryl groups include, for example, pyrrole, furan, thiophene, imidazole, oxazole, thiazole, pyrazole, pyridine, pyrazine, pyridazine, and pyrimidine, and the like.

The term“heteroatom” as used herein means an atom of any element other than carbon or hydrogen. Preferred heteroatoms are nitrogen, oxygen, and sulfur.

The terms“heterocyclyl”,“heterocycle”, and“heterocyclic” refer to substituted or unsubstituted non-aromatic ring structures, preferably 3- to 10-membered rings, more preferably 3- to 7-membered rings, whose ring structures include at least one heteroatom, preferably one to four heteroatoms, more preferably one or two heteroatoms. The terms“heterocyclyl” and “heterocyclic” also include polycyclic ring systems having two or more cyclic rings in which two or more carbons are common to two adjoining rings wherein at least one of the rings is heterocyclic, e.g., the other cyclic rings can be cycloalkyls, cycloalkenyls, cycloalkynyls, aryls, heteroaryls, and/or heterocyclyls. Heterocyclyl groups include, for example, piperidine, piperazine, pyrrolidine, morpholine, lactones, lactams, and the like. Heterocyclyl groups can also be substituted by oxo groups. For example,“heterocyclyl” encompasses both pyrrolidine and pyrrolidinone.

The term“heterocyclylalkyl”, as used herein, refers to an alkyl group substituted with a heterocycle group.

The term“hydrocarbyl”, as used herein, refers to a group that is bonded through a carbon atom that does not have a =O or =S substituent, and typically has at least one carbon-hydrogen bond and a primarily carbon backbone, but may optionally include heteroatoms. Thus, groups like methyl, ethoxyethyl, 2-pyridyl, and trifluoromethyl are considered to be hydrocarbyl for the purposes of this application, but substituents such as acetyl (which has a =O substituent on the linking carbon) and ethoxy (which is linked through oxygen, not carbon) are not. Hydrocarbyl groups include, but are not limited to aryl, heteroaryl, carbocycle, heterocyclyl, alkyl, alkenyl, alkynyl, and combinations thereof. The term“hydroxyalkyl”, as used herein, refers to an alkyl group substituted with a hydroxy group.

The term“lower” when used in conjunction with a chemical moiety, such as, acyl, acyloxy, alkyl, alkenyl, alkynyl, or alkoxy is meant to include groups where there are ten or fewer non-hydrogen atoms in the substituent, preferably six or fewer. A“lower alkyl”, for example, refers to an alkyl group that contains ten or fewer carbon atoms, preferably six or fewer. In certain embodiments, acyl, acyloxy, alkyl, alkenyl, alkynyl, or alkoxy substituents defined herein are respectively lower acyl, lower acyloxy, lower alkyl, lower alkenyl, lower alkynyl, or lower alkoxy, whether they appear alone or in combination with other substituents, such as in the recitations hydroxyalkyl and aralkyl (in which case, for example, the atoms within the aryl group are not counted when counting the carbon atoms in the alkyl substituent).

As used herein, the term“oxo” refers to a carbonyl group. When an oxo substituent occurs on an otherwise saturated group, such as with an oxo-substituted cycloalkyl group (e.g., 3-oxo- cyclobutyl), the substituted group is still intended to be a saturated group. When a group is referred to as being substituted by an“oxo” group, this can mean that a carbonyl moiety (i.e., - C(=O)-) replaces a methylene unit (i.e., -CH₂-).

The terms“polycyclyl”,“polycycle”, and“polycyclic” refer to two or more rings (e.g., cycloalkyls, cycloalkenyls, cycloalkynyls, aryls, heteroaryls, and/or heterocyclyls) in which two or more atoms are common to two adjoining rings, e.g., the rings are“fused rings”. Each of the rings of the polycycle can be substituted or unsubstituted. In certain embodiments, each ring of the polycycle contains from 3 to 10 atoms in the ring, preferably from 5 to 7.

