{"product_id":"sensora-the-berg-purcell-limit-physics-t-shirt","title":"Sensora – The Berg–Purcell Limit Physics T-Shirt","description":"\u003cp\u003eSensora listens to a drizzle of molecules landing on her skin, counting every one to learn how much is out there.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eHow precisely can a cell measure the concentration c of a chemical around it? Molecules arrive by diffusion one by one, so the count is noisy. Berg and Purcell showed in 1977 that a cell of radius a, averaging for a time T, can do no better than a fractional error of order 1\/√(Dac T).\u003c\/p\u003e\u003cp\u003eListen longer, or be bigger, to know better. Their paper also argued that a modest number of receptors spread over the surface captures most of the possible signal, and bacteria such as E. coli sense close to this physical limit.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eδc \/ c ~ 1 \/ √(D a c T)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eδc\/c: fractional error in concentration\u003c\/li\u003e\n\u003cli\u003eD: diffusion coefficient (m²\/s)\u003c\/li\u003e\n\u003cli\u003ea: cell radius (m)\u003c\/li\u003e\n\u003cli\u003ec: concentration (1\/m³)\u003c\/li\u003e\n\u003cli\u003eT: averaging time (s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eBerg \u0026amp; Purcell, “Physics of chemoreception”, Biophysical Journal 20, 193 (1977).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e This is a scaling law (“~”, not “=”); the careful “perfect instrument” result adds a numerical factor. Bacteria come close to the limit, not exactly to it.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Sensora, the pixel-art character, with “COUNTING EVERY MOLECULE”. Back: the scaling limit, what each symbol means, the listen-longer rule and the 1977 paper. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50960512385127,"sku":"15682847580797598860","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50960512417895,"sku":"19880828123284612135","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50960512450663,"sku":"15924710819063082987","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50960512483431,"sku":"20426290338733333664","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50960512516199,"sku":"15760145666008106504","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50960512548967,"sku":"11907358991230841490","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50960512581735,"sku":"85000154472167284725","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50960512614503,"sku":"19424182293305513347","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50960512647271,"sku":"98398193865376007191","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50960512680039,"sku":"31274921196575299534","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50960512712807,"sku":"58100309057885912176","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50960512745575,"sku":"96965091131875951973","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50960512778343,"sku":"28119076594922055928","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50960512811111,"sku":"28799799143294771950","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50960512843879,"sku":"47636934040916241417","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50960512876647,"sku":"13069465049391358331","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/berg-purcell_front_01_white.png?v=1793625655","url":"https:\/\/pixelatedphysics.com\/tr\/products\/sensora-the-berg-purcell-limit-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}