Two-step Differentiation Research Articles

A scalable, spin-free approach to generate enhanced induced pluripotent stem cell-derived natural killer cells forcancer immunotherapy.

Natural killer (NK) cells play a vital role in innate immunity and show great promise in cancer immunotherapy. Traditional sources of NK cells, such as the peripheral blood, are limited by availability and donor variability. In addition, in vitro expansion can lead to functional exhaustion and gene editing challenges. This study aimed to harness induced pluripotent stem cell (iPSC) technology to provide a consistent and scalable source of NK cells, overcoming the limitations of traditional sources and enhancing the potential for cancer immunotherapy applications. We developed human placental-derived iPSC lines using reprogramming techniques. Subsequently, an optimized two-step differentiation protocol was introduced to generate high-purity NK cells. Initially, iPSCs were differentiated into hematopoietic-like stem cells using spin-free embryoid bodies (EBs). Subsequently, the EBs were transferred to ultra-low attachment plates to induce NK cell differentiation. iPSC-derived NK (iNK) cells expressed common NK cell markers (NKp46, NKp30, NKp44, CD16 and eomesodermin) at both RNA and protein levels. iNK cells demonstrated significant resilience to cryopreservation and exhibited enhanced cytotoxicity. The incorporation of a chimeric antigen receptor (CAR) construct further augmented their cytotoxic potential. This study exemplifies the feasibility of generating iNK cells with high purity and enhanced functional capabilities, their improved resilience to cryopreservation and the potential to have augmented cytotoxicity through CAR expression. Our findings offer a promising pathway for the development of potential cellular immunotherapies, highlighting the critical role of iPSC technology in overcoming challenges associated with traditional NK cell sources.

Green directional conversion of food waste into glycerol in a two-step differentiation enzymolysis and facultative fermentation using Saccharomyces cerevisiae: Performance assessment and mechanism

Valorization of food waste into high value-added glycerol was designed and prepared via directional green transformation using multi-enzymolysis saccharification coupled facultative fermentation by Saccharomyces cerevisiae. The optimal conditions for the first step of multienzyme hydrolysis and the second step of facultative fermentation were 55 °C and pH 5.0 for 6 h, 30 °C and pH 7.0 for 70 h, respectively. The glycerol yield efficiency and kinetic rate constant were 73.6 % (w/w) and 0.681 h−1 for dry component of food waste, while the other 27.4 % was utilized as the growth energy substrate. The key points of transformation were the synergistic directed enzymolysis to produce 3 % glycerol and 95 % reducing sugars. Furthermore, the reducing sugars were converted into glycerol by switch the metabolic pathway from ethanol into glycerol through the quantitative expression of functional gpd1 and gpp2 genes activated GPD and GPP enzymatic activity and synchronous inhibition of adh gene for glycerol production with Na2SO3 regulation. The economic income was 135.52 USD/ton for converting 80 % water content of kitchen waste into glycerol. This finding provided an economic value-added approach to produce high-value glycerol for cost-effective recycling of food waste using commercial yeast.

Unconditional optimal [formula omitted]-norm error estimate and superconvergence analysis of a linearized nonconforming finite element variable-time-step BDF2 method for the nonlinear complex Ginzburg–Landau equation

In this paper, a linearized fully discrete scheme combining the variable-time-step two-step backward differentiation formula (VSBDF2) in time and the nonconforming finite element methods (FEMs) in space is constructed and analyzed for the nonlinear complex Ginzburg–Landau equation. A novel convergence analysis approach is proposed, which shows that the H1-norm error of this scheme can reach optimal order in space and sharp second-order convergence in time. The key ingredients of our analysis are temporal–spatial error splitting approach, a new positive definiteness property of discrete orthogonal convolution (DOC) kernels with respect to complex sequences, an energy projection operator and a discrete Laplace operator Δh related to the nonconforming element space, and a relationship between Δh and classical L2 projection operator in complex space. Furthermore, through a specific treatment of the error equation and the combination technique of interpolating operator and projection operator, we prove that the proposed scheme has the global superconvergence result of order O(τ2+h2) in H1-norm for the first time, which further improves the efficiency of numerical computation. Here τ and h are the maximum time and spatial step sizes, respectively. It should be pointed out that all these error results are rigorously established under mild assumptions of the time step, and get rid of the usual grid ratio constraints between temporal and spatial step sizes in linearized scheme. At last, numerical experiments are provided to verify the theoretical analysis.