The term“silyl” refers to a silicon moiety with three hydrocarbyl moieties attached thereto.

The term“substituted” refers to moieties having substituents replacing a hydrogen on one or more carbons of the backbone. It will be understood that“substitution” or“substituted with” includes the implicit proviso that such substitution is in accordance with permitted valence of the substituted atom and the substituent, and that the substitution results in a stable compound, e.g., which does not spontaneously undergo transformation such as by rearrangement, cyclization, elimination, etc. As used herein, the term“substituted” is contemplated to include all permissible substituents of organic compounds. In a broad aspect, the permissible substituents include acyclic and cyclic, branched and unbranched, carbocyclic and heterocyclic, aromatic and non-aromatic substituents of organic compounds. The permissible substituents can be one or more and the same or different for appropriate organic compounds. For purposes of this invention, the heteroatoms such as nitrogen may have hydrogen substituents and/or any permissible substituents of organic compounds described herein which satisfy the valences of the heteroatoms. Substituents can include any substituents described herein, for example, a halogen, a hydroxyl, a carbonyl (such as a carboxyl, an alkoxycarbonyl, a formyl, or an acyl), a thiocarbonyl (such as a thioester, a thioacetate, or a thioformate), an alkoxyl, a phosphoryl, a phosphate, a phosphonate, a phosphinate, an amino, an amido, an amidine, an imine, a , a nitro, an azido, a sulfhydryl, an alkylthio, a sulfate, a sulfonate, a sulfamoyl, a sulfonamido, a sulfonyl, a heterocyclyl, an aralkyl, or an aromatic or heteroaromatic moiety. It will be understood by those skilled in the art that substituents can themselves be substituted, if appropriate. Unless specifically stated as“unsubstituted,” references to chemical moieties herein are understood to include substituted variants. For example, reference to an“aryl” group or moiety implicitly includes both substituted and unsubstituted variants.

The term“sulfate” is art-recognized and refers to the group -OSO₃H, or a

pharmaceutically acceptable salt thereof.

The term“sulfonamide” is art-recognized and refers to the group represented by the general formulae

wherein R⁹⁰ and R¹⁰⁰ independently represents hydrogen or hydrocarbyl, such as alkyl, or R⁹⁰ and R¹⁰⁰ taken together with the intervening atom(s) complete a heterocycle having from 4 to 8 atoms in the ring structure.

The term“sulfoxide” is art-recognized and refers to the group -S(O)-R¹⁰⁰, wherein R¹⁰⁰ represents a hydrocarbyl.

The term“sulfonate” is art-recognized and refers to the group SO₃H, or a

pharmaceutically acceptable salt thereof.

The term“sulfone” is art-recognized and refers to the group -S(O)2-R¹⁰⁰, wherein R¹⁰⁰ represents a hydrocarbyl. The term“thioalkyl”, as used herein, refers to an alkyl group substituted with a thiol group.

The term“thioester”, as used herein, refers to a group -C(O)SR¹⁰⁰ or -SC(O)R¹⁰⁰ wherein R¹⁰⁰ represents a hydrocarbyl.

The term“thioether”, as used herein, is equivalent to an ether, wherein the oxygen is replaced with a sulfur.

The term“urea” is art-recognized and may be represented by the general formula

wherein R⁹⁰ and R¹⁰⁰ independently represent hydrogen or a hydrocarbyl, such as alkyl, or either occurrence of R⁹⁰ taken together with R¹⁰⁰ and the intervening atom(s) complete a heterocycle having from 4 to 8 atoms in the ring structure.

“Protecting group” refers to a group of atoms that, when attached to a reactive functional group in a molecule, mask, reduce or prevent the reactivity of the functional group. Typically, a protecting group may be selectively removed as desired during the course of a synthesis.

