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This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of constructing the integral factor of the first-order ordinary differential equation and finding the general solutions.

Glucose-responsive insulin delivery systems that mimic pancreatic endocrine function could enhance health and improve quality of life for people with type 1 and type 2 diabetes with reduced β-cell function. However, insulin delivery systems with rapid in vivo glucose-responsive behaviour typically have limited insulin-loading capacities and cannot be manufactured easily. Here, we show that a single removable transdermal patch, bearing microneedles loaded with insulin and a non-degradable glucose-responsive polymeric matrix, and fabricated via in situ photopolymerization, regulated blood glucose in insulin-deficient diabetic mice and minipigs (for minipigs >25 kg, glucose regulation lasted >20 h with patches of ~5 cm2). Under hyperglycaemic conditions, phenylboronic acid units within the polymeric matrix reversibly form glucose-boronate complexes that-owing to their increased negative charge-induce the swelling of the polymeric matrix and weaken the electrostatic interactions between the negatively charged insulin and polymers, promoting the rapid release of insulin. This proof-of-concept demonstration may aid the development of other translational stimuli-responsive microneedle patches for drug delivery.

Insulin administration for the management of diabetes is accompanied by hypoglycemia, which is expected to be mitigated by glucose-responsive smart insulin that has self-regulation ability in response to blood glucose level (BGL) fluctuation. Here, we have prepared a new insulin analog by modifying insulin with forskolin (designated as insulin-F), a glucose-transporter (Glut) inhibitor. In vitro, insulin-F is capable of binding to Glut on erythrocyte ghosts, which can be inhibited by glucose and cytochalasin B. Upon subcutaneous injection in type 1 diabetic mice, insulin-F maintains BGLs below 200 mg mL-1 for up to 10 h, and achieves 20 h with two sequential injections. Moreover, insulin-F also binds to endogenous Gluts. Upon a glucose challenge, the elevated level of glucose competitively replaces and liberates insulin-F that binds to Glut, rapidly restoring BGLs to the normal range.

Insulin therapy in the setting of type 1 and advanced type 2 diabetes is complicated by increased risk of hypoglycemia. This potentially fatal complication could be mitigated by a glucose-responsive insulin analog. We report an insulin-facilitated glucose transporter (Glut) inhibitor conjugate, in which the insulin molecule is rendered glucose-responsive via conjugation to an inhibitor of Glut. The binding affinity of this insulin analog to endogenous Glut is modulated by plasma and tissue glucose levels. In hyperglycemic conditions (e.g., uncontrolled diabetes or the postprandial state), the in situ-generated insulin analog-Glut complex is driven to dissociate, freeing the insulin analog and glucose-accessible Glut to restore normoglycemia. Upon overdose, enhanced binding of insulin analog to Glut suppresses the glucose transport activity of Glut to attenuate further uptake of glucose. We demonstrate the ability of this insulin conjugate to regulate blood glucose levels within a normal range while mitigating the risk of hypoglycemia in a type 1 diabetic mouse model.

Insulin therapy is necessary to regulate blood glucose levels for people with type 1 diabetes and commonly used in advanced type 2 diabetes. Although subcutaneous insulin administration via hypodermic injection or pump-mediated infusion is the standard route of insulin delivery, it may be associated with pain, needle phobia, and decreased adherence, as well as the risk of infection. Therefore, transdermal insulin delivery has been widely investigated as an attractive alternative to subcutaneous approaches for diabetes management in recent years. Transdermal systems designed to prevent insulin degradation and offer controlled, sustained release of insulin may be desirable for patients and lead to increased adherence and glycemic outcomes. A challenge for transdermal insulin delivery is the inefficient passive insulin absorption through the skin due to the large molecular weight of the protein drug. In this review, we focus on the different transdermal insulin delivery techniques and their respective advantages and limitations, including chemical enhancers-promoted, electrically enhanced, mechanical force-triggered, and microneedle-assisted methods.

The exploration of cell‐based drug delivery systems for cancer therapy has gained growing attention. Approaches to engineering therapeutic cells with multidrug loading in an effective, safe, and precise manner while preserving their inherent biological properties remain of great interest. Here, we report a strategy to simultaneously load multiple drugs in platelets in a one‐step fusion process. We demonstrate doxorubicin (DOX)‐encapsulated liposomes conjugated with interleukin‐15 (IL‐15) could fuse with platelets to achieve both cytoplasmic drug loading and surface cytokine modification with a loading efficiency of over 70 % within minutes. Due to their inherent targeting ability to metastatic cancers and postoperative bleeding sites, the engineered platelets demonstrated a synergistic therapeutic effect to suppress lung metastasis and postoperative recurrence in mouse B16F10 melanoma tumor models. [ABSTRACT FROM AUTHOR]

In Liu et al. [On the generalized time fractional diffusion equation: Symmetry analysis, conservation laws, optimal system and exact solutions, Int. J. Geom. Methods Mod. Phys. 17(01) (2020) 2050013], the generalized time-fractional diffusion equation Dtαu = aupu xx + buqu x2 is studied by the symmetry analysis method. Liu et al. obtained two group generators X1 = ∂ ∂x, X2 = 2t α ∂ ∂t + x ∂ ∂x and only one trivial solution u(t,x) = f(t) = C0 Γ(α)tα−1 for the equation. In this paper, we classify the Lie symmetry group admitted by the equation, and for the case p = q + 1, we obtain a richer set of group generators and some nontrivial solutions, including unprecedented exact solutions and power series solutions. In addition, we construct the one-dimensional optimal system of the Lie symmetry group admitted by the time-fractional diffusion-type equation by Olver’s method, and obtain the conservation laws for all the obtained Lie symmetries using the general method developed by Ibragimov. For the novel exact solutions and power series solutions, we analyze their dynamic behavior graphically. [ABSTRACT FROM AUTHOR]

Obstructive hypertrophic cardiomyopathy (oHCM) is a subtype of HCM characterized by left ventricular outflow tract obstruction resulting from cardiac muscle hypertrophy and anatomic alterations in the mitral valve and apparatus. Mavacamten, a cardiac myosin inhibitor metabolized primarily by CYP2C19 in the liver, is the first and only targeted medication approved for the treatment of symptomatic New York Heart Association (NYHA) class II–III oHCM. Previous pharmacokinetic (PK) results of mavacamten in healthy Caucasian, Japanese, and Asian participants demonstrated that mavacamten exposure was affected by CYP2C19 metabolism status. This open‐label, parallel‐group, phase I trial aimed to determine the PK and safety of mavacamten in healthy Chinese participants with different CYP2C19 genotypes. The primary outcome was to define the PK of mavacamten in healthy Chinese participants; the secondary outcome was to examine safety and tolerability. After a single oral dose of 15 or 25 mg mavacamten in fasted healthy adult Chinese individuals, Cmax was reached within a median Tmax of 0.6–1.5 h, indicating rapid absorption. Inter‐individual variability was moderate, and individuals carrying non‐functional CYP2C19 alleles (*2/*2, *3/*3, or *2/*3) exhibited longer half‐life and increased total exposure. After stratification of CYP2C19 genotypes, total mavacamten exposures were similar among different ethnic groups when compared with prior PK studies. No significant adverse events were observed in this study. Single oral administration of mavacamten at 15 mg was well tolerated across all CYP2C19 genotypes, and 25 mg dose was well tolerated in healthy participants with CYP2C19 genotypes UM/RM/NM. The PK profile of mavacamten in the healthy Chinese population was consistent with that in other healthy populations. [ABSTRACT FROM AUTHOR]