Pig blastocyst-like structure models from embryonic stem cells

Pluripotent stem cells have the potential to generate embryo models that can recapitulate developmental processes in vitro. Large animals such as pigs may also benefit from stem-cell-based embryo models for improving breeding. Here, we report the generation of blastoids from porcine embryonic stem cells (pESCs). We first develop a culture medium 4FIXY to derive pESCs. We develop a 3D two-step differentiation strategy to generate porcine blastoids from the pESCs. The resulting blastoids exhibit similar morphology, size, cell lineage composition, and single-cell transcriptome characteristics to blastocysts. These porcine blastoids survive and expand for more than two weeks in vitro under two different culture conditions. Large animal blastoids such as those derived from pESCs may enable in vitro modeling of early embryogenesis and improve livestock species’ breeding practices.

Asymptotically compatible energy of variable-step fractional BDF2 scheme for the time-fractional Cahn–Hilliard model

Abstract A novel discrete gradient structure of the variable-step fractional BDF2 formula approximating the Caputo fractional derivative of order $\alpha \in (0,1)$ is constructed by a local-nonlocal splitting technique, that is, the fractional BDF2 formula is split into a local part analogue to the two-step backward differentiation formula (BDF2) of the first derivative and a nonlocal part analogue to the L1-type formula of the Caputo derivative. Then a local discrete energy dissipation law of the variable-step fractional BDF2 implicit scheme is established for the time-fractional Cahn–Hilliard model under a weak step-ratio constraint $0.3960\le \tau _{k}/\tau _{k-1}<r^{*}(\alpha )$, where $\tau _{k}$ is the $k$th time-step size and $r^{*}(\alpha )\ge 4.660$ for $\alpha \in (0,1)$. The present result provides a practical answer to the open problem in [SINUM, 57: 218-237, Remark 6] and significantly relaxes the severe step-ratio restriction [Math. Comp., 90: 19–40, Theorem 3.2]. More interestingly, the discrete energy and the corresponding energy dissipation law are asymptotically compatible with the associated discrete energy and the energy dissipation law of the variable-step BDF2 method for the classical Cahn–Hilliard equation, respectively. To the best of our knowledge, such type energy dissipation law is established at the first time for the variable-step L2 type formula of Caputo’s derivative. Numerical examples with an adaptive stepping procedure are provided to demonstrate the accuracy and the effectiveness of our proposed method.

Establishment of human induced pluripotent stem cell-derived hepatobiliary organoid with bile duct for pharmaceutical research use

In vitro models of the human liver are promising alternatives to animal tests for drug development. Currently, primary human hepatocytes (PHHs) are preferred for pharmacokinetic and cytotoxicity tests. However, they are unable to recapitulate the flow of bile in hepatobiliary clearance owing to the lack of bile ducts, leading to the limitation of bile analysis. To address the issue, a liver organoid culture system that has a functional bile duct network is desired. In this study, we aimed to generate human iPSC-derived hepatobiliary organoids (hHBOs) consisting of hepatocytes and bile ducts. The two-step differentiation process under 2D and semi-3D culture conditions promoted the maturation of hHBOs on culture plates, in which hepatocyte clusters were covered with monolayered biliary tubes. We demonstrated that the hHBOs reproduced the flow of bile containing a fluorescent bile acid analog or medicinal drugs from hepatocytes into bile ducts via bile canaliculi. Furthermore, the hHBOs exhibited pathophysiological responses to troglitazone, such as cholestasis and cytotoxicity. Because the hHBOs can recapitulate the function of bile ducts in hepatobiliary clearance, they are suitable as a liver disease model and would be a novel in vitro platform system for pharmaceutical research use.