Examples of protecting groups can be found in Greene and Wuts, Protective Groups in Organic Chemistry, 3^rd Ed., 1999, John Wiley & Sons, NY and Harrison et al., Compendium of Synthetic Organic Methods, Vols.1-8, 1971-1996, John Wiley & Sons, NY. Representative nitrogen protecting groups include, but are not limited to, formyl, acetyl, trifluoroacetyl, benzyl, benzyloxycarbonyl (“CBZ”), tert-butoxycarbonyl (“Boc”), trimethylsilyl (“TMS”), 2- trimethylsilyl-ethanesulfonyl (“TES”), trityl and substituted trityl groups, allyloxycarbonyl, 9- fluorenylmethyloxycarbonyl (“FMOC”), nitro-veratryloxycarbonyl (“NVOC”) and the like. Representative hydroxylprotecting groups include, but are not limited to, those where the hydroxyl group is either acylated (esterified) or alkylated such as benzyl and trityl ethers, as well as alkyl ethers, tetrahydropyranyl ethers, trialkylsilyl ethers (e.g., TMS or TIPS groups), glycol ethers, such as ethylene glycol and propylene glycol derivatives and allyl ethers.

As used herein, a therapeutic that“prevents” a disorder or condition refers to a compound that, in a statistical sample, reduces the occurrence of the disorder or condition in the treated sample relative to an untreated control sample, or delays the onset or reduces the severity of one or more symptoms of the disorder or condition relative to the untreated control sample. The term“treating” includes prophylactic and/or therapeutic treatments. The term “prophylactic or therapeutic” treatment is art-recognized and includes administration to the host of one or more of the subject compositions. If it is administered prior to clinical manifestation of the unwanted condition (e.g., disease or other unwanted state of the host animal) then the treatment is prophylactic (i.e., it protects the host against developing the unwanted condition), whereas if it is administered after manifestation of the unwanted condition, the treatment is therapeutic, (i.e., it is intended to diminish, ameliorate, or stabilize the existing unwanted condition or side effects thereof).

The term“prodrug” is intended to encompass compounds which, under physiologic conditions, are converted into the therapeutically active agents of the present invention (e.g., a compound of formula I). A common method for making a prodrug is to include one or more selected moieties which are hydrolyzed under physiologic conditions to reveal the desired molecule. In other embodiments, the prodrug is converted by an enzymatic activity of the host animal. For example, esters or carbonates (e.g., esters or carbonates of alcohols or carboxylic acids) are preferred prodrugs of the present invention. In certain embodiments, some or all of the compounds of formula I in a formulation represented above can be replaced with the

corresponding suitable prodrug, e.g., wherein a hydroxyl in the parent compound is presented as an ester or a carbonate or carboxylic acid present in the parent compound is presented as an ester.

EXAMPLES

In order that the invention described herein may be more fully understood, the following examples are set forth. The synthetic and biological examples described in this application are offered to illustrate the compounds, pharmaceutical compositions and methods provided herein and are not to be construed in any way as limiting their scope. Example 1. Minimum Inhibition Concentration (MIC) Assay

Minimal inhibitory concentrations (MICs) were determined following CLSI

microdilution guidelines against 200 E. coli, 200 K. pneumoniae, 200 other Enterobacteriaceae, 200 P. aeruginosa, 200 A. baumannii from 2016-2017. Compounds tested included AO, EF, AO + EF in a 1:1 ratio, and comparator agents. As a siderophore antimicrobic, in vitro activity of AO may be affected by the presence of iron in the testing medium. All isolates were tested in cation-adjusted Mueller Hinton broth (CAMHB). MIC endpoints were determined at the lowest concentration of compound that exhibited a significant reduction in growth relative to the growth control.

The results of the MIC assay are summarized in Table 3.

Table 3.

