Introduction: What Is BETSE and Why Is It Important?

• This paper introduces the BioElectric Tissue Simulation Engine (BETSE), a computer tool designed to model and predict bioelectric signals in tissues.
• Bioelectric signals are electrical voltage differences that exist not only in nerve cells but in all cells; they help control how tissues develop, regenerate, and even how cancer can form.
• BETSE simulates how ions (charged particles such as sodium, potassium, chloride, calcium, etc.) move across cell membranes, interact through channels and junctions, and create patterns of voltage.
• The ultimate goal is to understand and eventually control these signals, much like following a recipe to create a desired dish.

Materials and Methods: How BETSE Works

• BETSE uses advanced mathematical techniques (finite volume methods) to simulate the movement of ions in tissues over time and space.
• It tracks key players:
  • Ion Channels: Think of these as doorways in the cell wall that open and close to let specific ions in or out.
  • Ion Pumps: These are like energy-powered conveyor belts (for example, the sodium-potassium pump) that actively move ions against a gradient.
  • Gap Junctions: Tiny bridges that electrically connect neighboring cells, allowing ions to flow between them.
  • Tight Junctions: Seal-like barriers at the cell cluster’s edge that restrict the free movement of ions, creating special voltage differences at boundaries.
• The engine models physical processes such as:
  • Electrodiffusion: The combined effect of ion movement due to concentration differences and electric voltage differences. Imagine people moving not only because of a crowd (concentration) but also because of a push or pull (voltage).
  • Electroosmosis: Fluid flow driven by electric fields, similar to water following a gentle slope.
  • Capacitance Calculations: Using a Maxwell Capacitance Matrix, BETSE computes how charges distribute across cell membranes to determine voltage differences (similar to calculating the voltage across a capacitor in a circuit).
• These methods allow BETSE to simulate real-life bioelectrical behavior in complex tissues.

Key Simulations and Step-by-Step Findings

• Simulation 1 – Validation with Xenopus Oocytes:
  • BETSE was tested by comparing its predictions with experiments on frog eggs (Xenopus oocytes).
  • The simulated resting membrane potential and ion concentrations were very close (within 10%) to experimental values.
• Simulation 2 – Resting Membrane Potential as a Stable “Attractor”:
  • Even when starting from unusual conditions (like equal ion levels inside and outside), cells settled into a normal resting voltage.
  • This shows that a cell’s resting potential is like water finding its level – it naturally returns to a stable state.
• Simulation 3 – Response to Perturbations:
  • Temporary changes in ion channel permeability or external ion concentration caused the cell voltage to shift.
  • After the disturbance, the voltage returned to its original resting state, demonstrating a self-correcting (homeostatic) behavior.
• Simulation 4 – Excitability and Action Potentials:
  • Introducing voltage-gated sodium and potassium channels showed that cells can fire electrical signals (action potentials) similar to nerve cells.
  • Different resting voltages affected how easily cells could become excited, much like a battery’s charge affecting a device’s performance.
• Simulation 5 – Effects of Heterogeneous Voltages in Cell Clusters:
  • Clusters of cells developed regions with different resting voltages (some more “charged” than others).
  • These differences influenced key factors such as calcium levels, osmotic pressure (the push of water in or out of cells), and overall ion current flows.
• Simulation 6 – Role of Gap Junction Connectivity:
  • The level of electrical connection between cells (via gap junctions) influenced how a change in one cell affected its neighbors.
  • Lower connectivity allowed individual cells to show a bigger voltage change, while higher connectivity kept the tissue’s voltage more uniform.
• Simulation 7 – Influence of Tight Junctions and the Trans-Epithelial Potential (TEP):
  • Tight junctions at the cluster’s edge restricted ion movement, creating a voltage difference (TEP) between the outer and inner cells.
  • This boundary voltage is similar to the way a dam creates different water levels on each side.
• Simulation 8 – Spontaneous Voltage Patterning:
  • Small differences in ion channel expression were amplified by positive feedback loops, resulting in clear voltage patterns across the tissue.
  • This self-organizing behavior may be the first step in how complex body patterns form during development.