Temporal error analysis of an unconditionally energy stable second-order BDF scheme for the square phase-field crystal model

In this paper, we first propose and study the second-order time-discrete numerical scheme for the sixth-order nonlinear parabolic problem of the square phase-field crystal model. Then, we demonstrate the two-step backward differentiation formula (BDF-2) scheme with mass conservation and energy dissipation, where the higher order nonlinear term is treated implicitly. Moreover, a rigorous error analysis is presented and we prove the optimal second-order convergence rate O(τ2) in H1- norm, where τ is the time step. Finally, some numerical results are provided to confirm our theoretical analysis.

A BDF2 method for a singularly perturbed transport equation

A singularly perturbed transport equation is considered. A variable two-step backward differentiation formulas (BDF2) on a Shishkin-type mesh is used to discrete the first-order derivatives of the singularly perturbed transport equation. The stability and error analysis are derived by using the discrete orthogonal convolution kernels. It is proved that the scheme is second-order uniformly convergent with respect to the small parameter, which improves previous results. Numerical experiments are presented to support the theoretical result.

High OXPHOS efficiency in RA-FUdr-differentiated SH-SY5Y cells: involvement of cAMP signalling and respiratory supercomplexes

Neurons are highly dependent on mitochondria to meet their bioenergetic needs and understanding the metabolic changes during the differentiation process is crucial in the neurodegeneration context. Several in vitro approaches have been developed to study neuronal differentiation and bioenergetic changes. The human SH-SY5Y cell line is a widely used cellular model and several differentiation protocols have been developed to induce a neuron-like phenotype including retinoic acid (RA) treatment. In this work we obtained a homogeneous functional population of neuron-like cells by a two-step differentiation protocol in which SH-SY5Y cells were treated with RA plus the mitotic inhibitor 2-deoxy-5-fluorouridine (FUdr). RA-FUdr treatment induced a neuronal phenotype characterized by increased expression of neuronal markers and electrical properties specific to excitable cells. In addition, the RA-FUdr differentiated cells showed an enrichment of long chain and unsaturated fatty acids (FA) in the acyl chain composition of cardiolipin (CL) and the bioenergetic analysis evidences a high coupled and maximal respiration associated with high mitochondrial ATP levels. Our results suggest that the observed high oxidative phosphorylation (OXPHOS) capacity may be related to the activation of the cyclic adenosine monophosphate (cAMP) pathway and the assembly of respiratory supercomplexes (SCs), highlighting the change in mitochondrial phenotype during neuronal differentiation.

A second order numerical method for a Volterra integro-differential equation with a weakly singular kernel

<p>In this paper, a second finite difference method on a graded grid is proposed for a Volterra integro-differential equation with a weakly singular kernel. The proposed scheme is obtained by using the two-step backward differentiation formula (BDF2) to discretize the first derivative term and the first-order interpolation scheme to approximate the integral term. The analysis of stability is proved and used to prove the convergence of our presented numerical method in the discrete maximum norm. Finally, Numerical experiments are given to verify the theoretical results.</p>

Decoupled second-order energy stable scheme for an electrohydrodynamic model with variable electrical conductivity

The motion of ions in the complex fluids widely appears in hydrodynamics, geodynamics and geophysics. Setting up suitable mathematical model, performing accurate and efficient numerical simulations are essential to understand the underlying physical principle in these phenomena. In this paper, we present a linear, second-order accurate in time, decoupled and unconditionally energy stable numerical scheme for solving an electrohydrodynamic power-law model with variable electrical conductivity. Based on a logarithm transformation for conductivity and the zero energy contribution property of the nonlinear coupling terms in the model, we derive an equivalent system by introducing a nonlocal auxiliary variable. The two-step backward differentiation scheme and the finite element method are used for the temporal and spatial discretizations, respectively. To decouple the system, the nonlocal splitting technique is employed to yield several linear subsystems, which can be solved very efficiently. Numerical simulations are carried out to demonstrate the second-order convergence in time and the unconditional energy stability. Moreover, the effects of Coulombic force and power-law fluid exponents are numerically investigated.