As noted in Table 3, AO exhibited potent in vitro activity against recent gram-negative isolates. The addition of EF improved the activity of AO against beta-lactamase producing Enterobacteriaceae (i.e., E. coli and K. pneumonia), but had less effect against A. baumannii and P. aeruginosa. Example 2. Dose-Fractionation Study

Briefly, duplicate, 24-hour in vitro chemostat models were used to carry out dose fractionation studies in order to determine the PK-PD exposure measure that best describes the efficacy of EF. All experiments were performed in duplicate. The starting inoculum for all studies was 10⁶ CFU/mL. The experiment duration was 24 hours. As described below, the treatment regimens each consisted of human simulated AO regimen selected from the dose range studies and a range of EF doses fractionated into different dose frequencies, administered every 4, 6, 8, and 12 hours, by area under the 24-hour concentration-time curve from (AUC0-24). The doses selected for EF were determined using the results of the dose ranging experiments and contained the dose which generates one half the maximal effect at 24 hours as well as a sub- and supra-optimal dose based on this condition. A minimum of three exposures was evaluated against a no-treatment control, representing 13 regimens in total. Specifically:

Bacterial and drug concentration samples were obtained serially at 0, 2, 4, 8, 12, and 24 hours post-inoculation. Samples were collected for evaluation of AO and EF concentrations at 1, 2, 3, 5, 7, 9, 11, 13, and 23 hours, from initiation of therapy.

The washed bacterial suspensions were quantitatively cultured onto antibiotic-free agar to determine the effect of each dosing regimen on the bacterial population. After an incubation period of 18 to 24 hours at 35°C, the change in log10 CFU/mL over the dosing interval was calculated and time-kill curves were constructed by plotting log10 CFU/mL against time.

Immediately after the drug concentration samples had been collected, they were stored at -80°C until analyzed via LC/MS-MS. Approximately 216 PK samples were generated in Mueller Hinton 2 broth.

The results of the dose fractionation studies are summarized in Figs.1-3 and Table 4.

Table 4.

Example 3. Dose-Ranging Study

Duplicate 24-hour chemostat models were used to measure the effect interisolate variability has upon a AO q8h regimen in combination with a range of EF doses infused over a one-hour infusion. The starting inoculum was 10⁶ CFU/mL, using a panel of six clinical

Enterobacteriaceae isolates (see Table 5). The chemostat study utilized a range of EF exposures administered every 8 hours. Samples were collected at 0, 2, 4, 8, 12, and 24 hours and plated on drug-free plates for the enumeration of bacterial densities. Samples were collected for evaluation of AO and EF concentrations at 1, 3, 5, 7, 9 and 23 hours, from initiation of therapy. Duplicate studies were completed and examples of the possible dosing regimens evaluated were as follows:

acter a an rug concentrat on samples were obtained serially at 0, 2, 4, 8, 12, and 24 hours post-inoculation. The washed bacterial suspensions were quantitatively cultured onto antibiotic-free agar to determine the effect of each dosing regimen on the bacterial population. After an incubation period of 18 to 24 hours at 35°C, the change in log10 CFU/mL over the dosing interval was calculated and time-kill curves were constructed by plotting log10 CFU/mL against time. Immediately after the drug concentration samples had been collected, they were stored at -80°C until analyzed via a chemical assay for drug. Approximately 500 PK samples were generated in Mueller Hinton 2 broth, analyzed via LC/MS-MS.

Table 5. Isolates utilized in the dose-ranging studies

The results of the dose fractionation studies are summarized in Fig.4 and Table 6.

Table 6.

The results of the Compounds AO + EF dose-ranging studies provided further insight into the activity of the inhibitor when utilized in combination with Compound AO. The

Compound EF exposure, in combination with a Compound AO 2 g dose, required to achieve non-clinical targets such net bacterial stasis, 1- and 2-log₁₀ reductions in bacterial burden from baseline were determined to be 4.13, 13.7, and 57.2, respectively. Very little development of on- therapy resistance was observed over the 24-hour period.

Table 7 highlights the calculated scaled-up human dosages. Specifically, if AO were dosed at 2g q8h and assuming AUC/MIC 1-log kill (regulatory standard), then a 500 mg q8h dose of EF will cover MIC of 2.9 and a 2 g q8h dose of EF will cover up to MIC of 11.7.