Discussion and Implications: What Does It All Mean?

• BETSE demonstrates that bioelectric signals are robust, self-correcting, and capable of forming complex patterns.
• These electrical patterns serve as instructive signals that help cells “decide” their fate during development and regeneration.
• Understanding these processes can lead to new biomedical applications, such as guiding tissue repair or even intervening in cancer progression.
• The simulations show that not only do individual cell properties matter, but also how cells are connected – much like both the ingredients and the cooking technique determine the final taste of a dish.
• Future enhancements of BETSE aim to include cell division, movement, and more detailed internal processes, expanding its potential as a research and therapeutic tool.

Key Terms and Analogies Explained

• Ion Channels: Imagine doorways that open or close to let in specific guests (ions) into a building (cell).
• Ion Pumps: These work like energy-powered conveyor belts that actively move ions to maintain balance.
• Gap Junctions: Tiny bridges connecting cells, allowing them to share electrical information directly.
• Tight Junctions: Seal-like barriers that control what passes between cells, especially at the edges of a tissue.
• Electrodiffusion: The process where ions move due to both differences in concentration and electrical pull; think of it as people moving in a crowd influenced by both the crowd’s density and a gentle push.
• Maxwell Capacitance Matrix: A mathematical tool that calculates how charge is stored across cell membranes, similar to figuring out the voltage across a battery.
• Resting Membrane Potential (Vmem): The steady electrical charge difference across a cell’s membrane, like a battery’s resting voltage.
• Attractor State: A stable condition that a system naturally returns to after disturbances, much like how a pendulum eventually settles in its resting position.
• Electroosmosis: Movement of fluid driven by an electric field, similar to how water flows downhill.

Conclusion

• BETSE is a powerful simulation tool that accurately models the complex interplay of bioelectric signals in tissues.
• It shows that cells use electrical signals not only to communicate locally but also to organize large-scale patterns that are crucial for development, healing, and disease control.
• This research lays the groundwork for future biomedical applications where controlling bioelectric states could lead to advances in regenerative medicine and cancer treatment.
• By bridging physics, biology, and engineering, BETSE opens new avenues for understanding and manipulating the electrical language of life.

引言：BETSE是什么，为什么它很重要？

• 本文介绍了生物电组织仿真引擎（BETSE），这是一种用于模拟和预测组织中生物电信号的计算工具。
• 生物电信号不仅存在于神经细胞中，而是存在于所有细胞中，并帮助调控组织的发育、再生，甚至癌症的形成。
• BETSE模拟离子（如钠、钾、氯、钙等带电粒子）如何穿过细胞膜、通过通道和细胞间连接相互作用，并产生电压模式。
• 其最终目标是理解并最终控制这些信号，就像遵循食谱制作出理想的菜肴一样。

材料与方法：BETSE如何运作

• BETSE使用高级数学技术（有限体积法）来模拟离子在组织中随时间和空间的运动。
• 它追踪关键角色：
  • 离子通道：可以把它们想象成细胞壁上的门，开放或关闭以允许特定的离子进出。
  • 离子泵：类似于利用能量推动的传送带（例如钠钾泵），主动将离子逆梯度移动。
  • 缝隙连接：细胞之间的微小桥梁，允许离子直接在细胞间流动传递电信号。
  • 紧密连接：位于细胞群边缘的密封屏障，限制离子自由移动，从而在边界处产生特殊的电压差。
• 该引擎模拟的物理过程包括：
  • 电扩散：离子在浓度差和电压差的共同作用下移动。就像人群不仅因为拥挤（浓度差）而移动，还会受到推动或拉扯（电压差）的影响。
  • 电渗：由电场驱动的流体运动，类似于水沿着缓坡流动。
  • 电容计算：利用Maxwell电容矩阵计算细胞膜上电荷的分布，从而确定电压差（类似于计算电路中电容器的电压）。
• 这些方法使BETSE能够模拟真实组织中复杂的生物电行为。