A finite element approach for nonlinear, transient heat conduction problems with convection, radiation or contact boundary conditions

Heat conduction problems with convection and/or radiation boundary conditions arise in nuclear and other engineering fields. This paper presents a finite element approach to solve transient, three-dimensional (3-D), nonlinear heat conduction problems using quadratic tetrahedral elements with area/volume coordinates and quadrature integrations. Boundary conditions modeled include surface convection, to-ambient radiation, and surface-to-surface radiation (using the radiosity matrix method, RMM). Instead of the commonly used hemi-cube method, L′Huilier’s theorem is used here to calculate view factors. Contact constraints are also imposed. Interface condition is set up for the interfaces of different material. The one- and two-step backward differentiation are used for time integration. Nonlinearities introduced by temperature-dependent material thermal properties and the Stefan–Boltzmann law for radiation are handled using the Picard and/or Newton–Raphson methods. The convergence rate of the numerical scheme is verified using an analytical solution obtained using the method of manufactured solutions (MMS). Several practical cases are simulated, including that of two spheres in contact with each other, and results are compared to those obtained using commercial codes.

Modified multi-phase diffuse-interface model for compound droplets in contact with solid

In this study, a novel diffuse-interface (phase-field) model is developed to efficiently describe the dynamics of compound droplets in contact with a solid object. Based on a classical four-component Cahn–Hilliard-type system, we propose modified governing equations, in which the solid is represented by an initially fixed phase. By considering Young's equality between surface tensions and microscale contact angles, equilibrium profiles of diffuse interfaces, and horizontal force balance between contact and interfacial angles, a correction term is derived and added into the phase-field equations to reflect the accurate contact line property for each component. The proposed model can be implemented on Eulerian grids in the absence of complicated treatment on the liquid-solid boundary. The standard finite difference method (FDM) is adopted to perform discretization in space. The linear second-order time-accurate method based on the two-step backward differentiation formula (BDF2) and a stabilization technique are adopted to update the phase-field variables. To accelerate convergence in solving the resulting fully discrete system, we use the linear multigrid method. At each time step, the calculations are completely decoupled. The numerical experiments not only indicate the desired accuracy but also show superior capability in complex geometries. Furthermore, the numerical and analytical results for the compound droplets on a flat solid are in good agreement with each other.

Uniform convergence analysis of the BDF2 scheme on Bakhvalov-type meshes for a singularly perturbed Volterra integro-differential equation

A singularly perturbed Volterra integro-differential problem is considered. At first, this problem is discretized by using the variable two-step backward differentiation formula (BDF2) and the trapezoidal formula on a Bakhvalov-type mesh to approximate the first-order derivative term and the integral term, respectively. Then, the stability and convergence analysis of the proposed numerical method are carried out. It is shown that the proposed numerical method is second-order uniformly convergent with respect to perturbation parameter ɛ in the discrete maximum norm. Finally, the theoretical find is illustrated by numerical experiments.

Linear, second-order, unconditionally energy stable scheme for an electrohydrodynamic model with variable density and conductivity

The motion of ions in the complex fluids widely appears in biofluids, hydrodynamics, geodynamics and geophysics. Performing efficient and accurate computation for electrohydrodynamic flows is challenging due to the multiphysics and complex nature of the problem. In this paper, we describe a new second-order linear energy stable time-stepping scheme for a variable density electrohydrodynamic power-law model, which satisfies an energy dissipation law. Firstly, a square root transformation for the fluid density and a logarithmic transformation for the electrical conductivity are used to enforce the positivity-preserving property for these two physical parameters. Secondly, by using the zero energy contribution property of the nonlinear coupling terms in the model and introducing a nonlocal auxiliary variable, an equivalent continuous formulation of the model is obtained. Finally, a two-step backward differentiation scheme is proposed for the resulting equivalent model to construct the time-stepping scheme, and the finite element method is used for spatial discretization. The scheme is proved to be unconditionally energy stable and a nonlocal splitting technique can be utilized to yield several linear subsystems, which can be solved more easily. Numerical simulations are carried out to demonstrate the accuracy and stability of the scheme. The dispersion of electrical conductivity and the effect of electrical force on the Rayleigh–Taylor instability are studied for both shear-thinning and shear-thicking fluids.