Table 7. MIC Coverage Based on Scaled Human Doses

Example 4: Single Dose Toxicology Results in Rats

Briefly, 15 rats(Sprague Dawley(Crl:CD(SD)), male, 6 weeks old, 140~190g weight) were randomly assigned to 5 groups of 3/group to determine the maximum tolerated dose of EF mono(1000,2000mpk), and AO/EF combination (2:1 ratio, 1000mpk/500mpk,

2000mpk/1000mpk) when administered once by the intravenous infusion (approximately 1 hour) via tail vein.(dosing volume: 10ml/kg) The dosing day was defined as Day 1. The animals of each group were observed for 14 days following dosing for signs of toxicity and were necropsied on Day 15.

No premature deaths in this study. During infusion, chromaturia (brown) was observed for animals being administered with Compound EF (1000 mg/kg) + Compound AO (2000 mg/kg), but it stopped after completion of infusion. No other specific clinical signs.

In addition, no effect on body weight profiles that were considered to be related to administration of the compounds was observed.

There was no specific findings visible post-necropsy. The MTDs in single dose phase were considered to be 2000mpk for Compound EF and 1000mpk: 2000mpk for Compound EF: Compound AO. Incorporation by Reference

All publications and patents mentioned herein are hereby incorporated by reference in their entirety as if each individual publication or patent was specifically and individually indicated to be incorporated by reference. In case of conflict, the present application, including any definitions herein, will control. Equivalents While specific embodiments of the subject invention have been discussed, the above specification is illustrative and not restrictive. Many variations of the invention will become apparent to those skilled in the art upon review of this specification and the claims below. The full scope of the invention should be determined by reference to the claims, along with their full scope of equivalents, and the specification, along with such variations.

Claims

What is claimed is: 1. A pharmaceutical composition comprising a cephalosporin derivative and an inhibitor of β-lactamase, wherein the cephalosporin derivative is a compound of Formula (I) or a pharmaceutically acceptable salt, ester, or prodrug thereof

wherein X is CR or N;

Y is C₁-C₂ alkyl, CH(CH₃)CO₂H, or C(CH₃)₂CO₂H;

L is CH₂ or CH=CHCH₂;

R is H, chloro or C1-C3 alkyl;

R1 is NH2, NHR11 or NH(CH2)mNR11R12;

R2 is NHR21, NH(CH2)nCOOH, NH(CH2)nNR21R22, or NHC(=O)(CH2)nNR21R22;

R3 is H or NH2,

R₁₁ and R₂₁ are independently H, C₁-C₃ alkyl, or a group selected from:

R₁₂ and R₂₂ are each independently H or C₁-C₂ alkyl; and

m and n are each independently an integer from 1 to 6; and

wherein the β-lactamase inhibitor is a compound of Formula (II) or a pharmaceutically acceptable salt, ester, or prodrug thereof:

wherein R⁵ and R⁶ are independently selected from H, hydroxyalkyl, -C(O)-NH₂, amido-, amino- , or guanidino-substituted alkyl, amido-, amino-, or guanidino-substituted alkoxyalkyl, and -(CH₂)_p-O-NHR⁷, or

R⁵ and R⁶ combine to form an amino-, or guanidino-substituted cycloalkyl ring, or an optionally substituted nitrogen-containing heterocyclyl ring;

p is an integer from 1 to 6; and

R⁷ is, independently for each occurrence, selected from H, lower alkyl, and -C(=NH)NH2.

2. The pharmaceutical composition of claim 1, wherein

X is CR or N;

Y is C₁-C₂ alkyl, CH(CH₃)CO₂H, or C(CH₃)₂CO₂H;

L is CH2 or CH=CHCH2;

R is H, chloro or C1-C3 alkyl;

R1 is NH2, NHR11 or NH(CH2)mNR11R12;

R2 is NHR21, NH(CH2)nNR21R22, or NHC(=O)(CH2)nNR21R22;

R₃ is H;

R₁₁ and R₂₁ are independently hydrogen, C₁-C₃ alkyl, or a group selected from:

R12 and R22 are independently hydrogen or C1-C2 alkyl; and

m and n are independently an integer of 1 to 6.