关键仿真与逐步发现

• 仿真1 – 与蛙卵（Xenopus卵）实验数据的验证：
  • 通过与蛙卵实验数据对比，BETSE预测的静息膜电位和离子浓度与实验值非常接近（误差在10%以内）。
• 仿真2 – 静息膜电位作为稳定“吸引子”状态：
  • 即使从非正常初始状态（如内外离子浓度相等）开始，细胞也能恢复到正常的静息电位。
  • 这表明细胞的静息电位就像水面一样，能够自动回到稳定状态。
• 仿真3 – 对扰动的响应：
  • 暂时改变离子通道通透性或外部离子浓度会使细胞电位发生偏移。
  • 扰动结束后，电位会恢复到原始静息状态，展示出自我修正（稳态）的特性。
• 仿真4 – 细胞激发性和动作电位：
  • 引入电压门控钠、钾通道显示细胞可以像神经细胞一样产生电脉冲（动作电位）。
  • 不同的静息电位会影响细胞的激发性，就像电池电量影响设备的运行一样。
• 仿真5 – 细胞群中不同电位的影响：
  • 细胞群中会形成区域性不同的静息电位（有的区域“充电”较高，有的较低）。
  • 这种差异会影响钙离子水平、渗透压（调控细胞内外水分流动）以及总体离子电流。
• 仿真6 – 缝隙连接的作用：
  • 细胞之间的电连接程度（通过缝隙连接）会影响单个细胞的变化如何影响周围细胞。
  • 连接较差时，个别细胞电位变化较大；连接良好时，整个组织的电位则更加均匀。
• 仿真7 – 紧密连接与跨上皮电位（TEP）的影响：
  • 紧密连接在细胞群边缘限制离子运动，产生了内外细胞间的电压差（TEP）。
  • 这种边界电压类似于大坝在两侧产生不同水位的现象。
• 仿真8 – 自发的电位模式形成：
  • 少量离子通道表达的微小差异通过正反馈循环被放大，形成了明显的组织电位模式。
  • 这种自组织行为可能是组织发育中复杂图案形成的第一步。

讨论与意义：这些发现说明了什么？

• BETSE证明了生物电信号具有稳健性和自我修正能力，能够形成复杂的模式。
• 这些电模式为细胞提供了指令信号，帮助细胞在发育和再生过程中“决定”自身命运。
• 理解这些过程有助于开发新型生物医学应用，如引导组织修复或干预癌症进程。
• 仿真结果显示，不仅单个细胞的性质重要，细胞间的连接也至关重要，就像烹饪中食材与烹饪方法共同决定菜肴的味道一样。
• 未来，BETSE将扩展以模拟细胞分裂、运动以及更多内部过程，从而成为一个更强大的研究和治疗工具。

关键术语与类比说明

• 离子通道：就像细胞膜上的门，控制着特定离子的进出。
• 离子泵：类似于能量驱动的传送带，用来主动移动离子以维持平衡。
• 缝隙连接：细胞之间的微小桥梁，使细胞能够直接分享电信号。
• 紧密连接：密封的细胞边界，控制细胞之间物质的流动。
• 电扩散：离子既因浓度差（像人群密度）又因电压差（像轻微的推动）而移动。
• Maxwell电容矩阵：一种数学工具，用于计算细胞膜上储存电荷的方式，就像计算电池电压一样。
• 静息膜电位（Vmem）：细胞在静止状态下膜内外的电压差，类似于电池的静止电压。
• 吸引子状态：系统在受到干扰后会自动恢复到的稳定状态，就像钟摆最终停在中间一样。
• 电渗：由电场引起的流体运动，类似于水顺着坡度流动。

结论

• BETSE是一种强大的仿真工具，能够准确模拟组织中复杂的生物电信号相互作用。
• 它展示了细胞如何利用电信号进行局部和全局的通信，从而调控发育、再生以及疾病的进程。
• 这项研究为未来通过调控生物电状态实现组织修复和癌症干预等生物医学应用奠定了基础。
• 通过结合物理、生物和工程学，BETSE为理解和操控生命的电信语言开辟了新途径。