Error estimate of BDF2 scheme on a Bakhvalov-type mesh for a singularly perturbed Volterra integro-differential equation

<abstract><p>A singularly perturbed Volterra integro-differential problem is considered. The variable two-step backward differentiation formula is used to approximate the first-order derivative term and the trapezoidal formula is used to discretize the integral term. Then, the stability and convergence analysis of the proposed numerical method are proved. It is shown that the proposed scheme is second-order uniformly convergent with respect to perturbation parameter $ \varepsilon $ in the discrete maximum norm. Finally, a numerical experiment verifies the theoretical results.</p></abstract>

On the two-step BDF finite element methods for the incompressible Navier–Stokes problem under boundary conditions of friction type

This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with slip boundary conditions of friction type. It studies the well-posedness and error analysis properties of the numerical scheme in L2-norm for all positive time using the two-step backward differentiation formula (BDF) in time and the finite element approximation in space. Error estimates are proved under feasible assumptions on the regularity of the solution and with the aid of different versions of discrete Grownwall lemmas. Finally, some numerical simulations are presented to illustrate our theoretical analysis.

Benchmarking brain organoid recapitulation of fetal corticogenesis

Brain organoids are becoming increasingly relevant to dissect the molecular mechanisms underlying psychiatric and neurological conditions. The in vitro recapitulation of key features of human brain development affords the unique opportunity of investigating the developmental antecedents of neuropsychiatric conditions in the context of the actual patients’ genetic backgrounds. Specifically, multiple strategies of brain organoid (BO) differentiation have enabled the investigation of human cerebral corticogenesis in vitro with increasing accuracy. However, the field lacks a systematic investigation of how closely the gene co-expression patterns seen in cultured BO from different protocols match those observed in fetal cortex, a paramount information for ensuring the sensitivity and accuracy of modeling disease trajectories. Here we benchmark BO against fetal corticogenesis by integrating transcriptomes from in-house differentiated cortical BO (CBO), other BO systems, human fetal brain samples processed in-house, and prenatal cortices from the BrainSpan Atlas. We identified co-expression patterns and prioritized hubs of human corticogenesis and CBO differentiation, highlighting both well-preserved and discordant trends across BO protocols. We evaluated the relevance of identified gene modules for neurodevelopmental disorders and psychiatric conditions finding significant enrichment of disease risk genes especially in modules related to neuronal maturation and synapsis development. The longitudinal transcriptomic analysis of CBO revealed a two-step differentiation composed of a fast-evolving phase, corresponding to the appearance of the main cell populations of the cortex, followed by a slow-evolving one characterized by milder transcriptional changes. Finally, we observed heterochronicity of differentiation across BO models compared to fetal cortex. Our approach provides a framework to directly compare the extent of in vivo/in vitro alignment of neurodevelopmentally relevant processes and their attending temporalities, structured as a resource to query for modeling human corticogenesis and the neuropsychiatric outcomes of its alterations.

The BDF2-Maruyama method for the stochastic Allen–Cahn equation with multiplicative noise

We investigate the numerical approximation of the stochastic Allen–Cahn equation on a bounded domain D under Dirichlet boundary conditions and with multiplicative noise. The considered numerical method combines the two-step backward differentiation formula (BDF2) for the temporal discretization in conjunction with an abstract Galerkin scheme for the spatial approximation. In dependence on the regularity of the exact solution we derive a rate of convergence for the BDF2-Maruyama method with respect to the root-mean-square error in discrete analogues of the spaces L∞([0,T];L2(D)) and L2([0,T];H01(D)). Our error analysis is based on the variational approach for stochastic evolution equations. Finally, several numerical experiments illustrate our theoretical results, where a finite element method is used as an example for a Galerkin scheme.

Stability of Variable-Step BDF2 and BDF3 Methods

We prove that the two-step backward differentiation formula (BDF) method is stable on arbitrary time grids; while the variable-step three-step backward differentiation formula scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the severe mesh restrictions in the literature and provide a new understanding of variable-step BDF methods. Our main tools include the discrete orthogonal convolution kernels and an elliptic type matrix norm.