3. The pharmaceutical composition of claim 1, wherein

X is CR or N;

Y is CH(CH3)CO2H or C(CH3)2CO2H;

L is CH2 or CH=CHCH2; R is H, chloro or C₁-C₃ alkyl;

R₁ is NH₂ or NH(CH₂)_mNH₂;

R₂ is NHR₂₁, NH(CH₂)_nNR₂₁, or NHC(=O)(CH₂)_nNR₂₁; and

R3 is H;

R₂₁ is a group selected from

m and n are independently an integer of 1 to 6.

4. The pharmaceutical composition of claim 1, wherein the cephalosporin derivative is a compound represented by one of the following chemical formulas:

or a pharmaceutically acceptable salt thereof.

5. The pharmaceutical composition of claim 1, wherein the cephalosporin derivative is

6. The pharmaceutical composition of any one of claims 1-5, wherein at least one of R⁵ and R⁶ is independently selected from

wherein p is an integer from 1 to 5.

7. The pharmaceutical composition of any one of claims 1-6, wherein R⁵ and R⁶ combine to form a structure of Formula A

wherein

Y and Z are each independently CHR⁸, NR⁹, or absent;

R⁸ is, independently for each occurrence, selected from H, amido-, amino-, or guanidino- substituted lower alkyl, and NHR³;

R⁹ is, independently for each occurrence, selected from H, amido-, amino-, or guanidino- substituted lower alkyl and -C(=NH)NH2; and

m and n are each independently an integer from 1 to 3;

provided that both Y and Z are not absent.

8. The pharmaceutical composition of any one of claims 1-6, wherein the β‐lactamase inhibitor is a compound having the structure of formula III or a pharmaceutically acceptable salt thereof:

and R¹ is an amido-, amino- or guanidino substituted alkyl, an amido-, amino-, guanidine substituted alkoxyalkyl, or -(CH₂)_p-O-NHR⁷.

9. The pharmaceutical composition of any one of claims 1-6, wherein the β‐lactamase inhibitor is a compound having the structure of formula IV or a pharmaceutically acceptable salt thereof:

and m is less than or equal to n.

10. The pharmaceutical composition of any one of claims 1-6, wherein the β-lactamase inhibitor is a compound selected from

or a pharmaceutically acceptable salt thereof.

11. The pharmaceutical composition of any preceding claim, further comprising a pharmaceutically acceptable carrier.

12. A method of treating an infection in a subject in need thereof, comprising administering to the subject the pharmaceutical composition of any preceding claim.

13. A method of treating an infection in a subject in need thereof, comprising conjointly administering to the subject a cephalosporin derivative and a β-lactamase inhibitor, wherein the cephalosporin derivative is a compound of Formula (I) or a pharmaceutically acceptable salt, ester, or prodrug thereof

wherein X is CR or N;

Y is C1-C2 alkyl, CH(CH3)CO2H, or C(CH3)2CO2H;

L is CH2 or CH=CHCH2;

R is H, chloro or C1-C3 alkyl;

R₁ is NH₂, NHR₁₁ or NH(CH₂)_mNR₁₁R₁₂;

R₂ is NHR₂₁, NH(CH₂)_nCOOH, NH(CH₂)_nNR₂₁R₂₂, or NHC(=O)(CH₂)_nNR₂₁R₂₂;

R₃ is H or NH₂,

R₁₁ and R₂₁ are independently H, C₁-C₃ alkyl, or a group selected from:

R12 and R22 are each independently H or C1-C2 alkyl; and

m and n are each independently an integer from 1 to 6; and

wherein the β-lactamase inhibitor is a compound of Formula (II) or a pharmaceutically acceptable salt thereof:

wherein

R⁵ and R⁶ are independently selected from H, hydroxyalkyl, -C(O)-NH₂, amido-, amino-, or guanidino-substituted alkyl, amido-, amino-, or guanidino-substituted alkoxyalkyl, and - (CH2)p-O-NHR⁷, or

R⁵ and R⁶ combine to form an amino-, or guanidino-substituted cycloalkyl ring, or an optionally substituted nitrogen-containing heterocyclyl ring;

p is an integer from 1 to 6; and

R⁷ is, independently for each occurrence, selected from H, lower alkyl, and -C(=NH)NH₂.

14. The method of claim 13, wherein

X is CR or N;

Y is C1-C2 alkyl, CH(CH3)CO2H, or C(CH3)2CO2H;

L is CH2 or CH=CHCH2;

R is H, chloro or C1-C3 alkyl;

R₁ is NH₂, NHR₁₁ or NH(CH₂)_mNR₁₁R₁₂;

R₂ is NHR₂₁, NH(CH₂)_nNR₂₁R₂₂, or NHC(=O)(CH₂)_nNR₂₁R₂₂;

R₃ is H;

R₁₁ and R₂₁ are independently hydrogen, C₁-C₃ alkyl, or a group selected from:

R₁₂ and R₂₂ are independently hydrogen or C₁-C₂ alkyl; and

m and n are independently an integer of 1 to 6.

15. The method of claim 13, wherein

X is CR or N;

Y is CH(CH₃)CO₂H or C(CH₃)₂CO₂H;

L is CH₂ or CH=CHCH₂;

R is H, chloro or C1-C3 alkyl;

R1 is NH2 or NH(CH2)mNH2;

R2 is NHR21, NH(CH2)nNR21, or NHC(=O)(CH2)nNR21; and R₃ is H;

R₂₁ is a group selected from:

m and n are independently an integer of 1 to 6.

16. The method of claim 13, wherein the cephalosporin derivative is a compound represented by one of the following chemical formulas:

or a pharmaceutically acceptable salt thereof.

17. The method of claim 13, wherein the cephalosporin derivative is

18. The method of any one of claims 13-17, wherein at least one of R⁵ and R⁶ is independently selected from

wherein p is an integer from 1 to 5.

19. The method of any one of claims 13-17, wherein R⁵ and R⁶ combine to form a structure of Formula A

wherein

Y and Z are each independently CHR⁸, NR⁹, or absent;

R⁸ is, independently for each occurrence, selected from H, amido-, amino-, or guanidino- substituted lower alkyl, and NHR³;

R⁹ is, independently for each occurrence, selected from H, amido-, amino-, or guanidino- substituted lower alkyl and -C(=NH)NH₂; and

m and n are each independently an integer from 1 to 3;

provided that both Y and Z are not absent.

20. The method of any one of claims 13-17, wherein β-lactamase inhibitor is a compound having the structure of formula III or a pharmaceutically acceptable salt thereof:

and R¹ is an amido-, amino- or guanidino substituted alkyl, an amido-, amino-, guanidino- substituted alkoxyalkyl, or -(CH₂)_p-O-NHR⁷.

21. The method of any one of claims 13-17, wherein β‐lactamase inhibitor is a compound having the structure of formula IV or a pharmaceutically acceptable salt thereof:

and m is less than or equal to n.

22. The method of any one of claims 13-17, wherein the β-lactamase inhibitor is a compound selected from

or a pharmaceutically acceptable salt thereof.

23. The method of any one of claims 12-22, wherein the infection is a bacterial infection.

24. The method of claim 23, wherein the bacterial infection is from a gram-negative bacterium.

25. The method of any one of claims 12-24, wherein the cephalosporin derivative and the β- lactamase inhibitor are administered intravenously.

26. The method of any one of claims 12-25, wherein the subject is a human.